ff2

FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingement

Table of Content

25th November 2013

Fluid Flow, Thermodynamics and Heat Transfer Laboratory

FTH-FF2: Frictional pressure loss through pipes and fittings, and jet impingement

College of Engineering and Physical Sciences

School of Chemical Engineering

University of Birmingham

Mustafa Iqbal - 1323293Laboratory Group 7: Colin Andrew Francis, Zareeen Zainal Azwar, Matthew Parker and

Jake Stanbridge

Understanding pressure drops in industry is vital. This report investigated the reasons behind pressure drops and sought to quantify where and to what magnitude they occurred. Using

results from a laboratory experiment completed in cohesion with the report, theoretical models for different pipe specifications in laminar and turbulent regimes were used to predict and

compare pressure drops and momentum changes between theoretical and experimental values. The experiment also included an orifice plate which was calibrated, and a jet impingement

section in order to enable momentum change to be calculated. The findings of the report show that theoretical models are accurate for laminar regimes, however in turbulent regimes as the flow rate increased the dissimilarities between theoretical and experimental values increased. There were many reasons for this, the most crucial factor lay in the assumptions made such as

the incompressibility of air and parameters used in the equations such as the pipe fitting constant. It was discovered that pipe bends and height drops caused a significant pressure drop

compared to a fluid flowing through a straight pipe, and including more bends only increased the pressure drop. It was also discovered that pipes with smaller diameters or/and greater relative

roughness exhibited a greater pressure drop.

Word Count: 3204


s1. Introduction...................................................................................................................................1

1.1 Background............................................................................................................................1

1.2 Aims and Objectives..............................................................................................................1

2. Theory...........................................................................................................................................2

2.1 Equations.....................................................................................................................................2

2.1.1 Pipe Bends, Orifice Plate, Momentum Change and Volumetric Flow Rate Calculations.......3

2.2 Relative Roughness......................................................................................................................3

3. Methods........................................................................................................................................3

4. Results...........................................................................................................................................5

4.1 P1-P2......................................................................................................................................5

4.2 P5-P6......................................................................................................................................7

4.3 P6-P7......................................................................................................................................9

4.4 P7-P8....................................................................................................................................11

4.5 P8-P9....................................................................................................................................13

4.6 P9-P10..................................................................................................................................15

4.7 Jet Impingement..................................................................................................................17

4.8 Calibration of the Orifice plate.............................................................................................18

5. Analysis of Results and Discussion...............................................................................................19

Conclusion...........................................................................................................................................21

Appendix.............................................................................................................................................22

Appendix A – Pipe bends, Orifice Plate, Momentum Change and Flow Rate Calculations..............22

1. Pipe Bends...........................................................................................................................22

2. Orifice Plate.........................................................................................................................22

3. Momentum Change.............................................................................................................22

4. Voumetric Flow Rate Calculations.......................................................................................23

Appendix B - Orifice Plate Calibration..............................................................................................24

Appendix C – Table of data..............................................................................................................25

References...........................................................................................................................................26

TablesTable 1: Pressure Drop across P1-P2

Table 2: Pressure Drop across P5-P6


1 | P a g eMustafa Iqbal 1323293





Table 7: Jet Impingement on a flat plate

Table 8: Table of Orifice Plate calibration calculations

Table 9: Table of data

(University of Birmingham, 2013)

FiguresFigure 1: Format of experimental equipment

Figure 2: P1-P2 Laminar- Measured and Theoretical Pressure drop (Pa) against Volumetric Flow Rate (Lmin-1)

Figure 3: P1-P2 Turbulent- Measured and Theoretical Pressure drop (Pa) against Volumetric Flow Rate (Lmin-1)

Figure 4: P1-P2 Laminar- Measured and Theoretical Momentum Change (gms-2) against Volumetric Flow Rate (Lmin-1)

Figure 5: P1-P2 Turbulent- Measured and Theoretical Momentum Change (gms-2) against Volumetric Flow Rate (Lmin-1)























Figure 26: Jet Impingement 5mm- Measured and Theoretical Momentum Change (gms-2) against Volumetric Flow Rate (Lmin-1)





1. Introduction1.1 BackgroundIn industry, production plant design requires a tedious level of detailed accuracy in order to understand and

therefore manipulate the several concise operations included. This advantage is a result of various theoretical methods permitting the prediction of required parameters in major equipment items such as pressure in pipes and temperature in heat exchangers. This empowers the designer to adjust and fine tune process parameters until an optimum efficiency is established.

Fluid flow is a vital part of a process. Materials need to be transferred between phases of the process for production, and then transferred to storage units for transportation to consumer bases. This transfer of material is achieved by using pipes and pumps to introduce pressure, resulting in fluid flow. However as is seen with Newton’s third law, when a body exerts a force on a second body, the second body instantaneously and continuously exerts a force of equal magnitude and opposite direction to that of the first body. (Newton, 1726) A fluid exerts a shear stress over an area of contact with a second body. In an industrial context, the fluid would be travelling through a pipe. Therefore its area of contact is the surface area of the cylindrical shape it assumes in the pipe. This shear stress, combined with Newton’s third law suggests an energy loss of the fluid in the form of surface friction between the pipe’s internal surface and the fluid’s outer surface. This energy loss is revealed as a pressure drop between two points in a pipe. Process engineers need to account for this in order to maintain accuracy in their design. (Baker, 2013)

Therefore a pressure drop is defined as the loss of pressure between two points in a pipe due to the internal friction between the pipe and fluid’s contacting surfaces. As a result the fluid loses energy, exposing a reduced velocity and pressure at the outlet compared to the inlet. Therefore in order to achieve a required volumetric flow rate the inlet pressure and system efficiency will need to be adjusted. (Compressed Air Challenge, 1998)

With the above context in mind, an inefficient system will require a higher inlet pressure to obtain the same volumetric flow rate as a more efficient system with a lower inlet pressure. Operating systems at high pressures requires specific materials to enclose the hazardous internal environments and ensure the safety of those working on site, this would cost more to build, maintain and monitor, therefore it is not in the interests of the project to use an inefficient system. (Compressed Air Challenge, 1998) Where water is used as the fluid, a severe pressure drop could cause its pressure to drop below the vapour pressure of water. This causes cavitation which is a serious cause of damage, further supporting the compulsion for an efficient system. (Baker, 2013)

Another factor to consider is local head losses, caused by the formation of eddies around pipe bends, junctions and fittings. In short pipes, such as those used in a process plant, these losses can be more than those due to friction, signifying the importance of the following experiment. (Baker, 2013)

Orifice plates are used in industry as they are a relatively cheap and easy method of measuring fluid flow rates. This is achieved using the same concept as a venturimeter, there is a change in the diameter of the pipe, causing a pressure drop. From this pressure drop a flow rate can be calculated. (Baker, 2013)

1.2 Aims and ObjectivesThe purpose of the laboratory was to first ascertain a method of accurately measuring pressure drops across

various scenarios in pipe flow, and then to proceed comparing said results to expected results acquired from theoretical calculations.

The aims of the laboratory were:


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingement To measure the pressure drop across various pipes and fittings To calibrate an orifice plate To compare the measured pressure drop to theory To investigate the momentum change of the air due to the impinging jet impacting on a flat

plate To compare the measured momentum change to theory To ascertain and discuss the differences between measurements and theoretical predictions

In the analysis of results, factors such as sources of error will be investigated.


2. Theory2.1 Equations

The following equations were used to calculate various parameters such as volumetric flow rate and predict variables such as pressure loss.

ℜ= ρVdμ

- Equation of Reynolds' Number [1]

υ= μρ

- Equation of Kinematic Viscosity [2]

Q=AV - Equation of Flow Rate [3]

A=πd2

4- Equation for Cross-sectional Area of Pipe [4]

∆ P=ρgh - Equation of Pressure Change [5]

P1ρg

+V 12

2g+z1=

P2ρg

+V 22

2 g+z2 - Bernoulli’s Equation [6]

ΔP=k LρV 2

2- Equation of pressure change as a proportion of the kinetic

energy in a system [7]

f=64ℜ - Equation of Darcy’s friction factor (laminar flow) [8]

f= 0.25

[ log( 1

3.7 ( dε )+ 5.74Re0.9 )]2

- Swamee-Jain’s equation of Darcy’s friction factor (turbulent

flow) [9]

ΔP=12f LdρV 2 - Darcy Pressure Loss equation [10]

Where:

Re = Reynolds’ Numberρ = Density (kgm-3)V = Velocity (ms-1)d = Diameter (m)


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementμ = Absolute Viscosity (Pas)υ = Kinematic Viscosity (m2s-1)Q=¿Flow Rate (m3s-1)A = Cross-sectional Area of Internal Pipe (m2)f = Darcy’s Friction Factor∆ P = Pressure Change (Pa)g = Gravitational Acceleration (ms-2)ε = Pipe Roughnessk L= Constant for a particular fittingz = Elevation above datum (m)L=¿ Length of pipe (m)(Baker, 2013) (Wiggert et al., 2008)

Further to the statement of these equations, they can be used to derive further equations which apply to specific circumstances.

2.1.1 Pipe Bends, Orifice Plate, Momentum Change and Volumetric Flow Rate Calculations

The equations derived follow:

ΔP=ρ( 64 LV2

2dRe+gz+

n K LV2

2) [11]

ΔP=ρV 2

2

2 [1−( d2d1 )4][12]

Q=C f AO√ 2 ΔPρ [13]

ℜ=dVv [14]

For an elaborate explanation and further calculations see Appendix A.

2.2 Relative RoughnessFor the theoretical pressure drops in turbulent flow roughness (ε ) depends on the material used. However as it

was assumed that the pipes used were smooth, relative roughness (εd

¿ was found as 0.000005 from the Moody

diagram. (University of Birmingham, 2013)

3. MethodsThe following figure outlines the setup of the experimental equipment.

The arrangement consisted of the following:

Rotameter


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingement Piping including joints and bends Differential Pressure Manometer Valves Mass Balance Orifice Plate

Figure 1: Format of experimental equipment

Referring to Figure 1, measurements were taken for the following arrangements:

1. P1-P2. 7mm internal diameter pipe of 1m length. 10mm external diameter. Surface finished in black.

2. P5-P6. 2 x 90° elbow bends. 7mm internal diameter pipe of length of 0.44m. Height drop of 0.22m. 10mm external diameter. Surface finished in blue.

3. P6-P7. 7mm internal diameter pipe of 1m length. 10mm external diameter.

4. P7-P8. 5mm orifice plate in nominal 10mm fitting. Surface finished in black.

5. P8-P9. 6 x 90° elbow bends. 7mm internal diameter pipe of 1m length. Total height drop of 0.22m. Surface finished in black.

6. P9-P10. 4mm internal diameter pipe of 1m length. 6mm external diameter. Surface finished in black.

A rotameter with a precision of between ±0.5 Lmin−1and ±2.5Lmin−1 (depending on arrangement of equipment) was used to set the required flow rates. The fluid used was air, which acts as a Newtonian fluid, enabling friction to be accounted for and pressure drop calculated by using equations [7] - [10].


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementWhen measuring between points using the differential pressure manometer, the tube connected to the positive

input was connect to the upstream in the system. Likewise the tube connected to the negative input was connected to the downstream in the system. An example is shown on Figure 1 for P1-P2. This same procedure was continued for each arrangement. The differential pressure monitor was calibrated to a max reading of 2500 Pa. The instrument also had a “smooth” feature, which was enabled. This allowed the accuracy of our readings to increase as the flow was allowed to fully develop and the reading stabilised by the instrument before being recorded.

The manometer had a precision of ±0.05Pa for readings below 100 Pa, and a precision of ±0.5Pa for readings above 100 Pa.

A mass balance with a precision of ±0.0005g was used to measure the mass of the jet impingement, which impacted on a flat plate.

The independent variables were the flow rate (Lmin−1) and the points between which pressure drops were measured. The dependent variables were the pressure drops (Pa) and the mass (g).

4. ResultsThe following tables and graphs include various parameters calculated by theory, and the measured pressure

drops. For a full set of tables, including calculated values of Q(m¿¿3 s−1)¿ and the measured values of m(g) from which experimental momentum change was calculated, see Appendix C.

4.1 P1-P2Table 1: Pressure Drop across P1-P2

V (ms-1)Q (Lmin-1) Re f Measured Pressure Drop (Pa)

Theoretical Pressure Drop (Pa)Experimental Momentum Change (gms-2)

Theoretical Momentum Change (gms-2)

Laminar

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.87 2.00 404.20 0.16 11.90 10.22 0.03 0.031.73 4.00 808.41 0.08 23.90 20.43 0.23 0.142.60 6.00 1212.61 0.05 38.40 30.65 0.34 0.313.46 8.00 1616.81 0.04 56.50 40.87 0.56 0.564.33 10.00 2021.02 0.03 74.40 51.08 0.87 0.87

Turbulen

t 8.66 20.00 4042.03 0.04 282.00 261.31 4.04 3.4812.99 30.00 6063.05 0.04 608.00 519.98 10.63 7.8217.32 40.00 8084.06 0.03 1021.00 851.12 21.33 13.9121.65 50.00 10105.08 0.03 1595.00 1250.35 40.64 21.7325.98 60.00 12126.09 0.03 1895.00 1714.58 53.71 31.2930.32 70.00 14147.11 0.03 2411.00 2241.48 80.93 42.59



0 2 4 6 80

10

20

30

40

50

60

P1-P2 LaminarMeasured and Theoretical P ressure dr op (Pa) against

Volumetr ic Flow Rate (Lmin-1)

Measured Pressure Drop (Pa) Theoretical Pressure Drop (Pa)

Volumetric Flow Rate (Lmin-1)

Pres

sure

Dro

p (P

a)


20 30 40 50 60 700

500

1000

1500

2000

2500

3000

P 1-P2 TurbulentMeasured and Theoretical P ressure drop (P a) against

Volumet ric Flow Rate (Lmin-1)



Pres

sure

Dro

p (P

a)


0 2 4 6 8 100.000.100.200.300.400.500.600.700.800.901.00

P 1-P2 LaminarExperiment al and Theoretical Rate o f Change in Mo -

mentum (gms-2) against Volumet ric Flow Rate (Lmin-1)

Measured Momentum Change Theoretical Momentum Change


chan

ge in

mom

entu

m (g

ms-

2)


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementFigure 4: P1-P2 Laminar- Measured and Theoretical Momentum Change (gms-2) against Volumetric Flow Rate

(Lmin-1)

20 30 40 50 60 700.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

P1-P 2 TurbulentExperiment al and Theoretical Rate o f Change in Mo -




chan

ge in

mom

entu

m (g

ms-

2)



V (ms-1)Q (Lmin-1) Re f Mass (g)

Measured Pressure Drop (Pa)Theoretical Pressure Drop (Pa)

Experimental Momentum Change (gms-2)


Laminar

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.87 2.00 404.20 0.16 0.00 6.50 3.69 0.04 0.03

1.73 4.00 808.41 0.08 0.02 15.40 13.55 0.16 0.14

2.60 6.00 1212.61 0.05 0.04 46.50 26.98 0.34 0.31

3.46 8.00 1616.81 0.04 0.06 75.60 44.00 0.57 0.56

4.33 10.00 2021.02 0.03 0.09 109.50 64.59 0.87 0.87

Turbulen

t 8.66 20.00 4042.03 0.04 0.43 344.00 221.21 4.24 3.4812.99 30.00 6063.05 0.04 1.10 722.00 467.27 10.82 7.8217.32 40.00 8084.06 0.03 2.26 1322.00 802.75 22.21 13.9121.65 50.00 10105.08 0.03 3.81 1976.00 1227.66 37.38 21.73



0.00 2.00 4.00 6.00 8.00 10.000.00

20.00

40.00

60.00

80.00

100.00

120.00

P5-P 6 LaminarMeasured and Theoretical P ressure drop (P a) against




Pres

sure

Dro

p (P

a)


20.00 30.00 40.00 50.000.00

500.00

1000.00

1500.00

2000.00

2500.00





Pres

sure

Dro

p (P

a)




0.00 2.00 4.00 6.00 8.00 10.000.000.100.200.300.400.500.600.700.800.901.00

P5-P 6 LaminarExperimental and Theoretical Rat e of Change in Mo -

ment um (gms-2) against Volumetr ic Flow Rat e (Lmin-1)



chan

ge in

mom

entu

m (g

ms-

2)


20.00 30.00 40.00 50.000.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00





chan

ge in

mom

entu

m (g

ms-

2)





Experimental Momentum Change (gms-2)Theoretical Momentum Change (gms-2)

Lamina 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.87 2.00 404.20 0.16 0.00 9.30 10.22 0.04 0.01


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementr

1.73 4.00 808.41 0.08 0.02 19.00 20.43 0.17 0.05

2.60 6.00 1212.61 0.05 0.03 31.10 30.65 0.32 0.10

3.46 8.00 1616.81 0.04 0.06 45.50 40.87 0.56 0.18

4.33 10.00 2021.02 0.03 0.09 62.20 51.08 0.90 0.28

Turbulen

t

8.66 20.00 4042.03 0.04 0.38 221.00 261.31 3.69 1.1412.99 30.00 6063.05 0.04 1.14 504.00 519.98 11.21 2.5517.32 40.00 8084.06 0.03 2.25 853.00 851.12 22.07 4.5421.65 50.00 10105.08 0.03 4.30 1345.00 1250.35 42.18 7.09

25.98 60.00 12126.09 0.03 5.25 1533.00 1714.58 51.50 10.22

30.32 70.00 14147.11 0.03 8.06 1995.00 2241.48 79.07 13.91

34.65 80.00 16168.12 0.03 12.70 2579.00 2829.16 124.59 18.16

0.00 2.00 4.00 6.00 8.00 10.000.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00





Pres

sure

Dro

p (P

a)




20.00 30.00 40.00 50.00 60.00 70.00 80.000.00

500.00

1000.00

1500.00

2000.00

2500.00

3000.00





Pres

sure

Dro

p (P

a)


0.00 2.00 4.00 6.00 8.00 10.000.000.100.200.300.400.500.600.700.800.901.00





chan

ge in

mom

entu

m (g

ms-

2)




20.00 30.00 40.00 50.00 60.00 70.00 80.000.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

P6-P7 TurbulentExperimental and Theoretical Rate of Change in Mo -

ment um (gms-2) against Volumet ric Flow Rat e (Lmin-1)



chan

ge in

mom

entu

m (g

ms-

2)



V (ms-1)Q (Lmin-1) Re Mass

(g)

Measured Pressure Drop (Pa)

Theoretical Pressure Drop

(Pa)

Experimental Momentum Change (gms-2)Theoretical Momentum Change (gms-2)

Lam

inar

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.27 1.50 594.18 0.00 1.30 0.72 0.03 0.08

2.55 3.00 1188.36 0.01 4.10 2.89 0.08 0.30

3.82 4.50 1782.54 0.02 7.20 6.50 0.17 0.68

5.09 6.00 2376.71 0.03 13.20 11.55 0.31 1.20

5.94 7.00 2772.83 0.04 17.60 15.72 0.43 1.64

Turb

ulen

t

11.88 14.00 5545.67 0.16 78.40 62.89 1.55 6.54

20.37 24.00 9506.86 0.70 361.00 184.82 6.82 19.23

28.86 34.00 13468.04 1.40 734.00 370.92 13.73 38.60

37.35 44.00 17429.23 2.73 1304.00 621.19 26.78 64.64

45.84 54.00 21390.42 4.70 1970.00 935.64 46.11 97.36

54.32 64.00 25351.61 7.15 2591.00 1314.26 70.14 136.76



0.00 1.50 3.00 4.50 6.00 7.000.002.004.006.008.00

10.0012.0014.0016.0018.0020.00





Pres

sure

Dro

p (P

a)


14.00 24.00 34.00 44.00 54.00 64.000.00

500.00

1000.00

1500.00

2000.00

2500.00

3000.00

P7-P8 TurbulentMeasured and Theoretical Pressure drop (Pa)

against Volumetric Flow Rate (Lmin-1)



Pres

sure

Dro

p (P

a)


0.00 1.50 3.00 4.50 6.00 7.000.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90





chan

ge in

mom

entu

m (g

ms-

2)


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementFigure 16: P7-P8 Laminar- Measured and Theoretical Momentum Change (gms-2) against Volumetric Flow Rate

(Lmin-1)

14.00 24.00 34.00 44.00 54.00 64.000.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00





chan

ge in

mom

entu

m (g

ms-

2)



V (ms-1)Q (Lmin-1) Re f Mass (g) Measured Pressure Drop (Pa)

Theoretical Pressure Drop (Pa)Experimental Momentum Change (gms-2)


Laminar

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.87 2.00 404.20 0.16 0.01 18.20 12.98 0.06 0.03

1.73 4.00 808.41 0.08 0.02 51.80 39.30 0.16 0.14

2.60 6.00 1212.61 0.05 0.03 100.10 76.34 0.33 0.31

3.46 8.00 1616.81 0.04 0.06 174.50 124.12 0.62 0.56

4.33 10.00 2021.02 0.03 0.10 256.00 182.63 0.96 0.87

Turbulen 8.66 20.00 4042.03 0.04 0.38 795.00 636.15 3.69 3.48

12.99 30.00 6063.05 0.04 1.14 1670.00 1357.95 11.21 7.82



t 15.16 35.00 7073.55 0.03 2.25 2090.00 1819.47 22.07 10.65

0.00 2.00 4.00 6.00 8.00 10.000.00

50.00

100.00

150.00

200.00

250.00

300.00





Pres

sure

Dro

p (P

a)


20.00 30.00 35.000.00

500.00

1000.00

1500.00

2000.00

2500.00





Pres

sure

Dro

p (P

a)




0.00 2.00 4.00 6.00 8.00 10.000.00

0.20

0.40

0.60

0.80

1.00

1.20





chan

ge in

mom

entu

m (g

ms-

2)


20.00 30.00 35.000.00

5.00

10.00

15.00

20.00

25.00





chan

ge in

mom

entu

m (g

ms-

2)





Experimental Momentum Change (gms-2)

Theoretical Momentum Change (gms-2)0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0016 | P a g e

Mustafa Iqbal 1323293

FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementLam

inar1.99 1.50 530.52 0.12 0.00 70.50 71.86 0.03 0.183.98 3.00 1061.03 0.06 0.01 153.00 143.73 0.10 0.735.97 4.50 1591.55 0.04 0.02 250.00 215.59 0.23 1.657.96 6.00 2122.07 0.03 0.03 364.00 287.46 0.33 2.93

Turbulen

t

15.92 12.00 4244.13 0.04 0.11 1097.00 1520.71 1.11 11.7417.24 13.00 4597.81 0.04 0.13 1275.00 1741.21 1.28 13.7818.57 14.00 4951.49 0.04 0.17 1479.00 1974.30 1.66 15.9819.89 15.00 5305.16 0.04 0.19 1673.00 2219.80 1.83 18.3421.22 16.00 5658.84 0.04 0.22 1892.00 2477.51 2.17 20.8722.55 17.00 6012.52 0.04 0.26 2117.00 2747.25 2.53 23.56

0.00 1.50 3.00 4.50 6.000.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

P9-P10 LaminarMeasured and Theoretical P ressure drop (P a) against




Pres

sure

Dro

p (P

a)




12.00 13.00 14.00 15.00 16.00 17.000.00

500.00

1000.00

1500.00

2000.00

2500.00

3000.00

P9-P 10 TurbulentMeasured and Theoretical P ressure drop (P a) against




Pres

sure

Dro

p (P

a)


0.00 1.50 3.00 4.50 6.000.00

0.20

0.40

0.60

0.80

1.00

1.20

P 9-P10 LaminarExper iment al and Theoretical Rat e of Change in Mo -

mentum (gms-2) against Volumetr ic Flow Rat e (Lmin-1)



chan

ge in

mom

entu

m (g

ms-

2)




12.00 13.00 14.00 15.00 16.00 17.000.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

P9-P10 TurbulentExper iment al and Theoretical Rat e of Change in Mo -

mentum (gms-2) against Volumetr ic Flow Rat e (Lmin-1)



chan

ge in

mom

entu

m (g

ms-

2)


4.7 Jet ImpingementTable 7: Jet Impingement on a flat plate

Height of jet outlet above plate Q (Lmin-1) Experimental Momentum Change (gms-2)Theoretical Momentum Change (gms-2)5mm 20 3.48 3.5550 21.73 35.7170mm 20 3.48 4.1750 21.73 34.34

20 500

5

10

15

20

25

30

35

40

Jet Impingement on a flat plat e from 5mm Exper imental and Theoretical Rate of Change in Momentum (gms-2)

Volumet ric Flow Rat e (Lmin-1)



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Jet Impingement on a flat plat e from 70mm Experimental and Theo retical Rat e of Chan ge in Moment um (gms-2)




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4.8 Calibration of the Orifice plateRearranging equation [13]:

C f=Q

AO√ 2 ΔPρair

By inputting experimental values of Q and ΔP and using the specifications of AO and ρair , C f can be calculated. See Appendix B. The calculated value of C f for each flow rate was average to obtain:

C f=0.855(3 sf )

Using this value it is possible to substitute values into equation [13] to, for example; determine the pressure drop for a given flow rate.

5. Analysis of Results and DiscussionOverall, assumptions were made in both the theoretical and practical prat of the experiment. These were

cause of inaccuracies and errors.

From the results, it is clear that both the measurements taken and theory used coincided with some degree of accuracy. Figures 2-14 plot this relationship visually. However in general it appears that as the flow rate increased, the measured pressure drop became greater than the theoretical pressure drop, reasons for this follow. A greater pressure drop (due to bends and height drops) also constituted a decrease in the expected quantity of mass compared to other readings of the same flow rates.

The assumption of the pipes being smooth was incorrect, as external work was done. Therefore the relative roughness value used was too small. This also falsifies the use of Bernoulli’s equation.

As flow rate increases in situations such as turbulent flow, there is a larger deviance in measured pressure drop to theoretical pressure drop. This relationship applied to all the readings. Therefore the predicted laminar


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementvalues seemed to be more accurate than the predicted turbulent values, this is because turbulent flow introduces more complex features to the theory combined with larger parameters increasing the necessity for accuracy and precision.

The experiment was executed in a climate controlled environment of 20 ͦC, however the temperatures of said ambient environment and the internal pipes were not measured. Therefore the assumed temperature was not verified and any temperature variances in the experimental equipment were not tested. The value of temperature affects the parameters used in the experiment for the density of air ( ρ), kinematic viscosity (v) and absolute viscosity (μ). It is clear from the majority of the equations used these parameters are included, consequently affecting the calculated pressure drops. Therefore this is a source of error in the experiment. In order to avoid this the temperatures of the environment and pipes would need to be measured, and their respective variables used in the theoretical calculations.

Continuing on the idea of temperature variance; the internals of the pipes would be subject to an increased temperature due to the frictional forces between the fluid and internal pipe surfaces generating heat. Therefore at higher flow rates with more friction, the varying parameters such as temperature and density would be cause to a growing deviance between the measured and theoretical values of pressure drop.

The rotameter used was subject to human errors such as those due to parallax. It has already been stated that the precision of the rotameter varied as great as ±5.5Lmin−1 at some points in the experiment. However further to this, at higher flow rates the bearings of which the measurements of flow rate were taken fluctuated greatly, as much as ±2Lmin−1. This further adds to the deviance between theoretical and measured values of pressure drop at higher flow rates. Referring to equations [3], [7] and [10]; it is clear that Q affects the value of V , which is then squared to calculate pressure drop. Therefore it is shown that ΔP∝Q2, quantifying the effect of an inaccurate value of flow rate, Q.

During the experiment, it was discovered the differential pressure manometer’s readings were offset by an approximate +5 Pa. This affected the accuracy of the laminar readings as they were of a magnitude 101−102Pa, however past this point and into the turbulent regime the magnitude of measured pressure drops (103 Pa) offset this inaccuracy. This error was clarified by disconnecting the manometer tubes and holding the positive and negative ends adjacent each other in atmospheric pressure (not connected to the apparatus), in this position there should have been no pressure difference but values between 4 Pa and 6 Pa were read.To resolve this issue a different differential pressure manometer with superior calibration could be used.

There was an uncertainty of the internal diameters of the pipes used, this is due to the fact they weren’t measured, only stated in the brief of the laboratory. Therefore their accuracy is up to the discrepancy of those who measured the pipes and provided them for the purpose of the experiment. Evidently this uncertainty could be quantified by measuring the internal diameters of the pipes. Nevertheless from equations [1], [3], [4], [9] and [10] it

is evident that ΔP∝ 1d , quantifying the error in theoretical pressure drop caused by this uncertainty. This

uncertainty can be further applied to the length of the pipes, which shows that ΔP∝L.

For specifications of the pipes in P1-P2 and P6-P7 were identical bar the dye of the pipes, this is shown in their identical theoretical pressure drop values. Evidently the different dyes affected the measured pressure drops in turbulent regimes (where ε is present), in which for the black pipe, P1-P2, the measured pressure drop was on average greater than the blue pipe, P6-P7. As mentioned before, the different dyes resulted in different finishes and

different surface frictions; succeeding in different relative roughness (εd

¿ values for each. Clearly the black pipe had

a greater relative roughness as it presented greater pressure drops for the same flow rate compared to the blue


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementpipe. This can be verified by back calculating the actual friction factor for each using the measured pressure drop values and equations [9] and [10].

Where 90° elbow bends and height drops were included were P5-P6 and P8-P9. Comparing both to readings without bends or height drops it is shown firstly that bends result in a greater pressure drop and that secondly several bends result in an even larger pressure drop. Therefore smaller flow rates resulted in much greater pressure drops, which is reflected in the small range of flow rates used for P8-P9 in turbulent flow. For both sets of data the measured pressure drop becomes greater than the theoretical pressure drop as the flow rate increases. Further to the sources of error mentioned before, there is an uncertainty in the height drops, as they were measured with a ruler of precision ±0.005m. These values effect the theoretical pressure drop constituted in equation [5]. There may also have been other energy losses not accounted for, or the fitting constant K L used may be incorrect.

Regarding the measurements of pressure drop through the orifice plate in P7-P8, the area used was that of the orifice’s opening, however realistically the correct area to use lies at the vena contracta. Therefore the theoretical values for pressure drop both laminar and turbulent flow show a deviance to the measured values of pressure drop. Due to this, the calculated flow coefficient may not be accurate.

Comparing the experimental and theoretical momentum changes, the theoretical model worked well for laminar regimes. However in turbulent regimes the experimental momentum change was greater than the theoretical momentum change, except for P7-P8 where for both results the theoretical momentum change was greater in both laminar and turbulent regimes. The theoretical data does not match the experimental data for both pressure drop and momentum change for a turbulent regime in P9-P10; the theoretical values are always greater, however there is some correlation between them. An anomaly may have occurred here or the calculations for the theoretical values may be incorrect. The error in the measurements of momentum change in the orifice may have been caused by the incorrect area used, as mentioned.

Continuing with the momentum changes, the theoretical values of momentum change deviated more as the flow rate increased. Increasing the height from which the jet discharged decreased the momentum change as expected. I.e. less air was impinging on the plate. Effectively a greater height resulted in a smaller mass reading, this could be due to the additional volume of atmosphere (air) that the jet of air had to travel through to get to the plate. Therefore the rate at which the jet impacted on the plate would be lower, as more resistance was faced resulting in less velocity. It is also possible that some of the flow deviated away from the plate affecting the reading, however this is unlikely considering the fact that the face of the plate was several times larger than the small diameter through which the jet was discharged at a high velocity. The mass balances were very temperamental, even standing near them would cause the reading to fluctuate. When the readings were taken the experiment waited for the readings to stabilise, this often took a while and even given time the readings wouldn’t stabilise, so in the interest of time an average reading was guessed. This was a major source of error in the mass readings, and so affected the accuracy of the experimental momentum change values.

ConclusionThe pressure drops across various pipes and fittings (including an orifice plate) were measured and

compared to theoretical predictions to assess their validity.

These measurements allow the importance of pressure drops to be quantified. In a production plant the pipe systems would be much more complex, with several height changes and movement between horizontal and vertical planes. Combined with the calculated parameters depending on the fluid used, sizes of equipment and scale; material specifications such as the material used and their dimensions (such as thickness) can be suggested to contain the hazardous environments in the pipe systems.


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementIt was established from the data that pressure drops do occur in pipes and fittings. Even for a simple system

as was used in the experiment, the differences between pressure drops in different setups was immensely significant. It was concluded that due to assumptions made in the theory, such as the incompressibility of air and incorrect relative roughness values; that the theoretical values when compared to their respective measured values were of a lesser magnitude. This statement excludes P7-P8, where the opposite is true.

The orifice was calibrated with a flow coefficient, Cf of 0.855(3 sf ).

In conclusion, the theoretical models work well for laminar flows. However in turbulent flows where the parameters are greater the deviance between the experimental and theoretical values increases. Therefore the accuracy of measurements in the experiment needed to be improved and the theoretical models used needed to be refined, an example would be to include the compressibility of air, which attested to be a major source of error in turbulent regimes.



AppendixAppendix A – Pipe bends, Orifice Plate, Momentum Change and Flow Rate Calculations

1. Pipe Bends

Part of the experiment constituted a pipe undertaking 90° elbow bends in a vertical plane, this caused an energy loss due to the formation of eddies at the pipe bends. Between the bends there are vertical sections which create a total height loss, z. In addition to this there was an energy loss due to the friction as the fluid moves through a pipe Δ L of diameter d , [10] accounts for this. These energy losses amount to a pressure drop. Therefore taking n as the number of 90° bends:

ΔP=ρ( 64 LV2

2dRe+gz+

n K LV2

2) [11]

For a 90° elbow bend, k L was found to be 1.98. (StatsoSphere, 2013)

2. Orifice Plate

An orifice plate has a different internal diameter between its inlet and outlet (similar to a venturimeter), therefore this needs to be accounted for by substituting the equation of flow rate [3] into Bernoulli’s equation [6]. This was then rearranged to give:

ΔP=ρV 2

2

2 [1−( d2d1 )4][12]

As stated in the aims of the experiment, the orifice plate needed to be calibrated. This could be achieved by using the equation:

Q=C f AO√ 2 ΔPρ [13]

Where:

C f=Flow Coefficient

AO=Areaof orifice plate(m2)

ρ=ρair (kgm3)

C f is used as this equation applies to turbulent regimes, so in order to decrease the value of Q to compensate for frictional forces C f<1. (K.N.Toosi University of Technology, N.D.)

3. Momentum Change

When calculating momentum change it is known that:

F=Δmv [14]


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementWhere:

F=Force(N )

Δmv=Change∈momentum (kgm s−2)

Dimensionally consistent as N=kgm s−2.

Therefore:

Experimental change∈momentum=mg

Theoretical change∈momentum=ρAV 2

4. Voumetric Flow Rate Calculations

In order to determine sensible ranges and intervals of flow rate to use for both laminar and turbulent flow respectively expected flow rates were calculated using equations [1] – [4].

By substituting [2] into [1] the following equation is obtained:

ℜ=dVv [14]

Using 0<ℜ<2000 for laminar flow and ℜ>4000 for turbulent flow the upper and lower bounds of flow rate can be predicted.

The calculations and resulting values follow. The internal dimensions of the pipes are given in the Methods section. As the precision of the rotameter was ±0.5 Lmin−1 values were rounded to the nearest integers. This also permitted easier calibration of the rotameter.

However it must be noted that there were two parts to the rotameter. One section controlled flow from between 0 Lmi n−1 and 10 Lmin−1. The other was able to output a flow between 0 Lmin−1 and 100 Lmin−1. In parts of the experiment such as where laminar flow was considered, only 0 Lmin−1 and 10 Lmi n−1 was used, so the precision at this part of the experiment was ±0.5 Lmin−1. Whereas when higher flow rates were used, the precision would be the combination of both sections of the rotameter; i.e. ±5.5Lmin−1 (±0.5 Lmin−1+±5Lmin−1 ). This would greatly increase error. This error was increased at higher flow rates due the unstable bearings from which measurements were taken.

3.1 Laminar Flow

Therefore considering laminar flow in a pipe of 7mm internal diameter:

At lower bound:

ℜ=0V=0ms−1

Q=0m3 s−1

At upper bound:

ℜ=2000


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementV=4.2857ms−1

Q=1.65×10−4m3 s−1

Q=10 Lmi n−1

And a 4mm internal diameter:

ℜ=2000V=7.5ms−1

Q=6Lmin−1


3.2 Turbulent Flow

Therefore considering turbulent flow in a pipe of 7mm internal diameter:

Lower bound:

ℜ=4000

V=2.3×10−4m3 s−1

Q=20Lmi n−1

And 4mm internal diameter:

ℜ=4000

V=15ms−1

Q=12 Lmin−1

The upper bound for turbulent flow rates is obtained experimentally by recording the flow rate as close to 2500 Pa as possible.


Appendix B - Orifice Plate CalibrationTable 8: Table of Orifice Plate calibration calculations

Cf Q (Lmin-1) Q (m3s-1) Measured Pressure Drop (Pa) Area (m2) Density (kgm-3)1.041370197 14.00 0.000233333 78.40 1.9635E-05 1.20410.831941484 24.00 0.0004 361.00 1.9635E-05 1.20410.826544094 34.00 0.000566667 734.00 1.9635E-05 1.20410.802507354 44.00 0.000733333 1304.00 1.9635E- 1.2041


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingement 050.801301188 54.00 0.0009 1970.00 1.9635E-05 1.20410.828097374 64.00 0.001066667 2591.00 1.9635E-05 1.2041

From these values an average of 0.855(3 sf ) was determine for the value of C f .


FTH-FF2 Frictional pressure loss through pipes and fittings, and jet impingementAppendix C – Table of dataTable 9: Table of data


P1-P2 Length: 1m 7mm diameter

V Q (L/min) Q (m3/s) Re f Mass (g) Measured Pressure Drop (Pa) Theoretical Pressure Drop (Pa) Measured Momentum Change Theoretical Momentum Change

Laminar 0 0 0 0 0 0 0 0 0.00 0.000.86614935 2 3.33333E-05 404.2030301 0.158336 0.003 11.9 10.21646138 0.03 0.03

1.7322987 4 6.66667E-05 808.4060601 0.079168 0.023 23.9 20.43292276 0.23 0.142.59844805 6 0.0001 1212.60909 0.052779 0.035 38.4 30.64938414 0.34 0.31

3.464597401 8 0.000133333 1616.81212 0.039584 0.057 56.5 40.86584552 0.56 0.564.330746751 10 0.000166667 2021.01515 0.031667 0.089 74.4 51.0823069 0.87 0.87

Turbulent 8.661493502 20 0.000333333 4042.030301 0.040498 0.412 282 261.3112229 4.04 3.4812.99224025 30 0.0005 6063.045451 0.035817 1.084 608 519.9793275 10.63 7.82

17.322987 40 0.000666667 8084.060601 0.032977 2.174 1021 851.115762 21.33 13.9121.65373375 50 0.000833333 10105.07575 0.031005 4.143 1595 1250.346679 40.64 21.73

25.9844805 60 0.001 12126.0909 0.029525 5.475 1895 1714.584086 53.71 31.2930.31522726 70 0.001166667 14147.10605 0.028358 8.25 2411 2241.479257 80.93 42.59

P5-P6 Length: 0.44m 7mm diameter


Laminar 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.87 2.00 0.00 404.20 0.16 0.00 6.50 3.69 0.04 0.031.73 4.00 0.00 808.41 0.08 0.02 15.40 13.55 0.16 0.142.60 6.00 0.00 1212.61 0.05 0.04 46.50 26.98 0.34 0.313.46 8.00 0.00 1616.81 0.04 0.06 75.60 44.00 0.57 0.564.33 10.00 0.00 2021.02 0.03 0.09 109.50 64.59 0.87 0.87

Turbulent 8.66 20.00 0.00 4042.03 0.04 0.43 344.00 221.21 4.24 3.4812.99 30.00 0.00 6063.05 0.04 1.10 722.00 467.27 10.82 7.8217.32 40.00 0.00 8084.06 0.03 2.26 1322.00 802.75 22.21 13.9121.65 50.00 0.00 10105.08 0.03 3.81 1976.00 1227.66 37.38 21.73



Laminar 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.87 2.00 0.00 404.20 0.16 0.00 9.30 10.22 0.04 0.031.73 4.00 0.00 808.41 0.08 0.02 19.00 20.43 0.17 0.142.60 6.00 0.00 1212.61 0.05 0.03 31.10 30.65 0.32 0.313.46 8.00 0.00 1616.81 0.04 0.06 45.50 40.87 0.56 0.564.33 10.00 0.00 2021.02 0.03 0.09 62.20 51.08 0.90 0.87

Turbulent 8.66 20.00 0.00 4042.03 0.04 0.38 221.00 261.31 3.69 3.4812.99 30.00 0.00 6063.05 0.04 1.14 504.00 519.98 11.21 7.8217.32 40.00 0.00 8084.06 0.03 2.25 853.00 851.12 22.07 13.9121.65 50.00 0.00 10105.08 0.03 4.30 1345.00 1250.35 42.18 21.7325.98 60.00 0.00 12126.09 0.03 5.25 1533.00 1714.58 51.50 31.2930.32 70.00 0.00 14147.11 0.03 8.06 1995.00 2241.48 79.07 42.5934.65 80.00 0.00 16168.12 0.03 12.70 2579.00 2829.16 124.59 55.62

P7-P8 Orifice Plate 5mm diameter

V Q (L/min) Q (m3/s) Re f Mass (g) Measured Pressure Drop (Pa) Theoretical Pressure Drop (Pa) Measured Momentum Change Theoretical Momentum ChangeLaminar

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001.27 1.50 0.00 594.18 0.00 1.30 0.72 0.03 0.042.55 3.00 0.00 1188.36 0.01 4.10 2.89 0.08 0.153.82 4.50 0.00 1782.54 0.02 7.20 6.50 0.17 0.345.09 6.00 0.00 2376.71 0.03 13.20 11.55 0.31 0.615.94 7.00 0.00 2772.83 0.04 17.60 15.72 0.43 0.83

Turbulent 11.88 14.00 0.00 5545.67 0.16 78.40 62.89 1.55 3.3420.37 24.00 0.00 9506.86 0.70 361.00 184.82 6.82 9.8128.86 34.00 0.00 13468.04 1.40 734.00 370.92 13.73 19.6937.35 44.00 0.00 17429.23 2.73 1304.00 621.19 26.78 32.9845.84 54.00 0.00 21390.42 4.70 1970.00 935.64 46.11 49.6754.32 64.00 0.001066667 25351.61 7.15 2591.00 1314.26 70.14 69.77

P8-P9 Length: 1m


Laminar 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.87 2.00 0.00 404.20 0.16 0.01 18.20 12.98 0.06 0.031.73 4.00 0.00 808.41 0.08 0.02 51.80 39.30 0.16 0.142.60 6.00 0.00 1212.61 0.05 0.03 100.10 76.34 0.33 0.313.46 8.00 0.00 1616.81 0.04 0.06 174.50 124.12 0.62 0.564.33 10.00 0.00 2021.02 0.03 0.10 256.00 182.63 0.96 0.87

Turbulent 8.66 20.00 0.00 4042.03 0.04 0.38 795.00 636.15 3.69 3.4812.99 30.00 0.00 6063.05 0.04 1.14 1670.00 1357.95 11.21 7.8215.16 35.00 0.00 7073.55 0.03 2.25 2090.00 1819.47 22.07 10.65



Laminar 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001.99 1.50 0.00 530.52 0.12 0.00 70.50 71.86 0.03 0.063.98 3.00 0.00 1061.03 0.06 0.01 153.00 143.73 0.10 0.245.97 4.50 0.00 1591.55 0.04 0.02 250.00 215.59 0.23 0.547.96 6.00 0.00 2122.07 0.03 0.03 364.00 287.46 0.33 0.96

Turbulent 15.92 12.00 0.00 4244.13 0.04 0.11 1097.00 1520.71 1.11 3.8317.24 13.00 0.00 4597.81 0.04 0.13 1275.00 1741.21 1.28 4.5018.57 14.00 0.00 4951.49 0.04 0.17 1479.00 1974.30 1.66 5.2219.89 15.00 0.00 5305.16 0.04 0.19 1673.00 2219.80 1.83 5.9921.22 16.00 0.00 5658.84 0.04 0.22 1892.00 2477.51 2.17 6.8122.55 17.00 0.000283333 6012.52 0.04 0.26 2117.00 2747.25 2.53 7.69

Jet Impingement

5mm above V Q (L/min) Q (m3/s) A Mass (g) Measured Momentum Change Theoretical Momentum Change8.661493502 20 0.000333333 3.84845E-05 0.362 3.55122 3.47643477521.65373375 50 0.000833333 3.84845E-05 3.64 35.7084 21.72771734

70mm above 8.661493502 20 0.000333333 3.84845E-05 0.425 4.16925 3.47643477521.65373375 50 0.000833333 3.84845E-05 3.5 34.335 21.72771734


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Baker, C. (2013). Fluid flow, thermodynamics and heat transfer lecture notes. University of Birmingham.

Engineered Software Inc. (2014). What is the relationship between the Discharge Coefficient (Cd) and the Flow Coefficient (Cv)? Available: http://kb.eng-software.com/questions/448/What+is+the+relationship+between+the+Discharge+Coefficient+%28Cd%29+and+the+Flow+Coefficient+%28Cv%29%3F+. Last accessed 3rd January 2014.K.N.Toosi University of Technology. (N.D.). Orifice Plate. Available: http://saba.kntu.ac.ir/eecd/ecourses/instrumentation/projects/reports/Flowmeter/orifice.htm. Last accessed 4th January 2014.

Newton, I. (1726). Philosophiæ Naturalis Principia Mathematica. Harvard. Cambridge University Press.

Potter, M; Wiggert, D.C. (2008). Schaum's Outline of Fluid Mechanics. US: McGraw-Hill. p212.

School of Chemical Engineering. (2013). FTH-FF2 Laboratory, 25th November 2013. University of Birmingham.

StasoSphere. (2013). Loss Of Head In Bends. Available: http://chestofbooks.com/home-improvement/construction/plumbing/Principle-Practice/Loss-Of-Head-In-Bends.html#.UrcXXfRdWSo. Last accessed 23rd December 2013.


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