school for mechanical engineering \u0026 applied mathematics fluid mechanics iii (mfm31bi / mfm32bi)...

$: School for Mechanical Engineering \u0026 Applied Mathematics FLUID MECHANICS III (MFM31BI / MFM32BI) COMPILED BY$
School for Mechanical Engineering

& Applied Mathematics

IMNDNG NDip: Engineering: Mechanical

ST

UD

Y G

UID

E

FLUID MECHANICS III

(MFM31BI / MFM32BI)

COMPILED BY:

Mr. JJ Du Preez

REVISED BY:

Mr. L Masheane

DATE REVISED: JANUARY 2015

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(1) SUMMARY OF ASSESSMENT RULES AND REGULATIONS: 2015

Please note the following regulations pertaining to assessment at the Central University of Technology, Free State for the year 2015. Students are responsible for ensuring that they are aware of and that they understand the various means of assessment for each of the subjects for which they are registered, as explained in the study guide. 1. DEFINITIONS 1.1 “Unit or assessment unit”: Courses/modules are sometimes divided into two or more

units that are assessed independently and possibly at different times of the year. Generally the

different units of a course/module do not have a final mark. The following unit assessment

guidelines apply:

(i) Assessments are usually conducted in June and November and students

must ensure that they are fully aware of which unit assessments will be

conducted and when.

(ii) Only the skills and outcomes covered in a unit are assessed during the summative

assessment.

(iii) A final mark is only calculated at the end of the course/module. 1.2 “Supplementary assessment”: An assessor may summon a candidate for assessment as

an extension of the original summative assessment and this may take the form of an oral, a project

or portfolio, or a practical work assessment. The learning aims and achievements covered in such

a supplementary assessment are the same as in the preceding summative assessment. The

following administrative provisions govern supplementary assessments:

(i) All students who have achieved a final assessment mark of between 48% and 49% at the

end of a module or unit are summoned by the assessor for a supplementary assessment to

confirm the assessment result.

(ii) A notice with the particulars of candidates summoned for a supplementary assessment is

published on the departmental/school notice-boards within four (4) working days after the

conclusion of the summative assessment in question. (iii) It is the responsibility of the student to be acquainted with a summons to attend a supplementary assessment, in particular the date, time and venue of assessment. The CUT accepts no responsibility/liability in this regard.

1.3 “Re-assessment”: Unless otherwise stated in the faculty rules, this is an additional

assessment opportunity granted to a candidate who has achieved a final mark of between 45%

and 49% for a course/module and who wishes to improve the final mark to 50%. Re-assessment is

granted under the following administrative conditions:

(i) Re-assessment of a year course/module (with two or more units) takes place

directly after the assessment of the last unit and covers the learning aims and

achievements of all units.

(ii) Re-assessment of all other modules takes place immediately after the formal

summative assessment sessions scheduled in June and November.

(iii) There is no further assessment opportunity additional to re-assessment.

1.4 “Final mark” or “final course mark” for a course/module: This is a composite

continuous assessment and summative assessment mark determined in a manner prescribed by

the Faculty Board.

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1.5 “Deferred assessment” or “deferred summative assessment”: This assessment

opportunity is offered to a student unable to participate in the scheduled summative assessment

sessions due to illness or special personal circumstances. Deferred assessment sessions are

governed by the following administrative rules:

(i) If needed, such a session is scheduled immediately or directly after the June and

November summative assessment schedule.

(ii) A deferred summative assessment may only be considered if the affected student makes a

formal application with proof (e.g. medical certificate, etc.) and submits the application to the

Assessment and Graduation Unit within three (3) working days after the scheduled summative

assessment session of a particular course/module. (iii) There is no further assessment opportunity additional to deferred assessment. 1.6 “Progress report” or “student progress report”: A report indicating the progress of each student is mailed to all registered students and their identified sponsors at the end of each quarter. Progress reports between the summative assessment periods are based on the student’s continuous assessment marks. 1.7 “Statement of results”: This is a summary of the final marks over all course/modules already completed and is issued to students following completion of the June and November summative assessments. 1.8 “Exit certificate”: A certificate issued on request to a student on completion of 1 or 2 formal credits of an instructional programme. 1.9 “Admission Mark”: A course mark of 40% needed to be allowed to write a summative

assessment.

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2. ASSESSMENT MODEL FOR ALL PROGRAMMES: 2015 Unless otherwise determined by a resolution of the Senate: 2.1 Year subjects

Course mark - 20%

Unit 1

(Jan - Jun) Final mark for

unit 1 (50%)

Assessment mark

- 30%

Subject Final mark for subject

Course mark - 20%

Unit 2 (Jul - Dec)

Final mark for unit 2 (50%)

Assessment mark

- 30%

45% - 49% Re-assessment directly after main assessment. First-semester subjects – June. Year subjects and second-semester subjects – November.

2.2 Semester subjects

Course mark - 40%

Subject Final mark for

subject Assessment mark

- 60%

45% - 49%

Re-assessment directly after main assessment.

3. ASSESSMENT AND RESULTS (ALL faculties unless otherwise specified)

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3.1 A Subject is considered a credit, and therefore the following provisions apply:

A student must pass any subject that is a prerequisite for another subject before he/she may register for the next level of the subject concerned.

The pass requirements for a specific subject are as follows: A result is determined from a calculated average of tests and assessment opportunities. The minimum pass mark per subject is 50%. The minimum final mark needed to pass a subject with distinction is 75%.

Please note that once a student has been granted a re-assessment or a special assessment as a result of illness or some other reason, no additional such assessment will be granted.

3.2 THE 2014 RULES FOR ALL PROGRAMMES: 1. A sub-minimum mark of 50% for all Engineering programmes accumulated for practical work and projects in specified subjects is compulsory to gain access to the relevant assessment session and to pass the subject. This rule applies to all those subjects identified as such in the study guides. 2. An admission mark of at least 40% is required for main assessments. 3. A re-assessment is granted to a candidate who has achieved a final mark of 45% - 49% in a subject. The re-assessment of a year subject – covering the subject content of the entire year – takes place directly after the main assessment in November. The re-assessment of semester subjects takes place immediately after the main assessment in June, while the re-assessment of second-semester and year subjects takes place in November. 3.3 Assessment timetables 3.3.1 Assessment timetables are not mailed to students. 3.3.2 The assessment timetable is published on the central notice-boards and the internet (www.cut.ac.za) in accordance with the year programme. 3.3.3 It is the duty of every student to be fully aware of the dates, times and venues of assessments. The Central University of Technology, Free State accepts no responsibility/liability for any damages, now or in the future, of any nature whatsoever, resulting from or related in any manner to a student's failure to attend an assessment.

http://www.cut.ac.za/

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3.4 Publication of summative assessment results 3.4.1 Following the summative assessments and in accordance with the year programme, the

Assistant Registrar: Assessment and Graduation forwards the summative assessment results to

candidates by means of a statement of results. The summative assessment results are also

published on the official notice-boards of the CUT. No results are supplied telephonically.

Assessment results are available on the internet and via the MTN telephone service, but the CUT

accepts no liability of any nature for the accuracy, correctness or timeliness of these notices.

Assessment results on the notice-boards are identified by means of student numbers only so as to

protect the privacy of each individual.

3.4.2 With the exception of the official notice of assessment results published by the Assessment

and Graduation Unit, no academic or support personnel may divulge summative assessment

results to any candidate. The CUT accepts no responsibility for any consequences of such

unofficial communication of assessment results, nor does it accept any liability whatsoever for any

consequences arising from refusal to divulge assessment results.

3.4.3 A candidate who has any CUT fees in arrears or who does not comply with the admission

requirements is not entitled to receive his/her final marks in the courses/modules in which he/she

enrolled. The CUT accepts no responsibility for any consequences arising from the withholding of

any results. 3.5 Supplementary assessment

3.5.1 Grounds for granting a supplementary assessment

(1) In accordance with the approved rules formulated by the relevant faculty and on completion

of the prescribed summative assessment, the assessor may summon a candidate for a

supplementary assessment in any course/module as an extension of the original assessment.

Such a supplementary assessment is administrated as a whole, at the discretion of the relevant

school, provided it does not take place more than four (4) working days after the closing of the

summative assessment period announced in the CUT Calendar and/or year programme. If a

candidate fails to report for a supplementary assessment, his/her original marks are then confirmed

as the summative assessment mark.

(2) No supplementary assessment is granted on the grounds that a student has mistaken the

time, date or place of a summative assessment opportunity. This rule applies to all other

assessment opportunities, as well as all assignments and projects.

3.5.2 Nature and requirements of supplementary assessment

(1) An assessor may summon a candidate for assessment as an extension of the original

summative assessment and this may take the form of an oral, a project or portfolio, or a practical

work assessment. The learning aims and achievements covered in such a supplementary

assessment are the same as in the preceding summative assessment. The following administrative

provisions govern supplementary assessments:

(i) All students who have achieved between 48% and 49% in the summative

assessment at the end of a module or unit are also summoned by the assessor for a

supplementary assessment to confirm the assessment result.

(ii) A notice with the particulars of candidates summoned for a supplementary

assessment is published on the departmental/school notice-boards within four (4) working days

after the conclusion of the summative assessment in question.

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(iii) It is the responsibility of the student to be acquainted with a summons to attend a

supplementary assessment, in particular the date, time and venue of such assessment. The CUT

accepts no responsibility/liability in this regard.

(2) The assessor may verbally advise students of the supplementary assessment schedule

and it is the responsibility of the student to ask the assessor about this assessment opportunity.

The CUT also accepts no responsibility/liability in this regard.

3.6 Re-assessment

3.6.1 Unless otherwise stated in the faculty rules, this is an assessment opportunity granted to a

candidate who has achieved a final mark of between 45% and 49% for a course/module and who

wishes to improve the final mark to 50%. Re-assessment is granted under the following

administrative conditions:

(2) Re-assessment of a year course/module (with two or more units) takes place directly

after the summative assessment of the last unit and covers the learning aims and

achievements of all units.

(3) Re-assessment shall in all material academic respects conform to the planned

summative assessment stipulations of the course/module.

(4) Re-assessment of all other modules takes place immediately after the formal

summative assessment sessions scheduled in June and November.

(5) There is no further assessment additional to a re-assessment.

3.6.2 The candidates qualifying for re-assessment are identified by the assessor and their names are communicated to the Assistant Registrar: Assessment and Graduation for publication on the central notice-boards at least four (4) working days before the re-assessment is to be conducted. Again, it is the responsibility of every student to be acquainted with such notices, and the CUT accepts no responsibility in this regard.

3.7 Deferred assessment

3.7.1 This assessment opportunity is offered to a student unable to participate in the scheduled

summative assessment session(s) due to illness or on medical grounds or due to special personal

circumstances. Deferred assessment sessions are governed by the following administrative rules:

(1) If needed, they are scheduled immediately or directly following conclusion of the June and

November summative assessment schedule.

(2) A deferred summative assessment may only be considered if the affected student makes a

formal application with proof (e.g. medical certificate, etc.) and submits the application to the

Assessment and Graduation Unit within three (3) working days after the scheduled summative

assessment session of a particular course/module.

(3) There is no further assessment opportunity additional to a deferred assessment.

3.7.2 The same grounds listed above also apply to an application for a deferred assessment or

other assessment opportunity called for and administered within a particular faculty. No deferred

assessments are considered or granted on the grounds that a student has mistaken the date, time

or place of an assessment

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3.7.3 Application for deferred assessment should be lodged on the prescribed form in

accordance with policy and procedure, but no later than three (3) working days after the

assessment. A medical or other registered professional report or other appropriate credible

evidence must support the application, and the report must specifically include the following

information:

(1) The date of professional consultation (applications in cases where the medical practitioner

was visited after the date of the assessment opportunity will not be considered).

(2) The severity and duration of the complaint.

(3) The medical practitioner’s opinion on how the reported condition could adversely impact on

the student’s assessment preparation and/or performance.

3.7.4 If a student qualifies for a deferred assessment opportunity but nevertheless participates in

a course/module assessment, he/she loses all rights or claims to a deferred assessment.

3.7.5 Should a student contract a communicable disease (e.g. chicken pox, measles, etc.) during

the period of the summative assessment, he/she must consult a medical practitioner immediately

to determine whether he/she is medically fit to continue participating in any or all further

assessments. If the recommendation is that the student is unable to participate in any

assessment(s), the absence will be treated as absence on valid grounds; otherwise arrangements

will be made to hold the assessment(s) in a quarantine room.

3.7.6 Special assessment opportunity: A student who only requires a single course/module to

meet all the requirements for a degree/diploma/certificate, but who participated unsuccessfully

during the preceding semester/year in the course/module in question, qualifies for a special

assessment opportunity in the course/module concerned, provided s/he complies with the following

criteria.

(1) Only one (1) course/module is outstanding in order for the registered qualification to

be awarded.

(2) The student must have earned an official admission mark for the course/module and must

have unsuccessfully participated during his/her final year of study in the course/module

outstanding for the qualification to be awarded. In cases where the University fails to present a

course/module or where courses/modules are presented in cycles over a year or longer, special

permission may be granted by the faculty for a special assessment opportunity if the

course/module was offered before.

A student who qualifies for but subsequently fails the special assessment at the end of the first

semester will not qualify for a second special assessment at the end of the year.

A student who requires only one (1) course/module at the end of an academic year and who

qualifies for assessment in the subject during his/her final year of study will qualify for a special

assessment. If a student qualifies for a first-semester course/module, the existing course mark will

be carried over.

(3) A candidate must apply in writing at the Assessment and Graduation Unit for a special

assessment opportunity (on form LS124.3) or must submit his/her application by registered mail.

An administrative fee is payable before any application will be processed

(4) All applications for a special assessment opportunity must reach the Assessment and

Graduation Unit within two (2) weeks after publication of the assessment outcomes/results. The

CUT will not change this time stipulation on any account.

3.7.7 Scheduling of deferred and special assessments

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(1) Unless the Senate decides otherwise, deferred and special assessments are conducted at

the end of each semester.

(2) Subject to the special circumstances stipulated, the Assistant Registrar: Assessment and

Graduation may schedule alternative dates for special assessment opportunities and communicate

the dates, times and venues for these opportunities to the affected students.

(3) Deferred and special assessments shall in all material academic respects conform to the

planned summative assessment stipulations of the course/module. 3.7.8 Rules of student conduct during assessments (1) All students must be seated 15 (fifteen) minutes before the assessment is scheduled to

start. (2) No student will be admitted to the assessment venue if more than thirty (30) minutes have elapsed from the published starting time of the assessment. Only students with a valid reason for being late will be allowed into the assessment venue after the starting time.

3.8 Assessment result/outcome notations

3.8.1 Assessment result/outcome symbols

All courses/modules are assessed and a final mark is awarded. The final mark (irrespective of

any numeric value) is coded according to the following approved academic progress symbols:

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(6) Prog

ress

(7) Notat

ion

(8) Meaning (9) Notional

%

(10) PD (11) Pass or successful completion with

distinction (12) 75 – 100

(13) PE (14) Credit (Recognition) (15) 50

(16) P (17) Pass, i.e. successful completion (18) 50 – 74

(19) PU (20) Provisional pass or provisionally

successful completion, subject to investigation

(21) 50 and

higher

(22) F (23) Fail or unsuccessful completion (24) Below

50

(25) FD (26) Fail due to disciplinary sanctions (27) 0

(28) FT/FS (29) Deferred-assessment opportunity

granted

(30)

(31) FX (32) Fail or unsuccessful completion

due to absence without prior notice

(33)

(34) FN (35) Results/assessment outcomes not

yet available

(36)

(37) FC (38) Continuous assessment

results/assessment outcomes not available

(39)

(40) F9 (41) Re-assessment opportunity

granted

(42) 45 - 49

(43) P4 (44) Recognised in terms of the policy

on the recognition of prior learning

(45)

(46) FR (47) Fail subminimum (48)

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3.8.2 Date of issue of qualifications

The date of issue of a qualification is the first day of the month following the month in which

the assessment results/outcomes of the last summative assessment were published by the

Assessment and Graduation Unit.

3.8.3 Awarding of qualifications cum laude (i.e. with honours)

Subject to the approval of the Senate, as well as compliance with the applicable rules of the

relevant faculty, a qualification can be awarded cum laude provided the candidate meets the

following criteria:

(1) The candidate has participated in and successfully completed all courses/modules

prescribed for a qualification of the CUT;

(2) The candidate has passed or successfully completed all the prescribed courses/modules of

the qualification on the first attempt;

(3) The candidate achieved an overall average of 75% or above for all courses/modules

prescribed for the qualification;

(4) The candidate achieved an overall average of 75% or above for all exit-level

courses/modules prescribed for a qualification. 3.8.4 The following qualifications are awarded during official CUT graduation ceremonies: 3.8.4.1 National diplomas 3.8.4.2 Degrees 3.8.4.3 MTech degrees 3.8.4.4 DTech degrees 3.8.4.5 PhD degrees Only national certificates, national higher certificates and postgraduate certificates issued on completion of an official, registered qualification are awarded during the graduation ceremonies. No exit certificates or exit higher certificates will be awarded during a graduation ceremony. If a student wishes to be issued with an exit certificate, he/she must apply for such to the Assessment and Graduation Unit. This exit certificate will then be issued to the student, but will not be handed over during an official graduation ceremony. 3.9 Academic review of student progress 3.9.1 Unsatisfactory academic progress

3.9.1.1 A student is considered to be academically unsuccessful:

When a first-year student failed all his/her subjects;

When a senior student failed 50% of credits for subjects enrolled for in two consecutive attempts and/or cancelled some or all courses/modules after registration control day.

3.9.1.2 In the case of fulltime students, the qualification must be completed in the minimum stipulated study period plus an additional complement / add-on of half of the minimum study period. In essence this implies that the period will be rounded off to the next complete academic year, and a three year qualification for example, must therefore be completed within the maximum period of five years.

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3.9.1.3 Part-time students must complete the qualification in double the minimum study period allowed. This means that a three year qualification for example, must be completed within the maximum period of six years by part-time students.

3.9.1.4 Students must, however, note that if the qualification is phased out, Senate will decide on

ad hoc arrangements which need to be implemented to resolve the matter.]

3.9.2 Prognosis of unsatisfactory academic progress

A student is identified as “academically at risk” on the basis of the same criteria as

stipulated in par. 3.9.1, but applied only to the continuous assessment marks as on the third

Monday in April (for the first semester) and September (for the second semester) or the working

day immediately thereafter. To make this determination, faculties must ensure that each student

have a continuous assessment mark on official database.

3.10 Procedure for student objections or appeals The following objection or appeal procedure is available to students against whom the

Assessment Working Group or the faculty invoked the academic progress support as outlined in

the assessment manual:

(1) Supported by the relevant evidence a student may lodge a written objection to the Access

and Admissions Working Group regarding the decision.

(2) Student objections must be lodged by on the last working day on or before the dates

specified below. Alternative dates may be published in the annual programme.

Courses/modules offered during the first semester and the

entire year 21 January

Courses/modules offered during the second semester 10 July

(3) On receipt of an appeal or objection the Access and Admissions Working Group will

convene an Appeal Committee.

(4) When objections or appeals are considered by the Appeal Committee, the following factors

will be taken into account:

(i) The academic ability of the specific student as measured by the academic

record of the student, as well as the time limit allowed for completion of the

courses/modules prescribed by the curriculum or the enrolment contract;

(ii) The institutional duty to encourage and support:

(a) Student success, even if this success is based on reduced learning

targets; and/or

(b) Student compliance with contractual obligations.

(iii) If applicable, the current enrolment against any enrolment limits, if any. In

this regard, the Appeal Committee have no jurisdiction to vary existing

enrolment limits.

(5) The decision of the Appeal Committee will be communicated in writing to the student by

Assessment and Graduation Unit. Likewise, the decision will be reported to the Access and

Admissions Working Group.

(6) A student aggrieved by the decision of the Appeal Committee may lodge a final appeal or

objection to the Executive Committee of Senate for a final ruling on the matter. 4. RE-MARKING

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Re-marking means that an assignment/answer script, which has not been altered or extended by the student, is marked for a second time. 4.1 In accordance with the provisions in the Student Assessment Manual of the Central University of Technology, Free State, should a student feel that an individual assignment/answer script has been marked unfairly or inappropriately, a request for re-marking (on the prescribed form) may be addressed to the Assistant Registrar: Assessment and Graduation within three (3) weeks after publication of the results. An administrative fee per subject is payable before any application will be processed. 4.2 An assignment may only be submitted once for re-marking. 4.3 If the re-marking culminates in an amended mark or result, that result is the final result. 5. EXTRA TIME DURING ASSESSMENTS In accordance with the Policy and procedure for the granting of extra time and other concessions during officially scheduled tests and assessments at the Central University of Technology, Free State, extra time is allocated to persons with obvious physical, psychological or emotional disabilities to allow them to complete their tests and assessments. Alternative arrangements are also made where necessary, e.g. oral assessments may be permitted. 5.1 A maximum of 15 minutes extra per hour is allowed. 5.2 The allocation of extra time is indicated on the diploma/degree/certificate of the student. 5.3 Students must apply for extra time at the Centre for Counselling, using form LS227.1 (Application for the granting of extra time or other concessions during officially scheduled tests and/or assessments of the Central University of Technology, Free State), at least two (2) weeks before classes begin. Applications must be accompanied by supporting documentation. 6. SUBJECT RECOGNITION 6.1 In accordance with the Policy and procedure with regard to subject recognition of prior learning, qualifying for the issuing of a qualification, and recognition of qualifications of South African as well as foreign students, applicants requesting credit must address a written application on the prescribed form to the Assistant Registrar: Assessment and Graduation. Satisfactory documentary evidence in support of such applications must be provided. An administrative fee per subject is payable before any application will be processed. 6.2 “The holder of a University qualification certificate must have (a) Complied with the admission requirements for the qualification, including the admission requirements of the courses/module prescribed for the qualification: (b) Been assessed and found competent in all the competences and skills prescribed for the qualification; (c) Completed more than 50 % of the credits of the prescribed courses/modules for the qualification with the University; and (d) Completed more than 60 % of the credits of the exit or final academic year of the prescribed curriculum for the qualification with the University”. 6.3 Final dates for the submission of applications for subject recognition at the Assessment and Graduation Unit: For registration during semester 1 and for year courses: 20 January For registration during semester 2: 15 July

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7. GENERAL INFORMATION 7.1 The results and assessment timetables for the various assessment opportunities are available as follows:

Publication on central notice-boards

Results mailed to each candidate (NB: Assessment timetables are not mailed to candidates)

MTN answering service: 083 123 1000

Internet: www.cut.ac.za 7.2 Please note that it is sometimes necessary to divide large class groups into smaller groups during assessments. Student must consult the individual assessment timetables on the central notice-boards for information on the venue in which the assessment is to be conducted. 7.3 No cellular phones are permitted in the venues. The CUT accepts no responsibility/liability for any loss of, or damage to, personal property in assessment venues. 7.4 The central notice-boards are situated between the Artec Hall and the Gymnasium. NB: The building codes are published below for your convenience.

BUILDING CODE

ROOM NUMBER BUILDING

12 0001, 0003, 0005, 0200, 0222,

0225, 0227, 0229,

BhpBilliton Building

14 023, 025, 026, 027, 028, 138, 136,

159, 161

bhpBilliton Building

50 0001 Old Main Hall

52 Dirk Coetzee Building

54 Hotel School

58 0100 Boet Troskie: Hall

58 0000 Boet Troskie: Cellar

77 0105, 0109, 0110, 0111 Distance Education –

Former BCE

78 0110, 0114, 0117 Faculty: Management

Sciences

81 0001 Artec Hall

http://www.tofs.ac.za/

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AIM OF THIS STUDY GUIDE

The aim of this study guide is to act as a preparation instrument for you as student in order to:

participate actively during the formal tuition sessions,

and to execute problems and tasks independently.

The study guide does not replace the prescribed handbook for the subject and it is not a summary of

class notes.

The study guide is supplementary to the handbook to enable you as student to study and understand

the subject.

Extra sources are also available in the library to help you to obtain an in depth knowledge of this

subject. It is important that you must understand the work rather than just try to learn it for a test or

examination.

Course mark

The student is expected to attend the formal tuition sessions, to perform the practical work and

problems and to write all the scheduled tests and the examination. Evaluation of the gained

knowledge of the student is done by taking into account the marks obtained ( expressed as

percentage ) during the first class test ( CT1 ), the main test ( MT ) as well as the practical work

done ( PW ) ( which includes the experiments done and formal tasks ) to obtain a course

mark ( CM ). The course mark together with the examination mark ( EM ) contributes as follows

towards the final mark ( FM ):

CM = ( 0,25 x CT1 ) + ( 0,40 x MT ) + ( 0,35 x PW )

FM = ( 0,4 x CM ) + ( 0,6 x EM )

A course mark of 40% and an average of 50% for the practical mark must be obtained for

admission to the main evaluation.

Late submittal penalties

Unless an extension has been sought and granted, late assignments will be penalized

when marking. The penalty rate will be –20% if late and still handing in on same

day. No assignments will be taken after submission day. Thus it is in your interest to

aim to complete the work at least a week earlier than the due date.

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PRESCRIBED TEXT BOOKS

SOLVING PROBLEMS IN FLUID MECHANICS (VOLUME 1), 3rd Ed., Douglas J F &

Matthews R D, Longman Group Limited, 1996.

SOLVING PROBLEMS IN FLUID MECHANICS (VOLUME 2), 3rd Ed., Douglas J F &

Matthews R D, Longman Group Limited, 1996.

REMARKS

The prescript handbook covers the syllabus. The problems in the handbook are of a good standard

and the student could expect similar standard in the examination.

TEXT BOOKS FOR REFERENCE

SOURCE 1:

SOLVING PROBLEMS IN FLUID MECHANICS ( VOLUME 1 ) - JF DOUGLAS

SOURCE 2:

SOLVING PROBLEMS IN FLUID MECHANICS ( VOLUME 2 ) - JF DOUGLAS

SOURCE 3:

APPLICATIONS OF FLUID MECHANICS ( PART 1 ) - CF MEYER

SOURCE 4:

FLUID MECHANICS ( 3rd Edition ) - DOUGLAS & GASIOREK & SWAFFIELD

SOURCE 5:

FUNDAMENTALS OF FLUID MECHANICS, 2nd Ed., Munson B R, Young D F &

Okiishi T H, John Wiley & Sons, 1994.

SOURCE 6:

FUNDAMENTALS OF FLUID MECHANICS, Gerhardt R T, Addison-Wesley Publishing

Company, 1992.

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SYLLABUS

SECTIONS

1. Flow under variable head

2. Hydrodynamic Force of a Jet

3. Turbulent flow in pipelines

4. Reciprocating pumps

5. Free and Forced Vortexes

6. Viscous flow

7. Dimensional analysis

PROJECT:

Water hammer (Date will be given in class)

(i) What is water hammering? (Explain)

(ii) Where does water hammering occur?

(iii) How will you neutralize water hammering?

Assignment should consists of the following:

1. Index

2. Contents

3. References

Plagiarism is when the learner makes use of exactly the same sentence in a book/article and then uses it as his own work without giving recognition to the author. The learner can make use of certain terminologies, phrases and known facts from a source when he/she give recognition to the author. Plagiarism is not seen as a crime yet, but is disapproved on the ground of moral offence. Good academic writing practices include the following norms:

must be clear, the reader must be aware of who is addressing him the learner have to refer clearly and regularly to the sources he/she uses the learner must express him/her as an individual with independent thinking extending from

existing knowledge must include paraphrases that represent the same contents of the source

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AIM OF THE SECTIONS:

At the end of each section the student must be able to:

1. solve any problem related to flow under varying head,

2. determine the hydrodynamic force exerted when a jet of water is striking different

surfaces when it is stationary, or moving in the direction of the jet,

3. determine which type of flow occurs in a pipeline. The student must also be able to use

all the losses in a pipeline to determine the discharge or the required pipe diameters,

4. solve any problem relating to positive displacement pumps,

5. solve any problem relating to free and forced vortexes. The students must also know the

application of vortexes,

6. know the difference between laminar and turbulent flow to solve practical directed

problems,

7. consider and compare the relation between certain equations and units by means of the

basic dimensions (M,L,T).

- 19 -

SECTION 1: FLOW UNDER VARIYNG HEAD

AIM:

At the end of this section the student must be able to solve any problem related to flow under

varying head.

CONTENTS:

Time required to empty a reservoir through a orifice in the bottom.

Time required to empty a reservoir through a pipe.

Time required to flow from one tank to another.

Time required to fill a reservoir.

REFERENCE: SOURCE 1: p.227 - 241.

SOURCE 3: p.89 - 110.

EXERCISE: SOURCE 1: p.236 No.1, 2, 3, 4, 5, 6, 11, 14, 19, 20, 21, 22, 23, 26.

Self study 3. No 1-8

SECTION 2: HYDRODYNAMIC FORCES

SECTION 2.1: FORCE OF A JET AGAINST A FLAT SURFACE

AIM:

At the end of this section the student must be able to determine the hydrodynamic force exerted

when a jet of water is striking a flat surface when it is stationary, or moving in the direction of the

jet.

CONTENTS:

Power available in a jet of water.

Force against a flat surface.

Force against a moving flat surface.

Force against the moving plates of an undershot waterwheel.


SOURCE 3: p.175 - 197.

SOURCE 4: p.108 - 129.

EXERCISE: SOURCE 1: p.147 No.1, 2.


SECTION 2.2: FORCE EXERTED BY A JET ON AN INCLINED FLAT PLATE

AIM:


when a jet of water is striking a flat inclined surface when it is stationary, or moving in the direction

of the jet.

- 20 -

CONTENTS:

Force against a stationary flat plate positioned at a angle .

Force against a flat plate moving in the direction of the jet.

Force against a flat plate moving in the direction of the normal to its surface.


SOURCE 3: p.175 - 197.

SOURCE 4: p.108 - 129.

EXERCISE: SOURCE 1: p.148 No. 5, 7, 9.

Self study 4. No 5, 6.

SECTION 2.3: INFLUENCE OF A JET ON A HANGING PLATE

AIM:


when a jet of water is striking a flat hanging plate and its striking position.

CONTENTS:

Force against a hanging flat plate and the angle of deflection of the plate.


SOURCE 3: p.175 - 197.

SOURCE 4: p.108 - 129.

EXERCISE: SOURCE 1: p.148 No. 3, 4.

Self study 4. No 3, 4.

SECTION 2.4: REACTION OF A JET

AIM:

At the end of this section the student must be able to determine the reaction of a jet of water and the

resultant force acting on reducers and bends.

CONTENTS:

Reaction of a jet on a nozzle.

Forces on reducers.

Reaction of a jet on rotating nozzles (Barker’s mill).


SOURCE 3: p.175 - 197.

SOURCE 4: p.108 - 129.


Self study 4. No 7-11.

- 21 -

SECTION 2.5: FORCE EXERTED BY A JET ON CURVED VANES

AIM:


when a jet of water is striking a single curved vane or a series of curved vanes.

CONTENTS:

Force on a stationary curved vane.

Force on a single moving curved vane.

Force on a series of moving curved vanes.

REFERENCE: SOURCE 128 - 153.

SOURCE 3: p.175 - 197.

SOURCE 4: p.108 - 129.

EXERCISE: SOURCE 1: p.150 No.14,15,17,18,20,22.


SECTION 3: TURBULENT FLOW

SECTION 3.1: FLOW IN PIPES

AIM:

At the end of this section the student must be able to determine which type of flow occurs in a

pipeline. The student must also be able to use all the losses in a pipeline to determine the discharge

or the required pipe diameters.

CONTENTS:

Mean velocity, Maximum velocity, Reynolds number, Relation between Reynolds number and

Friction coefficient, Friction losses, Shock losses, Bernoulli's equation, Continuity of flow, Velocity

of flow at nozzles.

REFERENCE: Source 1: p.154 - p.186.

Source 2: p.97 - p115.

Source 3: p.1 - p17, p.58 - p.68.

Source 4: p.296 - p.319.

EXERCISE: SOURCE 1:

p 164 No 1,4,7,14,15,16,17.

p 182 No 2,4,5.


- 22 -

SECTION 3.2: POWER TRANSMISSION IN PIPELINES

AIM:

At the end of this section the student must be able to determine the power which can be transmitted

through a pipeline. The student must also be able to use the conditions for maximum power

transmission.

CONTENTS:

Formulas for hydraulic power and the conditions for maximum power transmission. Nozzle

diameter for maximum power transmission. Power transmission for a certain nozzle diameter.

REFERENCE: Source 1: p.187 - p.197.

Source 3: p.82 - p.89.

EXERCISE: SOURCE 1:

p 194 No 1, 2, 3, 6, 7, 8, 11, 12, 13.


SECTION 3.3: ENERGY IN PIPELINES

AIM:

At the end of this section the student must be able to solve any pipeline problem relating pipelines

connected in series and in parallel. The student must also be able to draw the hydraulic gradient and

total energy line.

CONTENTS:

Hydraulic gradient line.

Total energy line.

Friction losses in series and parallel pipelines.

REFERENCE: Source 1: p.154 - 186.

Source 3: p.58 - p.78.

EXERCISE: SOURCE 1:

p 183 No 6,7,8.

p 175 No 11,8 ; 11,9.

p 185 No 14, 15, 17, 18, 21, 24, 26.


- 23 -

SECTION 4: RECIPROCATING PUMPS

SECTION 4.1: FORCE PUMPS

AIM:

At the end of this section the student must be able to solve any problem relating to positive

displacement pumps.

CONTENTS:

Suction pump

Single-acting pump

Double-acting pump

Theoretical indicator diagram


SOURCE 3: p.18 - 57.

SOURCE 4: p.713 - 734.

EXERCISE: Self study 6. No 2

SECTION 4.2: EFFECT OF ACCELERATION AND FRICTION

AIM:

At the end of this section the student must be able to know the effect of acceleration and

deceleration of water in pipelines at positive displacement pumps (SHM).

CONTENTS:

Acceleration head

Frictional head

Work done against friction

Total work done

Separation


SOURCE 3: p.18 - 57.

SOURCE 4: p.713 - 734.

EXERCISE: SOURCE 2: p.252 No.1, 2, 3, 4, 5, 6, 8, 11, 12.

Self study 6. No 3

SECTION 4.3: EFFECT OF AIR VESSELS ON SUCTION AND DELIVERY PIPES

AIM:

At the end of this section the student must be able to know the effect of air vessels on positive

displacement pumps (SHM).

- 24 -

CONTENTS:

Separation

Effect of air vessels.

Frictional losses without an air vessel fitted.

Frictional losses with an air vessel fitted.

Percentage of power saved by fitting an air vessel.


SOURCE 3: p.18 - 57.

SOURCE 4: p.713 - 734.

EXERCISE: Page 252 No 3, 6.

Self study 6. No 1,4

SECTION 5: FREE AND FORCED VORTEXES

AIM:

At the end of this section the student must be able to solve any problem relating to free and forced

vortexes. The students must also know the application of vortexes.

CONTENTS:

Free vortexes. Forced vortexes. Compound vortexes


SOURCE 2: p.28 - 37.

SOURCE 3: p.157 - 174.

SOURCE 4: p.181 - 189.

EXERCISE: SOURCE 1: p.68 No.3, 4, 6.

SOURCE 2: p.36 No.1, 6, 9, 10.

Self study 5. No. 1 - 11.

SECTION 6: VISCOUS OR LAMINAR FLOW

SECTION 6.1: DEFINITIONS

AIM:

At the end of this section the student must be able to know the difference between laminar and

turbulent flow to solve practical directed problems.

CONTENTS:

Viscosity, Kinematic viscosity, Reynolds number and Poiseuille's equation.

- 25 -


SOURCE 1: p.198 - 209.

SOURCE 3: p.130 - 156.

SOURCE 4: p.287 - 303.

EXERCISE: SOURCE 2:

p 94 No. 10, 11, 12.

SECTION 6.2: VISCOUS FLOW IN ROUND PIPES

AIM:

At the end of this section the student must be able to solve any pipeline problem related to laminar

flow in round pipes.

CONTENTS:

Velocity of flow at any radius. (Hagen-Poisseuille)

Flow rate under viscous flow conditions.

Mean velocity of flow.

Maximum velocity of flow.

Relation between f and Reynolds number for viscous flow.


SOURCE 1: p.198 - 209.

SOURCE 3: p.130 - 156.

SOURCE 4: p.287 - 303.

EXERCISE: SOURCE 2:

p 95 No 13, 14, 16, 17, 18, 20.


ADDITIONAL PROBLEMS: SOURCE 4: p.325 No. 9, 10, 11, 12, 13.

SECTION 6.3: VISCOUS FLOW BETWEEN FLAT PARALLEL SURFACES

AIM:

At the end of this section the student must be able to solve any problem related to laminar flow

between parallel plates.

CONTENTS:

Velocity of flow on any point from the centre.

Maximum velocity.

Flow rate.

Mean velocity.

Shear stress on any distance from the centre.

- 26 -


SOURCE 1: p.198 - 209.

SOURCE 3: p.130 - 156.

SOURCE 4: p.287 - 303.


Self study 2. No.11 - 13.

SECTION 6.4: VISCOUS FLOW DURING LINEAR AND ROTATING MOTION

AIM:

At the end of this section the student must be able to solve any problem related to laminar flow

when the motion is linear and rotating.

CONTENTS:

Flow through annular space.

Dashpot

Sliding friction

Viscous flow in pipes

Rotating disc

Viscous flow in journal bearings


SOURCE 1: p.198 - 209.

SOURCE 3: p.130 - 156.

SOURCE 4: p.287 - 303.

EXERCISE: SOURCE 2: p.93 No.2, 3, 4, 5.

SOURCE 1: p.208 No.10, 11, 12, 13, 14, 15, 16, 17, 18.

Self study 2. No.14 - 26.

SECTION 7: DIMENSIONAL ANALYSIS

AIM:

At the end of this section the student must be able to consider and compare the relation between

certain equations and units by means of the basic dimensions (M,L,T).

CONTENTS:

Units

Dimensions

Checking equations


SOURCE 4: p.233 - 255.

EXERCISE: Problems will be given in the class.

- 27 -

SELF STUDY 1

1. Fresh water flows through a pipe with a diameter of 0,3 m at a rate of 0,283 m

3/s. The pipe

diameter enlarges suddenly to 0,6 m in diameter. The axis of the pipe is horizontal and the water in a vertical tube connected to the larger pipe stands 0,36 m higher than the level in a tube connected to the smaller pipe. Calculate the coefficient K if the shock loss is expressed as K v

2/2g, where v is the velocity in the smaller pipe. (0,4986)

2. A pipe, 0,093 m

2 in area, carries a discharge of 283 kg/s of water. If it enlarges suddenly to

0,372 m2 and the pressure in the smaller section is 4,8 kPa, find: (a) the head lost, (b) the

pressure in the larger part, (c) the power needed to force the water through the enlargement. (0,265 m; 6,54 kPa; 737 W) 3. A pipeline carrying 0,236 m

3/s is reduced suddenly from 450 mm to 300 mm in diameter.

Calculate the change in: (a) the total energy head, (b) the pressure energy head. Take CC = 0,67. (0,1379 m; 0,5939 m)

4. Determine the loss of head due to friction in a cast-iron pipe 360 m long and 150 mm in

diameter which carries 0,042 m3/s. Take f = 0,005. (13,8 m)

5. Using the Chezy formula, find the loss of head in a pipe 120 m long and 75 mm in diameter

when the velocity of flow is 4,8 m/s. Take C = 54,6 SI units. (49,5 m) 6. Water is discharged from a reservoir through a pipe 1200 m long which is 400 mm in

diameter for the first 600 m of pipe length, and 250 mm in diameter for the rest. The far end of the pipe is 30 m below the water level in the reservoir and f for the 400 mm pipe is 0,004 and for the 250 mm pipe 0,006. Calculate the flow, taking only friction into account.(0.151 m

3/s)

7. Two reservoirs whose difference of level is 13,5 m are connected by a pipe ABC, whose

highest point B is 1,5 m below the level in the upper reservoir A. The portion AB has a diameter of 200 mm and the portion BC a diameter of 150 mm, the coefficient of friction for each being 0,005. The total length of the pipe is 3 km. Find the maximum allowable length of the portion AB if the pressure at B is not to be more than 3 m below atmospheric pressure. Neglect the velocity head in the pipe and the shock losses. (2034 m)

8. A pipe of 50 mm in diameter and 45 m long is connected to a large tank, the entrance to the

pipe being 3 m below the surface. The lower end of the pipe which is 6 m below the upper end is joined to a horizontal pipe of 100 mm in diameter and 75 m long, which discharges to the atmosphere. Calculate the discharge taking into account all the losses. Take f = 0,008.

(4,65 x 10-3 m3/s)

9. Two reservoirs, whose surface levels differ by 30 m, are connected by a pipe 0,6 m in

diameter and 3 km long. The pipeline crosses a ridge whose summit is 9 m above the level of and 300 m distant from the higher reservoir. Find the minimum depth below the ridge at which the pipe must be laid if the absolute pressure in the pipe is not to fall below 3 m of water and calculate the discharge. Take f = 0,0075 and Hatm = 10,32 m of water.

(0,559 m3/s; 4,87 m)

- 28 -

10. A pump supplies water to a nozzle of 25 mm in diameter through a pipe 180 m long and 75 mm in diameter. The nozzle is at a level 9 m above the pump and f for the pipe is 0,012. Calculate the pressure required at the pump outlet to give a discharge of 8 dm

3/s in the

pipeline. (408 kPa) 11. Calculate the maximum power available at the outlet end of a hydraulic pipeline which is

4,8 km long and 200 mm in diameter. The pressure at the inlet of the pipe is 6,9 MPa. Take f = 0,007. (378 kW)

12. A pipeline, 1800 m long and 375 mm in diameter, is fitted with a nozzle, with an effective

diameter of 50 mm, at the pipe outlet. The coefficient of velocity for the nozzle is 0,972. If f for the pipe is 0,005, calculate: (a) the velocity of the jet, (b) the discharge, (c) the power of the jet. Assume that the pressure at the pipe inlet is 240 m. (66 m/s; 0,1296 m

3/s; 279,9 kW)

13. Water is to be conveyed to a Pelton Wheel through a pipe 1200 m long with a fall between

open level and the nozzle of 126 m. If the output power is to be 300 kW with a turbine efficiency of 70 %, calculate the smallest size pipe which could be employed. Take f = 0,008.

(459 mm) 14. What is the maximum rate at which energy can be transmitted through a 150 mm diameter

pipeline, 3 km long, supplied with water at a pressure of 8,3 MPa? Take f = 0,01. (257 kW) 15. Determine the diameter of pipe required to supply a turbine developing 1500 kW under a

gross head of 150 m. Assume pipe transmission efficiency of 95 % and a turbine efficiency of 86 %. The pipe is 3000 m long and Chezy's constant is 66 SI units. (0,985 m)

16. A pipeline transmits 260 kW over a distance of 2,4 km. If the supply pressure is 3,3 MPa,

calculate the number of 150 mm diameter pipes required to transmit this power with an efficiency of 92 %. Take f = 0,01. (6)

17. Two reservoirs 4,8 km apart are connected by a pipeline which consists of a 150 mm diameter

pipe for the first 1,6 km, sloping 5,7 m/km, and a 225 mm diameter pipe for the remaining distance, having a slope of 1,9 m/km. The water levels above the pipe openings in the respective reservoirs are 6 m in the upper reservoir and 3,6 m in the lower reservoir. Taking f = 0,0075, calculate the discharge through the pipeline. Take all the losses into account and draw the hydraulic gradient and total energy gradient. (16,3 dm

3/s)

18. Two tanks are joined by a 100 mm diameter pipe 30 m in length. The difference in level in

the tanks is 6 m and the ends of the pipe are 3 m under water. Both pipe ends are sharp. Sketch the hydraulic gradient and calculate: (a) the velocity in the pipe, (b) the pressure head in the pipe midway along its length. Take f = 0,01. (2,95 m/s; 2,68 m)

19. Two reservoirs having a difference of level of 6 m are connected by a single pipeline, with a

diameter of 600 mm, for the first 3000 m of pipe length. This pipe branches into two parallel pipes, each with a diameter of 300 mm and a length of 3 km, which discharges the water into the lower reservoir. Take f = 0,01. What will be total discharge? (72,5 dm

3/s)

- 29 -

20. Two reservoirs, whose surface levels differ by a constant 66 m, are connected by a pipe 225 mm in diameter and 4 km long. The pipe branches at a distance of 1,6 km from the upper reservoir and discharges some of the water directly to the atmosphere at a rate of 42,5 dm

3/s.

Calculate the discharge into the lower reservoir, neglecting the shock losses. Take f = 0,009. Sketch the hydraulic gradient for the pipeline. (35,5 dm

3/s)

21. A reservoir, 60 m above the datum, supply water to a junction box through a 300 mm

diameter pipeline which is 1500 m in length. From the junction box discharges two other pipes, each with a diameter of 300 mm and 1500 m long, water to two reservoirs whose surface levels are 15 m and 30 m above the datum respectively. Determine the flow rate entering each reservoir. Take f = 0,01. (27,8 dm

3/s; 90,2 dm

3/s)

22. Water flows from a reservoir through a pipe, 150 mm in diameter and 180 m long, to a point

13,5 m below the open surface of the reservoir. Here it branches into two pipes, each of 100 mm in diameter, one of which is 48 m long, discharging to the atmosphere at a point 18 m below the reservoir level, and the other 60 m long, discharging to atmosphere 24 m below the reservoir level. Assuming a coefficient of friction of 0,008 and neglect the loss in the junction, calculate the discharge from each pipe. (19,5 dm

3/s; 25,8 dm

3/s)

23. Water is discharged from a reservoir through a pipe 150 mm in diameter and 120 m long.

This pipe divides into two pipes each of 75 mm in diameter. One is 30 m long and discharges into a second reservoir with water level 12 m below the first. The other is 60 m long and discharges into a third reservoir with water level 24 m below the first. Taking f = 0,01 for each pipe, find the discharge into each reservoir. Neglect all losses other than pipe friction.

(13,55 dm3/s; 15,35 dm

3/s)

SELFSTUDY 2

1. Fresh water with a viscosity of 0,012 Poise flow through a pipe 50 mm in diameter at a

discharge of 2,8 dm3/s. Calculate the pressure drop over a length of 6 m of pipe. Given that

f = 0,064 Re-0,23

. (2,488 kPa) 2. Oil with a density of 880 kg/m

3 flows under a head of 30 m through a pipe 300 mm in

diameter and 3 km in length. Due to cooling the viscosity changes along the length and may be taken as 0,57 kg/ms over the first 1,5 km and 1,14 kg/ms over the second 1,5 km. Verify that laminar flow conditions exist and determine the discharge. Hint: For laminar flow assume that f = 16/Re. (20,07 dm

3/s)

3. Oil of viscosity of 0,048 Pas flows through an 18 mm diameter pipe with a mean velocity of

0,3 m/s. Calculate the loss in pressure over as length of 45 m of pipe, as well as the velocity at a distance of 3 mm from the wall of the pipe. (64 kPa; 0,332 m/s)

4. Oil of viscosity of 0,048 Pas flows through a 25 mm diameter pipe with a mean velocity of

0,3 m/s. Calculate the loss in pressure over a length of 30 m of pipe, as well as the velocity at a distance of 6 mm from the wall of the pipe. (22,1 kPa; 0,438 m/s)

5. A pipe 75 mm in diameter and 900 mm long conveys oil with a specific gravity of 0,85 and a

kinematic viscosity of 3,3 stokes at a rate of 40 Mg per hour. Confirm that the flow is laminar and find the power absorbed in overcoming friction in the pipe. (Hint: For laminar flow is f = 16/Re). (55,4 kW)

- 30 -

6. The velocity along the centre-line of a 150 mm diameter pipe conveying oil is 3 m/s. The viscosity of the oil is 1,2 Poises and its density is 900 kg/m

3. Assuming that the velocity

distribution across the pipe is parabolic, calculate flow rate, as well as the shear stress in the oil at the pipe wall. Also verify that the flow is laminar. (26,51 dm

3/s; 9,6 Pa)

7. An oil cooler consists of tubes of 12 mm in diameter and 3,5 m long. Oil with a specific

gravity of 0,9 is pumped through the tubes at a velocity of 1,8 m/s. The viscosity of the oil changes from 0,28 Poises to 1 Poises across the inlet and outlet of the tubes. It may be taken to vary as a linear function of the length. Calculate the power required to pump the oil through a group of 200 tubes. (3,65 kW)

8. Oil of viscosity of 0,048 Pas flows through a 50 mm diameter pipe with a mean velocity of

0,12 m/s. Calculate the loss in pressure over a length of 65 m of pipe, as well as the velocity at a distance of 10 mm from the wall of the pipe. (4,8 kPa; 0,153 m/s)

9. Oil with a specific gravity of 0,9 and a kinematic viscosity of 0,00033 m

2/s is pumped, at a

rate of 25 Mg/hour, through a 75 mm diameter pipe which is 1,5 km in length. Confirm that the flow is laminar and find the power required by the pump. Assume a mechanical efficiency of 70 % for the pump. (Re = 396,9 SI units; 48,8 kW)

10. Calculate the shear stress in the oil at the pipe wall for the data given in problem No 9. (55,3 N/m

2) 11. Oil having a viscosity of 0,083 kg/ms flows between two very large parallel flat plates 24 mm

apart. The mean velocity of the oil is 0,15 m/s. What is the shearing stress at 6 mm and 12 mm from the lower plate? (1,56 N/m

2; 0) 12. Oil of viscosity 0,8 Poises leaks from a container through a joint which is 0,6 m wide, 50 mm

long in the direction of flow. The gap between the parallel surfaces is 0,25 mm. Calculate the volume of oil escaping per hour if the pressure difference between the inside and outside is 35 kPa. (24,6 dm

3/hour)

13. A fluid with a density of 1260 kg/m

3 and viscosity of 0,9 kg/ms flows through two infinite

large parallel flat plates 2 cm apart. If the flow rate is 0,5 dm3/s per unit width, calculate the

pressure drop per unit width if both plates are stationary. (675 Pa/m) 14. A smooth cylinder 50,1 mm in diameter and 100 mm long is placed with its axis vertical. If

the clearance space is entirely filled with oil of viscosity of 2,5 Poises, calculate the force required to push a shaft of 50 mm in diameter through the cylinder with a velocity of 0,6 m/s.

(47,1 N) 15. A piston with a diameter of 100 mm and 150 mm long slides concentrically in a stationary

cylinder of 100,1 mm in diameter. The clearance space is filled with oil of viscosity 0,175 kg/ms. Find the force required to slide the piston along the cylinder at a speed of 3 m/s against the viscous resistance of the oil. (494,8 N)

16. The radial clearance between a plunger and the walls of a cylinder is 0,075 mm. The length of

the cylinder is 250 mm and its diameter is 100 mm. There is a difference in pressure of the water on the two ends of the plunger of 207 kN/m

2 and the dynamic viscosity of the water is

1,31 x 10-3 kg/ms. Treating the flow as if it occurred between parallel flat plates, calculate the rate of leakage in dm

3/hour. (25,1 dm

3/h)

- 31 -

17. A storage tank containing oil of viscosity 0,7 Poises is cylindrical with its axis vertical and is 6 m in diameter. When the oil is under pressure at 345 kPa, leakage occurs at a circumferential seam which consists of a riveted lap joint. The effective gap between the plates is 0,025 mm and the plates overlap by 100 mm. The rivets reduce the effective circumferential length of the opening by 40 %. Calculate the rate of leakage in dm

3/h.

(2,61 dm3/h)

18. A dashpot consists of a piston 143,5 mm in diameter working concentrically in a cylinder of

143,6 mm bore. The cylinder contains oil with a viscosity of 0,8 Poises. The length of the piston is 250 mm. Calculate the force which must be applied to the piston to give it a velocity of 0,003 m/s. (3342 kN)

19. The radial clearance between an hydraulic plunger and the cylinder wall is 0,1 mm. The

length of the plunger is 0,3 m and its diameter 100 mm. Find the velocity and the rate of leakage past the plunger at an instant when the difference of pressure between the two ends of the plunger is 9 m of water. Use µ = 1,31 x 10

-3 kg/ms. (0,187 m/s; 0,353 dm

3/min)

20. A shaft of 75 mm in diameter revolves concentrically in a bearing 150 mm in length. The

radial clearance is 1 mm and the speed is 3000 r/min. The viscosity of the oil is 3 Poises. Find the resisting torque due to viscosity and the power absorbed in overcoming it.

(4,68 Nm; 1,47 kW) 21. A shaft of 75 mm diameter revolves concentrically in a fixed tube of diameter 75,5 mm and

300 mm in length. The annular space is full of oil and it is found that a torque of 1 Nm is required to drive the shaft at 2400 r/min. What is coefficient of viscosity of the oil? What would be the critical velocity of this oil when flowing in a pipe of 75 mm in diameter if the critical Reynolds number is taken as 2300 and the density of the oil is 960 kg/m

3?

(0,01 Pas; 0,319 m/s) 22. A shaft of 150 mm in diameter turns concentrically in a sleeve 150,15 mm in diameter and

225 mm long. The clearance space is filled with oil. The power required to turn the shaft at 1000 r/min is 2,2 kW. Calculate the viscosity of the oil. (0,252 Poises)

23. A shaft, 100 mm in diameter, revolves concentrically in a bearing 150 mm long. The radial

clearance is 1,25 mm and the speed is 3000 r/min. The viscosity of the oil is 2,8 Poises. Find the resisting torque due to viscosity and the power absorbed in overcoming it.

(8,29 Nm; 2,6 kW) 24. A shaft, 150 mm in diameter, runs in a 300 mm long bearing at a speed of 300 r/min. If an oil

of viscosity 1,54 Poises fills the space between the shaft and the bearing, find the power absorbed due to viscous drag. Cr = 0,625 mm. (1,934 kW)

25. The thrust of a shaft is taken by a collar bearing. A thin film of oil of uniform thickness is

maintained between the surfaces of the collars and the bearing pads. The bearing surfaces are three annular pads of inside diameter 100 mm and outside diameter 150 mm. The thickness of the oil film is 0,25 mm and its viscosity is 0,85 Poises. Find the power lost in overcoming the viscous torque in the bearing when the shaft rotates at 1400 r/min. (874 W)

26. The thrust of a shaft is taken by a collar bearing fitted with a forced lubrication system which

maintains a film of oil of constant thickness of 0,3 mm between the surface of the collar and the surface of the bearings. The outer and inner diameters of the collar are 160 mm and 120 mm respectively. The viscosity of the oil is 0,12 kg/ms. Calculate the power lost in the bearing due to viscous drag when the shaft rotates at 500 r/min. (48 W)

- 32 -

SELF STUDY 3

1. A vertical cylindrical tank, 0,6 m in diameter and 1,5 m high, has an orifice of 25 mm

diameter in the bottom. The discharge coefficient is 0,61. If the tank is originally full of water, what time is required to lower the level by 0,9 m? (192 sec)

2. Water is discharging from a bell-mouthed orifice (Cd = 1) of 50 mm diameter in the base of a

tank having a surface area of 9 m2. How long will it take to reduce the depth in the tank from

1,2 m to 0,3 m above the orifice? (1135 sec) 3. A cylindrical vessel with its axis vertical is filled with water and discharges through an orifice

25 mm in diameter at the bottom with a coefficient of 0,623. If the diameter of the vessel is 0,6 m, find the time required for the water level to drop from 1,8 m to 0,6 m above the orifice when the supply is cut off. (237 sec)

4. Discharge takes place from a 1 m diameter cylindrical tank whose axis is vertical, through a

25 mm diameter pipe and 3 m in length. The pipe is connected to the base of the tank and discharges to atmosphere 2 m below the base. Initially the level in the tank is steady, water entering and leaving at a constant rate of 2 litres per second. If the supply of water is suddenly stopped, calculate the time required to empty it completely. Assume that the friction coefficient for the pipe is constant at 0,01, and that the tank outlet is sharp. (27 min 2 sec)

5. A vertical cylindrical tank is 4,8 m in diameter and discharges through a pipe 90 m long and

225 mm in diameter. How long will it take for the water level in the tank to fall from 2,7 m above the pipe exit to 1,2 m above that level? Assume that f = 0,01, and that the tank outlet is sharp. (470,8 sec)

6. Two water tanks A and B, whose constant cross-sectional areas are 7,4 m

2 and 3,7 m

2

respectively, are connected by a 50 mm diameter pipe, 120 m long, for which f = 0,01. The initial difference in the water levels are 1,5 m. Find the time taken for 2250 litres of water to pass from tank A into tank B. (42 min 25 sec)

7. Two cylindrical tanks, with its axis vertical, stand on a horizontal floor. One is 1,8 m in

diameter, the other is 1,2 m in diameter, and they are joined by a pipe, 75 mm in diameter and 1,8 m long, with sharp entrance and exit. The tanks are partly filled with water and at a given instant the level in the smaller tank is 1,2 m higher than that in the larger. Assuming f = 0,009, calculate the time taken for the difference of levels to become 0,3 m. (67,4 sec)

8. Two vertical-sided reservoirs each have a surface area of 186 m

2 and are connected by a

submerged opening of area 0,186 m2, which can be considered as an orifice with a coefficient

of discharge of 0,8. If the initial difference of surface levels is 2,7 m, how long will it be before this difference is 1,2 m? (2 min 34,5 sec)

SELF STUDY 4

1. An undershot waterwheel consists of a series of flat vanes, mounted radially on a wheel of

large diameter, which are struck normally by a jet of water 0,3 m in diameter. If the velocity of the water leaving the nozzle is 7,5 m/s and the velocity of the vanes is 4,8 m/s, what is the force exerted by the jet on the vanes, the work done per second and the hydraulic efficiency?

(1,431 kN; 6,87 kW; 46 %)

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2. A flat plate is struck normally by a jet of water 50 mm in diameter with a velocity of 18 m/s. Calculate (a) the force on the plate when it is stationary, (b) the force on the plate when it moves in the same direction as the jet at 6 m/s, (c) the work done per second and the hydraulic efficiency in case (b). (636 N; 283 N; 1,696 kW; 29,6 %)

3. A square plate, mass 12,7 kg, of uniform thickness and 300 mm edges, is hung so that it can

swing freely about its upper horizontal edge. A horizontal jet of water, 20 mm in diameter, strikes the plate with a velocity of 15 m/s normally at its centre when the plate hangs vertical. Find: (a) what force must be applied at the lower edge of the plate to keep it vertical, (b) what inclination to the vertical the plate will assume under the action of the jet if allowed to swing freely. (35,34 N ; 34,57° )

4. A rectangular plate of mass 5,45 kg is suspended vertically by a hinge on the top horizontal

edge. The centre of gravity of the plate is 10 cm from the hinge. A horizontal jet of water of 25 mm in diameter, whose axis is 15 cm below the hinge, impinges normally on the plate with a velocity of 5,65 m/s. Find the horizontal force applied at the centre gravity to maintain the plate in its vertical position. Find the alteration of the velocity of the jet if the plate is deflected through an angle of 30 degrees, and the same horizontal force continues to act at the centre of gravity of the plate. (23,5 N; 2,35 m/s)

5. A jet of water, 50 mm in diameter, with a velocity of 18 m/s, strikes a flat plate inclined at an

angle of 25° to the axis of the jet. Determine the normal force exerted on the plate when: (a) the plate is stationary, (b) the plate is moving at 4,5 m/s in the direction of the jet, and (c) determine the power transferred and the hydraulic efficiency for case (b).

(268,9 N; 151,2 N; 287,6 W; 5 %) 6. A jet of water, 75 mm in diameter, strikes a flat plate with a velocity of 24 m/s. The normal to

the plate is inclined at 30° to the axis of the jet. Calculate the normal force on the plate when: (a) the plate is stationary, (b) the plate has a velocity of 12 m/s in the same direction as the jet.

(2,2 kN; 0,551 kN) 7. A tanker discharges a jet of water horizontally backwards with a velocity of 4,8 m/s. If the

rate of discharge is 85 dm3/s, what force is required to keep the tanker at rest? (407,99 N)

8. Calculate the reaction of a jet on a nozzle connected to a pipe. The diameter of the pipe is

0,1 m and the mean velocity of flow in the pipe is 15 m/s. The pressure in the pipe is 2070 kPa. Take Cv = 0,96. (5,5 kN)

9. A horizontal pipe gradually reduces in diameter from 300 mm to 150 mm. Determine the

thrust exerted on the reducer if at the larger end the pressure is 275 kPa and the velocity of the water is 3 m/s. (13,863 kN)

10. Water flows through a 910 mm diameter pipe at the end of which there is a reducer

connecting to a 590 mm diameter pipe. If the pressure at the entrance to the reducer is 400 kPa and the velocity is 2 m/s, determine the resultant thrust on the reducer, assuming that the frictional loss of head in the reducer is 1,2 m. (153 kN)

11. A jet-propelled vessel takes in water through ducts amidships and discharges it through ducts

astern. The discharge is 34 m3/min and the velocity of flow through the ducts is 9 m/s. The

speed of the vessel is 4,5 m/s. Calculate the magnitude of the propulsive force. (2,55 kN)

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12. A jet of water, 6,5 cm2 in cross-sectional area, moving at 12 m/s, is turned through an angle of

135° by a curved plate. The plate is moving at 4,5 m/s in the same direction as the jet. Neglecting any loss of velocity by shock or friction, find the power transferred to the plate.

(281 W) 13. A jet of water, 75 mm in diameter, with velocity 21 m/s flows tangentially onto a stationary

vane which deflects it through 120°. What is the magnitude and direction, referred to the direction of the jet, of the resultant force on the vane? If this jet flows onto a series of vanes similarly oriented with regard to it but moving in the direction of the jet with a velocity of 10,5 m/s, determine: (a) the force on the system of vanes in the direction of motion, (b) the work done per second, (c) the efficiency. (3375 N; 30°; 1461 N; 15,342 kW; 75 %)

14. A jet of water of 50 mm in diameter, having a velocity of 24 m/s impinges tangentially on a

series of vanes which, when stationary, deflect the jet through an angle of 120°. Calculate the magnitude of the force on the vanes in the direction of motion when they are: (a) stationary, (b) moving with a velocity of 9 m/s in the same direction as the jet. (c) Calculate the work done per second and the hydraulic efficiency for case (b).

(1,696 kN; 1,061 kN; 9,54 kW; 70,3 %) 15. A jet of water, flowing at a rate of 20 kg/s and at a velocity of 25 m/s, impinges on a series of

vanes moving at 12 m/s in a direction making an angle of 25° to the jet. Determine the inlet angle of the blade for no shock entry. If the vane exit angle is 150° to the direction of motion and the power developed if friction reduces the water velocity relative to the vanes by 20 % during its passage over the vanes. (45°; 421,1 N; 5,053 kW)

16. A jet of water discharges 13,6 kg/s at 24 m/s in a direction making 30° to the direction of

motion of a series of curved vanes moving at 10,5 m/s. If the outlet angle of the vanes is 20°, determine: (a) the inlet angle of the vanes such that there is no shock at entry, (b) the work done per second on the wheel. (49,4°; 3,589 kW)

17. A nozzle, having a coefficient of velocity of 0,96, operates under a head of 90 m of water and

directs a 50 mm diameter jet of water on to a ring of axial flow impulse blades, which have an inlet angle of 40°, measured relative to the direction of blade motion. The blades turn the water through an angle of 105° and because of friction the velocity of the water relative to the blades is reduced by 15 % during its passage over the blades. The blade speed is to be 18 m/s and the water is to flow on to the blades without shock. Calculate: (a) the angle which the line of the jet will make with the direction of motion of the blades, (b) the power developed by the blade ring, (c) the hydraulic efficiency. (23,3°; 51,8 kW; 80,4 %)

18. A jet of fresh water, moving at a velocity of 25 m/s, strikes a series of vanes on the periphery

of a turbine wheel which moves at a pitch line velocity of 12 m/s in a direction making an angle of 20° to the jet. The vane outlet angle is 20°. Neglect the frictional losses across the vanes. Calculate: (a) the inlet vane angle for no shock, (b) the power/kg of water exerted by the wheel, (c) the efficiency of the system. (36,65°; 299 W; 95,7 %)

19. A jet of water with a velocity of 30 m/s strikes a series of vanes moving at a speed of 15 m/s

in a direction making an angle of 30° to the jet. The jet leaves the vanes relative at 15°. Neglect friction loss across the vanes. Calculate: (a) the vane inlet angle for no shock, (b) the work done by the wheel/kg of water/sec, (c) the hydraulic efficiency. (53,8°; 434 W; 96,4 %)

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20. A jet of fresh water strikes a single vane type of turbine at 30° with the direction of motion, and leaves it at 160° absolute with the direction of motion. The absolute velocity at inlet is 25 m/s and the vane moves at a velocity of 12 m/s. Ignore friction across the vane. Calculate: (a) the vane inlet angle and outlet angle, (b) the power/kg of water, (c) the hydraulic efficiency. (52,33°; 4,94°; 304,6 W; 97,5 %)

21. A technician employed at a company which manufacture turbines must determine the required

height of a reservoir above a certain turbine which has to develop 2,635 kW. The diameter of the jet is 100 mm. The jet strikes the vanes tangentially. The vanes deflect the water through an angle of 110°. The speed of the vanes is 5 m/s in the direction of the jet. Cv = 0,65. Ignore the losses in the supply pipe and across the vanes. Find: (a) the jet velocity to generate the required power, (b) the height of the water level in the reservoir above to the turbine.

(10 m/s; 12,06 m) 22. A stream of fresh water flows through a rectangular duct and collides against the flat blades

of an undershot water wheel. The blades are 1,2 m in width, 0,5 m high and are fully in contact with the water. The pressure head is 4 m and the pitch circle diameter of the blades is 5 m. The wheel turns at a speed of 20 r/min. Find: (a) the force exerted on each blade, (b) the power transmitted to the wheel, assuming that one blade is continuously in contact with the stream, (c) the hydraulic efficiency of the wheel. (19,26 kN; 100,8 kW; 48,3 %)

SELF STUDY 5

1. It is found that at a free vortex, which started in a large reservoir, is a point on the free surface

at a diameter of 300 mm, 75 mm below the level of the free surface of the water in the reservoir. What will be the level of the surface at a diameter of 600 mm below the water level in the reservoir? (18,75 mm)

2. A cylindrical tank has a height of 1,2 m and a diameter of 0,6 m and is three-quarters filled

with water when stationary. If the tank rotates about its vertical axis at 150 r/min some of the water is spilled over the sides. Calculate: (a) the depth of the water below the depression of the vortex while the cylinder rotate, (b) the total depth of the water in the cylinder when it is stationary again, (c) the quantity of water spilled in litres. (68 mm; 634 mm; 75,2 dm

3)

3. A cylindrical vessel is 1,5 m high and 0,8 m in diameter. It rotates about its vertical axis at

120 r/min. The vessel is open at the top, and was completely filled with water before the rotation started. Calculate how many litres of water are left in the vessel after the rotation.

(430,3 dm3)

4. A cylindrical tank has a diameter of 0,6 m, a height of 1,15 m and is open to the atmosphere

at the top. It rotates about its vertical axis at a speed of 105 r/min. Before the rotation started the tank was full of water. Calculate how many water remain in the tank after the rotation.

(247 dm3)

5. A closed cylindrical tank has a diameter of 650 mm and rotates about its vertical axis at a

speed of 600 r/min. If the tank is fully filled with water, calculate the pressure generated inside the cylinder. (208,5 kPa)

6. A cylindrical drum, with its axis vertical, has a inside- diameter of 600 mm and is completely

filled with water. An impeller, with a diameter of 200 mm, rotates at the bottom of the drum at a speed of 120 r/min. Calculate: (a) the velocities of the water on radii of 75 mm and 225 mm respectively, (b) the corresponding pressure heads at these radii, measured from the bottom of the forced vortex. (0,942 m/s; 0,559 m/s; 45,2 mm; 145,1 mm)

- 36 -

7. A compound vortex formed in a large reservoir having a free surface comprises a central forced vortex surrounded by a free vortex. The assembly is completely developed. The separation between the forced- and free vortex occurs at a radius of 200 mm. The total depression is 900 mm. Find the rotational speed of the forced vortex. (141,9 r/min)

8. The impeller of a centrifugal pump discharges fresh water at a velocity of 20 m/s against a

pressure of 12 m of water. The pump must deliver the water against a pressure of 20 m of water. Calculate the required diameter of the vortex chamber if the impeller has a diameter of 600 mm. (769,7 mm)

9. A centrifugal pump rotates at a speed of 800 r/min with its delivery valve closed. The

impeller has a diameter of 250 mm. The pressure at the inlet to the impeller is -25 mm of mercury. Assume that a forced vortex is generated in the impeller. Find now the pressure at the periphery of the impeller. (51,49 kPa)

10. Water is discharged from the impeller of a centrifugal pump against a pressure of 10,5 m and

a tangential velocity component of 14 m/s. The impeller has a diameter of 60 cm. Calculate the required diameter of the vortex chamber to increase the delivery pressure to 15 m.

(809 mm) 11. A centrifugal pump has a diameter of 260 mm and a vortex chamber with a diameter of

340 mm. Calculate the required speed for the pump if a pressure of 18 m of water is gained inside the vortex chamber. (2142,5 r/min)

SELF STUDY 6

1. A single-acting reciprocating piston pump has a piston diameter of 200 mm and a stroke length of 600 mm. The speed of the pump is 20 r/min. Discharge occurs through a pipe with a length of 45 m and a diameter of 100 mm, with f = 0,008. Calculate the saving in power if an air vessel is fitted near the delivery side of the pump. (161,75W)

2. The vertical suction pipe of a single-acting piston pump is 2 m in length and 50 mm in

diameter. The piston has a diameter of 150 mm and a stroke length of 300 mm. The pump is 1,9 m above the water level in the sump. Find the maximum allowable speed for the pump just before separation occurs. Assume the atmospheric pressure to be 10,3 m of water, and that separation will occur if the absolute pressure drop below 1,8 m of water. (46,8 r/min)

3. The piston diameter of a single-acting reciprocating piston pump is 115 mm and a stroke

length of 230 mm. The diameter of the suction pipe is 90 mm and 4,2 m long. If separation occurs at an absolute pressure of 1,2 m, calculate the maximum allowable speed at which the pump can be operated before separation will occur. Assume a barometer reading of 757,5 mm of mercury. The water level in the sump is 3 m below the pump centre. Find also the power needed to overcome friction in the suction pipe at this speed. ( f = 0,01) (83,2 r/min; 5,5 W)

4. A double-acting reciprocating piston pump which has a stroke length of 350 mm and a bore

of 175 mm, takes water in from a sump 3 m below and deliver it at a height of 46 m above the pump level. Both the suction and delivery pipes have a diameter of 100 mm and lengths of 6 m and 75 m respectively. The pump piston follows the motion of simple harmonic at 40 double strokes per minute. Large air vessels are fitted on both sides of the pump. On the suction side is the air vessel 1,5 m and on the delivery side 4,5 m away from the pump. The coefficient of friction for both pipes is 0,008. Calculate the pressure difference across the piston at the beginning of the stroke. (57,5 m)

- 37 -

5. A double-acting reciprocating pump has a piston diameter of 200 mm and a stroke of 0,6 m and runs at 20 r/min. It discharges through a 150 mm main 75 m long ( f = 0,0075) with a vertical lift of 45 m. Assuming the piston to have s.h.m. and that no air vessel is used, sketch the part of the indicator card corresponding to discharge giving the heads in the cylinder at the ends and middle of the stroke. Neglect friction at the discharge valve. (62,9 m, 45,96 m, 27,1 m)

6. A single-acting reciprocating pump has a plunger diameter of 250 mm and a stroke of

450 mm. The delivery pipe is 110 mm diameter and 48 m long. If the plunger moves with simple harmonic motion, find the power saved in overcoming friction in the delivery pipe by the provision of a large air vessel on this pipe close to the cylinder when the pump is driven at 20 rev/min, taking ƒ = 0,01. (215 W)

7. A double-acting reciprocating pump is used to raise water to a height of 42 m through a delivery pipe of diameter 75 mm and length 81 m. The pump speed is 180 r/min, the stroke is 250 mm and the piston diameter is 115 mm. A large air vessel is fitted in the delivery pipe at 6 m from the cylinder, measured along the pipe. Determine the absolute pressure at the end of each delivery stroke, given that the friction coefficient for the pipe is 0,007. It should be assumed that the piston moves with simple harmonic motion, that the effect of the piston rod is negligible, and that the atmospheric pressure is 10,2 m of water. (6,94 m of water)

8. A double-acting single-cylinder reciprocating pump of 190 mm bore and 380 mm stroke runs at 36 double strokes/min, suction head 3,6 m, and discharge head 30 m. The length of the suction pipe is 9 m and of the discharge pipe 60 m, and the diameter of each pipe 100 mm. Large air vessels are provided 3 m away from the pump on the suction side, and 6 m away on the discharge side, both measured along the pipelines, ƒ = 0,008. Neglecting entrance and exit losses for the pipes, estimate for the beginning of the stroke: (a) the head in the two ends of the cylinder, (b) the load on the piston rod, neglecting the size of the piston rod and assuming simple harmonic motion. (34,04 m, -4,75 m, 10,8 kN)

9. A single-acting reciprocating pump has a piston of 200 mm diameter and 600 mm stroke. It run at 20 r/min with simple harmonic motion. Delivery is through a 100 mm diameter pipe of length 45 m for which ƒ = 0,008. Find the power which would be saved by fitting an air vessel to the delivery side assuming that there would then be no acceleration in the pipe. (66 W)

10. Sketch theoretical indicator diagrams for a single-cylinder single-acting reciprocating pump not fitted with air vessels. Use your diagram to explain clearly the effect of acceleration and friction on both suction and delivery strokes. Assuming simple harmonic motion of the piston, develop an expression for the acceleration head in the cylinder at the beginning of the suction stroke in such a pump. The following data relate to a pump of the type described above: length of suction pipe, 9 m; diameter of suction pipe, 75 mm; suction lift, 3 m; plunger diameter, 125 mm; stroke, 300 mm; speed, 30 rev/min. Calculate the theoretical absolute pressure head in meter of water at the beginning and end of the suction stroke. Barometric pressure corresponds to 10,2 m of water. (3,43 m, 10,97 m)

11. A reciprocating pump has three single-acting cylinders the pistons of which are operated by

cranks at 120° apart. The pistons are 75 mm diameter and have a stroke of 150 mm. The cylinders discharge water into a single pipe 50 mm diameter and 60 m long. The pump speed is 60 r/min and there is no air vessel on the delivery side. Give diagrams on a crank angle base showing how the water velocity and acceleration in the discharge pipe differ from those obtained with a single-acting single-cylinder pump of the above dimensions and speed. If the pipe discharges to air 30 m above the level of the cylinders calculate the range of pressure in the pipe just beyond the pump. Take ƒ for the pipe as 0,01. (52,46 to 11,66 m of water)

- 38 -

12. Explain the object of fitting an air vessel on (a) the suction side and (b) the delivery side of a reciprocating pump. A single-acting reciprocating pump with plunger diameter of 100 mm and stroke of 150 mm has a speed of 75 r/min. The centre of the pump cylinder is 1,5 m above the level of the water in the sump. The 75 mm diameter suction pipe is 7,2 m long. The level of the delivery tank is 30 m above the centre of the pump cylinder, and the 63 mm diameter delivery pipe is 75 m long. The friction coefficient for the suction and delivery pipes is 0,01. There is no air vessel on the suction side, but one, which may be assumed to be perfectly efficient, is installed on the delivery side. Assuming that the plunger moves horizontally with simple harmonic motion, determine (a) the pressure on the plunger at the beginning, middle and end of the suction stroke; (b) the water power of the pump. Also obtain the pressure on the plunger at the beginning of the delivery stroke if no air vessel had been fitted on the delivery side. ((a) –7,56 m, -l,71m, +4,56 m of water, (b) 465W, 119m of water)

13. A reciprocating pump has a cylinder of 75 mm bore x 150 mm stroke and draws water from a

sump whose level is 1,5 m below the axis of the pump. If the suction pipe is 2,4 m long and 50 m in diameter, find the speed of the pump in rev/min at which separation occurs if this takes place at a vacuum head of 7,9m of water. Assume simple harmonic motion of the piston. If ƒ = 0,01 for the pipe, what is the friction head at mid-stroke when running at this speed?

(119 r/min, 0,435 m) 14. A double-acting single-cylinder reciprocating pump has a cylinder diameter of 150 mm and

450 mm stroke. The suction and delivery pipes have diameters and lengths of 100 mm, 6 m and 75 mm, 60 m respectively. The sump is 4,5 m below and the reservoir 45 m above the centre-line of the pump. If the pump runs at 60 rev/min, determine the power of the driving motor if its efficiency is 0,85. Take ƒ = 0,005 and assume simple harmonic motion for the plunger. (12,6 kW)

school for mechanical engineering \u0026 applied mathematics fluid mechanics iii (mfm31bi / mfm32bi)...

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