final_mehb223-ss-2013-2014

COLLEGE OF ENGINEERINGPUTRAJAYA CAMPUSFINAL EXAMINATION

SPECIAL SEMESTER 2013 / 2014

PROGRAM : Bachelor of Mechanical Engineering (Honours)PROGRAM

KOD MATAPELAJARAN : MEHB223 SUBJECT CODE

MATAPELAJARAN : Mechanics of Fluids 1SUBJECT

TARIKH : April 2014DATE

MASA : 3 HoursTIME

Instructions to candidates:

1. Write your student ID, section and table number on the answer script.

2. This paper contains FIVE (5) questions in THIRTEEN (13) pages.

3. Answer ALL questions.

4. Write all answers in the answer booklet provided.

5. Write answer to each question on a new page.

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE INSTRUCTED TO DO SO

THIS QUESTION PAPER CONSISTS OF 13 PRINTED PAGES INCLUDING THIS COVER PAGE.

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MEHB223, Special Semester, 2013/2014

QUESTION 1 [15 marks]

a) i) Write the equation relating the shearing stress and rate of shearing strain of any

Newtonian fluid.

[1 mark]

ii) Give two examples of Newtonian fluids.

[2 mark]

b) A pivot bearing used on the shaft of an electrical instrument is shown in Figure 1.

A uniform 0.025mm gap between the rotating shaft and the stationary base is

filled with oil that has a viscosity of µ = 0.479 N.s/m2. Determine the frictional

torque on the shaft when it rotates at 4,500 rpm.

[12 marks]

Figure 1

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4500 rpm



A homogeneous, 1.2-m-wide, 2.4-m-long rectangular gate weighing 3.6 kN is held in

place by a horizontal flexible cable as shown in Figure 2. Water acts against the gate

which is hinged at point A. Friction in the hinge is negligible. (Use γH2O = 9790 N/m3)

a) Determine the hydrostatic force, FR exerted on the gate.

[5 marks]

b) Determine the inclined distance of the hydrostatic force from the hinge.

[4 marks]

c) Determine the tension, T in the cable.

[4 marks]

d) Draw the free-body diagram (FBD) of the gate.

[2 marks]

Figure 2

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T

1.8 m 2.4 m



Figure 3 shows the schematic diagram of a draining tank.

a) By referring to Figure 3, show that the velocity at the circular exit (vexit) of the

cylindrical tank is √2gh

, where g is the gravitational acceleration and h is the

instantaneous water height measured from the bottom of the tank.

[8 marks]

b) Determine how long it will take for the water level in the cylindrical tank

(illustrated in Figure 3) to drop to 2m (measured from the bottom of the tank)

from the initial water height h0 of 4m. Assume Dexit = 0.5m and Dtank = 3.0m.

[12 marks]

Figure 3

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Water flows through a nozzle shown in Figure 4 at a rate of 0.5 m3/s and discharges into

the atmosphere. The diameter of the nozzle at point (1) and at the nozzle exit are D1 = 40

cm and D2 = 15 cm respectively. The flow is assumed to be irrotational flow and the

gravitational effect is neglected.

(Use H2O = 1000 kg/m3, g = 9.81 m/s2)

a) Using continuity equation, calculate velocity V1 and V2

[5 marks]

b) Using Bernoulli equation between point (1) and (2), find pressure p1. Assume z1

equals z2.

[4 marks]

c) Using linear momentum equation, determine the magnitude and direction of the

force (in kN) required at the flange to hold the nozzle in place.

[6 marks]

Figure 4


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A differential mercury manometer is connected to two pressure taps in an inclined

commercial steel pipe as shown in the Figure 5. The inclined distance between the

pressure taps is 2 m and the diameter D of the pipe is 20 mm. Kerosene (μ = 1.9×10−3

N·s/m2) is flowing through the pipe and the deflection of mercury in the manometer is 5

cm. (Use H2O = 1000 kg/m3 , γH2O = 9810 N/m3)

a) Show that the difference in piezometric pressure between the two pressure taps in

the pipe is:

pz ,1−pz , 2=12.79 γ H 2 O ∆ h

[7 marks]

b) By using suitable charts and tables, find the velocity and direction of the flow in

the pipe. Justify your answer.

[28 marks]

Figure 5

END OF QUESTION PAPER

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KeroseneSG = 0.81

Mercury (SG = 13.6)

2 m

D = 20 mm


APPENDIX A: SUPPLEMENTARY DATA AND FORMULA

1. Atmospheric Pressure = 1.0135 bar

2. Pressure distribution in a rotated inviscid fluid

p+γz− ρ r2 ω2

2=Cons tan t

3. The constant pressure line in a rotated mass of fluid is given by:

z−zo=ω2 r2

2g

4. Bernoulli’s equation

pγ+ V 2

2 g+z=H

5. Stagnation pressure ps=p+ 1

2ρV 2

6. General Mass Conservation :

dmc

dt=∑m

¿

in−∑ m¿

out

7. General Force Momentum Equation :

dM xc

dt=∑ F x+∑ M

¿

xin−∑ M¿

xout

8. General Energy Conservation Equation :

dEc

dt=Q−W +∑ E

¿

in−∑ E¿

out

9. Hydrostatic Force on Plane Surface : F=ρg h¿

A ;

ycp− y=I xx

y¿

A

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10. Hydrostatic Force on Curved Surface : Fh= ρg h¿

v Av ;

ycpv=I xxv

h¿

v A

Fv=ρgV

11. General Single Pipeline Energy Equation :

P1

ρg+α1

V12

2g+z1+h p=

P2

ρg+α 2

V22

2 g+z2+h t+ ∑

all−length

fℓd

V 2

2g+ ∑

min or

kV 2

2 g

12. Friction factors.

f = 0. 25

[ log10( k s

3 .7 D+ 5 .74

Re0. 9 )]2

; f =64

Re

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Appendix B: Moody Chart

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Appendix C: Dynamic Viscosity of certain gases and liquids

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Appendix D: Pipe fitting loss tables

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final_mehb223-ss-2013-2014

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