FRICTIONAL LOSSES IN PIPES

Date:2nd June,2025
Group Members: Berchie Bright Amoah, Amoatey Joel Kwao, Okai Mark Nii Kotey, Adjah Richmond

Elikem

REPORT INFO ABSTRACT

Keywords: In industrial
Department of Chemical Engineering, Kwamefluid transport
Nkrumah systems,offriction
University Sci. andlosses
Tech.represent an
Major loss important source of energy dissipation. These losses show up as
Pressure loss pressure losses or drops along the entire length of the pipeline
Fanning friction and can influence the overall efficiency and operation costs
factor. drastically. The main aim of this experiment is to investigate the
Valves. effect of the flow regime, pipe diameter, and fittings on the
Fittings. pressure drop along the length of the pipe. Using a virtual
Density friction loss simulation application, the pressure losses across

Fluid velocity five different pipes were measures at different flowrates under
varying conditions such as in the presence of a valve or fittings
Flow regime.
or both. The experiment embedded both major and minor losses
Elbow
and employed the Fanning friction factor. Results demonstrated
Length of pipe
that pressure drop increases with the flowrate and that smaller
Pipe diameter
pipe diameters and additional fittings significantly increase
Minor losses frictional losses.

1. INTRODUCTION

In many industrial applications, pipelines are essential for transporting fluids such as water, gases and
most importantly, oil. However, a portion of the mechanical energy of the fluid is lost inevitably, due
to friction between the internal surface of the pipe and the moving fluid. This friction loss, causes a
pressure drop along the pipeline, which must be overcome by applying additional pressure at the inlet
if a specific outlet pressure is desired. This has direct consequences on the cost of operation, especially
on large-scale industries such as oil and gas, and chemical processing (Munson et al., 2013).

1
Fluid flow in pipes is continuously impacted by the resistance to flow offered by the roughness of pipe
at the walls based on the law of similarity. Smooth pipes offer little or negligible resistance to flow
while rougher surfaces offer increasing resistance depending on the degree of roughness. Such
resistance affects flow rate (Q) and velocity distribution of process fluid in the pipe. The resistance
increases for Q values in transition and turbulent regions. Studies elsewhere have shown that high
velocities produce high resistances to flow in pipes. Darcy Weisbach, Hazen-Williams, Moody and
Fanning showed that for any flow of fluid in a pipe exhibiting some form of roughness; head losses (hL)
due to friction were produced. Decisions could be made early about the size and type of roughness of
the pipe and appropriate Q of the fluid during design or plant operation based on the correlations
presented in this paper. The challenge with the delivery of fluids is either non delivery or insufficient
delivery to the desired destination. Oftentimes, it is either the insufficient pumping due to faulty pumps
or high friction losses in the delivery system.

Friction losses in pipes are classified into major losses and minor losses. Major losses are those that
occurs in straight pipelines due to several factors such as flow velocity, pipe diameter, fluid density and
pipe length. These losses are quantified using the Fanning friction factor – a dimensionless factor that
represents the resistance brought about by the inner walls of the pipes. Major losses can be computed
by:
𝐿 𝑣2
∆𝑃 = 4𝑓 ( ) ( ) 𝜌
𝐷 2

Minor losses arise from the presence of components that disrupt the flow pattern, such as valves,
fittings, elbows, expansions and contractions. These are modelled by replaced the length term in the
major loss equation with an equivalent length, 𝑳𝒆 , which represents the length of a straight pipe that
would cause the same amount of head loss as the valve or fitting. Minor losses are computed by:
𝐿𝑒 𝑣 2
∆𝑃 = 4𝑓 ( ) ( ) 𝜌
𝐷 2

The effect of both major and minor losses becomes very prominent as fluid velocity increases, pipe
diameter decreases or, more importantly in the oil industry, as pipe length increases. Also, flow
behaviour is affected strongly by the flow regime, characterized by the Reynolds number (Re).

2
The objective of this experiment is to determine the effect of flow regime, pipe diameter, and fittings
on the pressure drop across pipes. With the help of a virtual friction loss application, different pipes
were analysed under varying conditions. This experiment provides insight into energy costs associated
with pipeline are essential for improving the design and operation of fluid transport systems across
engineering fields such as petroleum, chemical, civil, and mechanical engineering.

3
2.0 METHODOLOGY
This experiment was conducted using a virtual friction loss software made to model friction
losses in pipe systems due to fluid friction. The app was launched. The two gate valves
connected to the reservoir were opened to allow fluid flow. The manometer was connected to
the sensors on pipe 1.The flow rate was set to 4cm3/s, and the ball valve at the end of the pipe
was opened, after this the corresponding head loss across the pipe was recorded. This was
repeated for flow rates of 8, 10,12 ,16 and 20 cm3/s. Next, the manometer was disconnected
and attached to the Pipe 2 sensors. The same set of flow rates used in pipe 1 were applied, and
the resulting head losses were measured and recorded. The procedure was then repeated for
Pipe 3, both the globe and ball valve on it was opened and the head loss readings across it
were taken starting with a flow rate of 5 cm3/s, and continuing with 10, 15, 20, and 25 cm3/s.
After this the manometer was connected to pipe 4 and the pressure drops across it were
recorded with the same flowrates as used in pipe 3. Finally, pressure drops across pipe 5 were
measured after opening its globe and ball valve, using the same set of flow rates as Pipe 3,
with the manometer attached accordingly.

All results were recorded for comparison and analysis to understand how changes in flow rate
and pipe characteristics influence frictional losses.

APPARATUS
1. Virtual Friction Loss app
2. Built-in simulation models for different pipe diameters and materials
(simulated within software)
3. 5(1m long pipes)
4. Manometer
5. Ball valves
6. Globe valves
7. Gate valve

4
3.0 TABLE OF RESULTS

Pipe 1

Experiment N◦ Reynold’s Number Pressure drop (Pa) Friction factor

1 848.8263632 509.2958179 0.959247

2 1697.652726 1018.591636 0.934266

3 2546.479089 1527.887454 0.925939

4 3395.305453 2037.183272 0.924274

5 4244.131816 2546.479089 0.919278

Pipe 2

Experiment N◦ Reynold’s Number Pressure drop (Pa) Friction factor

1 509.2958179 666.6118 1.284999

2 1018.591636 1733.191 0.835249

3 1527.887454 3733.026 0.799555

4 2037.183272 6266.151 0.754937

5 2546.479089 9599.211 0.740159

Pipe 3

Experiment N◦ Reynold’s Number Pressure drop (Pa) Friction factor

1 374.4822 533.2895 1.531396

2 748.9644 1066.579 0.765698

3 1123.447 1999.836 0.638082

4 1497.929 3333.059 0.598202

5 1872.411 5199.572 0.597244

Pipe 4

5
 Experiment N◦ Reynold’s Number Pressure drop (Pa) Friction factor

1 374.4822 266.6447 2.053081

2 748.9644 666.6118 1.283175

3 1123.447 933.2566 0.79842

4 1497.929 1466.546 0.705746

5 1872.411 2133.158 0.656986

Pipe 5

Experiment N◦ Reynold’s Number Pressure drop (Pa) Friction factor

1 374.4822 533.2895 1.266646

2 748.9644 1199.901 0.712489

3 1123.447 2533.125 0.668508

4 1497.929 4132.993 0.613532

5 1872.411 6266.151 0.595324

6
 Re against Fanning factor (Pipe 1)
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0.915 0.92 0.925 0.93 0.935 0.94 0.945 0.95 0.955 0.96 0.965

Re against Fanning factor (Pipe 2)

3000

2500

2000

1500

1000

500

0
0 0.2 0.4 0.6 0.8 1 1.2 1.4

Re against Fanning factor (Pipe 3)

2000
1800
1600
1400
1200
1000
800
600
400
200
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

7
 Re against Fanning factor (Pipe 4)
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0 0.5 1 1.5 2 2.5

Re against Fanning factor (Pipe 5)

2000
1800
1600
1400
1200
1000
800
600
400
200
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4

Re Pressure drop (Pipe 1)

180000
160000
140000
120000
100000
80000
60000
40000
20000
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500

8
 Re Pressure drop (Pipe 2)
12000

10000

8000

6000

4000

2000

0
0 500 1000 1500 2000 2500 3000

Pressure drop (Pipe 3)

Re
6000

5000

4000

3000

2000

1000

0
0 200 400 600 800 1000 1200 1400 1600 1800 2000

Re Pressure drop (Pipe 4)

2500

2000

1500

1000

500

0
0 200 400 600 800 1000 1200 1400 1600 1800 2000

9
 Pressure drop (Pipe 5)
Re
7000

6000

5000

4000

3000

2000

1000

0
0 200 400 600 800 1000 1200 1400 1600 1800 2000

4.0 DISCUSSION

The results generally show that pressure drop increases with flowrate, and smaller pipe
diameters and additional fittings lead to higher frictional losses. As flow rate increases, the
fluid moves faster. This results in greater frictional shear stress between the fluid and the pipe
wall. At higher flow rates, flow typically transitions from laminar to turbulent. Turbulence
introduces additional vortices and eddies, which consume energy and further raise resistance
to flow. This results in greater pressure drop per length of pipeline as observed in this
experiment for increasing the flowrate at the same conditions of pipelines.
For Pipe 1 and Pipe 2, flow rates were set in multiples of 4 while retaining the same flow
conditions. The two pipes differ in their diameters — Pipe 1 has a diameter of 6 mm, while
Pipe 2 has a larger diameter of 10 mm. This resulted in higher pressure drops in Pipe 1 due to
its narrower flow path at each step of the experiment or the same flowrate. In a narrow pipe, a
larger portion of liquid is close to the wall, where frictional interactions slow down its
movement. This forms a greater resistance to flow — pressure drops more — because
momentum is constantly disrupted by these collisions.

For pipe 3 and 4, flowrates were set to multiples of 5. Both pipes had the same diameter but
different components which contributed to minor losses. Pipe 3 had a globe valve while pipe 4
had a returned bend. From the experimental results, at the same conditions of flowrate, Pipe 3
had a higher pressure drop as compared to pipe 4. This indicates that globe valves contribute
to a higher minor loss than returned bends which is evident as the equivalent length of
component in pipe diameter was 300 and 75 respectively. Thus, a higher equivalent diameter
in the same conditions will result to a higher pressure drop predicted by the Darcy friction
equation. A globe valve forces fluid to make a dramatic change in direction — typically nearly
90º — and flows through a narrower seat or opening. This abrupt change in direction and flow
area creates turbulence and energy losses. The liquid must accelerate, then decelerate, causing
additional pressure drop due to flow separation and vortical formations. The flow also
frequently forms eddies and vortices within the valve body, further adding resistance. A return
10
bend (typically a 180º pipe bend) guides flow gradually and smoothly back in the opposite
direction. While there is some pressure drop due to changing direction, it’s less severe than in
a globe valve because the flow is more streamlined and less disrupted.

Pipe 5, had both a globe valve and returned bend. Comparing pipe 5 to 3 and 4 since they had
the same diameter and flowrate, it was observed that pipe 5 had the highest pressure drop at
the same flowrate condition. At flowrate of 10cm3/s, the pressure drops of pipe 3, 4 and 5
were 1066.579 Pa, 666.6118 Pa, and 1199.901 Pa respectively. A similar trend is observed in
all other flowrates.

The relationship between Reynolds number, flow regime, and pressure drop in each pipe was
also investigated. It was observed that at lower Reynolds numbers (laminar flow), pressure
drop increases gradually and nearly linearly. However, as Reynolds number increases and
flow transitions from the laminar to the turbulent regimen, pressure drop rises significantly in
each pipe.
For instance, in Pipe 1, a pressure drop of 6,399.47 Pa was recorded at a Reynolds number of
848.83 (laminar flow). When the flow rate was raised to 8 cm³/s, Reynolds number increased
to 1,697.65, and pressure drop jumped to 24,931.28 Pa — reflecting a rise of 18,532 Pa. As
flow further transitioned into turbulence at a flow rate of 12 cm³/s (with Reynolds number
2,546.48), pressure drop reached 55,595.43 Pa — an additional increase of over 30,000 Pa.
This illustrates that pressure drop under laminar flow is significantly less than under
turbulent flow.
The graphs show a marked increase in pressure drop as flow transitions from laminar to
turbulent. This trend was similar across all the pipes in the experiment, emphasizing the
strong influence of flow regimen on pressure drop.
For Reynold’s number against fanning factor, an inverse relationship is observed since
viscosity dominates much in laminar flow hence the fanning factor is higher at low flow rates.
This experiment shows that pressure drop is influenced by flow rate, flow regimen, pipe
diameter, and pipeline components. Higher flow rates, narrower pipes, and flow obstructions
all contribute to greater resistance and pressure drop, while a smooth flow path results in
lower pressure drops. The results highlight the importance of understanding these
relationships when designing pipeline systems, as this knowledge can aid in reducing energy
losses and optimizing flow delivery under various conditions.

11
5.0 SOURCES OF ERROR

1. Software bugs or glitches affecting data output

2. Limitations or simplifications in the simulation model
3. Incorrect data input by user may contribute to errors in output recorded.

6.0 PRECAUTIONS
1. Carefully enter all input values to prevent errors that could affect the results.
2. Double all parameters’ units and ensure they are in consistent units before calculations
to prevent errors.
3. Conduct each simulation at least four times and compare results to detect any
inconsistencies.
7.0 CONCLUSIONS
The experiment successfully investigated the impact of flow regime, pipe diameter, and
fittings on pressure drop in fluid transport systems. Results consistently demonstrated that
pressure drop increases with higher flow rates. Furthermore, smaller pipe diameters and the
inclusion of fittings significantly contributed to increased frictional losses. These findings
underscore the importance of considering these factors in the design and operation of pipelines
to minimize energy dissipation and associated costs.

8.0RECOMMENDATIONS

1. Carefully enter all input values to prevent errors that could affect the results.

12
 2. Double all parameters’ units and ensure they are in consistent units before calculations

to prevent errors.

3. Conduct each simulation at least four times and compare results to detect any

inconsistencies.

9.0 References

1.Fox, R.W., McDonald, A.T., & Pritchard, P.J. (2011). Introduction to Fluid Mechanics.
2. Cengel, Y.A., & Cimbala, J.M. (2014). Fluid Mechanics: Fundamentals and Applications.
3. Coulson, J.M., & Richardson, J.F. (1999). Chemical Engineering Volume 1: Fluid Flow,
Heat Transfer and Mass Transfer.
4.White, F.M. (2016). Fluid Mechanics. McGraw-Hill Education.
5.Munson, B.R., Okiishi, T.H., Huebsch, W.W., & Rothmayer, A.P. (2013). Fundamentals of
Fluid Mechanics. John Wiley & Sons.
6. Streeter, V.L., Wylie, E.B., & Bedford, K.W. (1998). Fluid Mechanics. McGraw-Hill.
7. Brater, E.F., King, H.W., Lindell, G.E., & Wei, C.Y. (1996). Handbook of Hydraulics.
McGraw-Hill.
8. Idelchik, I.E. (2006). Handbook of Hydraulic Resistance. Begell House.
9. Douglas, J.F., Gasiorek, J.M., Swaffield, J.A., & Jack, L. (2011). Fluid Mechanics. Pearson
Education.
10.0 Appendix

CALCULATIONS

For major losses

Q=vA , A=𝜋d2/4

V=Q/A

𝐿 𝑣2𝜌
∆P=4𝑓 (𝐷) 2

For minor losses

𝐿𝑒 𝑣 2 𝜌
∆P=4𝑓 ( 𝐷 ) 2

Making f the subject

13
 𝐷 1
𝑓 = ∆P( 𝐿 ) × 2𝑣2 𝜌

For pipe 1 (No minor loss)

At Q=4 cm3/s ,∆P=4.8 cmHg ,L=1m, D=6mm=6× 𝟏𝟎−𝟑 m

103
∆P1(Pa)=4.8 × (10 × 101.325 × 760) =6399.473684

(6×10−3 )2
A=𝜋 × =2.82743339×10-5
4

Q(m3/s)=4× 10−6

4×10−6
V=2.82743339×10−5 =0.141471

6×10−3 1
𝑓 = 6399.473684 × ( ) × 2(0.141471)2 ×1000 =0.959247
1

𝜌𝑣𝑑 1000×0.141471×6×10−3
Re1= = =848.826363156775
𝜇 0.001

At Q=8 cm3/s ,∆P=18.7 cmHg ,L=1m, D=6mm=6× 𝟏𝟎−𝟑 m

103
∆P2(Pa)=18.7 × (10 × 101.325 × 760) =24931.28
(6×10−3 )2
A=𝜋 × =2.82743339×10-5
4

Q(m3/s)=8× 10−6

8×10−6
V=2.82743339×10−5 =0.282942
6×10−3 1
𝑓 = 24931.28 × ( ) × 2(0.282942)2 ×1000 =0.934266
1

𝝆𝒗𝒅 𝟏𝟎𝟎𝟎×𝟎.𝟐𝟖𝟐𝟗𝟒𝟐×𝟔×𝟏𝟎−𝟑
Re2= = =1697.65272631355
𝝁 𝟎.𝟎𝟎𝟏

Pipe 2 (No minor loss)

At Q=4 cm3/s ,∆P=0.5 cmHg ,L=1m, D=10mm=10× 𝟏𝟎−𝟑 m

103
∆P1(Pa)=0.5 × (10 × 101.325 × 760) = 666.6118
(10×10−3 )2
A=𝜋 × = 7.85×10-5
4
Q(m3/s)=4× 10−6

14
 4×10−6
V= 7.85×10−5 =0.05093
10×10−3 1
𝑓 = 666.6118 × ( ) × 2(0.05093)2 ×1000 =1.284999
1
𝜌𝑣𝑑 1000×0.05093×10×10−3
Re1= = =509.295817894065
𝜇 0.001

At Q=8 cm3/s ,∆P=1.3 cmHg ,L=1m, D=10mm=10× 𝟏𝟎−𝟑 m

𝟏𝟎𝟑
∆P2(Pa)=𝟏. 𝟑 × (𝟏𝟎 × 𝟏𝟎𝟏. 𝟑𝟐𝟓 × 𝟕𝟔𝟎) =1733.191
(𝟏𝟎×𝟏𝟎−𝟑 )𝟐
A=𝝅 × =7.85×10-5
𝟒
Q(m3/s)=8× 𝟏𝟎−𝟔

𝟖×𝟏𝟎−𝟔
V=7.85×10−5 =0.101859

𝟏𝟎×𝟏𝟎−𝟑 𝟏
𝒇 = 24931.28 × ( ) × 𝟐(𝟎.𝟐𝟖𝟐𝟗𝟒𝟐)𝟐 ×𝟏𝟎𝟎𝟎 =0.835249
𝟏

𝝆𝒗𝒅 𝟏𝟎𝟎𝟎×𝟎.𝟏𝟎𝟏𝟖𝟓𝟗×𝟏𝟎×𝟏𝟎−𝟑
Re2= = =1018.59163578813
𝝁 𝟎.𝟎𝟎𝟏

Pipe 3 (Major and Minor loss)

At Q=5 cm3/s ,∆P=0.4 cmHg ,L=1m, D=17mm=10× 𝟏𝟎−𝟑 m

𝟏𝟎𝟑
∆P2(Pa)=𝟎. 𝟒 × (𝟏𝟎 × 𝟏𝟎𝟏. 𝟑𝟐𝟓 × 𝟕𝟔𝟎) =533.2895
(𝟏𝟕×𝟏𝟎−𝟑 )𝟐
A=𝝅 × =0.000227
𝟒
3 −𝟔
Q(m /s) =5× 𝟏𝟎

𝟓×𝟏𝟎−𝟔
V=0.000227 =0.022028
The presence of a wide-open globe valve contributed to the minor loss. For this type of valve, Le/D=300

𝐿𝑒 𝑣 2 𝜌 𝐿 𝑣2𝜌
∆P=4𝑓 ( ) +4𝑓 ( )
𝐷 2 𝐷 2

(0.022028)2 (1000) 1 (0.022028)2 (1000)

533.2895=4𝑓(300) +4𝑓 (17×10−3 )
2 2

Making f the subject,

𝒇 =1.531396

At Q=10 cm3/s ,∆P=0.8 cmHg ,L=1m, D=17mm=10× 𝟏𝟎−𝟑 m

15
 𝟏𝟎𝟑
∆P2(Pa)=𝟎. 𝟖 × (𝟏𝟎 × 𝟏𝟎𝟏. 𝟑𝟐𝟓 × 𝟕𝟔𝟎) = 1066.579
(𝟏𝟕×𝟏𝟎−𝟑 )𝟐
A=𝝅 × =0.000227
𝟒
Q(m3/s) =10× 10−6

10×10−6
V=0.000227 = 0.044057
The presence of a wide-open globe valve contributed to the minor loss. For this type of valve, Le/D=300

(0.044057)2 (1000) 1 (0.044057)2 (1000)

1066.579=4𝑓(300) +4𝑓 (17×10−3 )
2 2
Making f the subject,

𝒇 = 0.765698

Pipe 4
At Q=5 cm3/s ,∆P=0.2 cmHg ,L=1m, D=17mm=10× 𝟏𝟎−𝟑 m

𝟏𝟎𝟑
∆P2(Pa)=𝟎. 𝟐 × (𝟏𝟎 × 𝟏𝟎𝟏. 𝟑𝟐𝟓 × 𝟕𝟔𝟎) = 266.6447
(𝟏𝟕×𝟏𝟎−𝟑 )𝟐
A=𝝅 × =0.000227
𝟒
3 −𝟔
Q(m /s) =5× 𝟏𝟎

𝟓×𝟏𝟎−𝟔
V=0.000227 =0.022028
The presence of a returned bend contributed to the minor loss. For this type of valve, Le/D=75

𝐿𝑒 𝑣 2 𝜌 𝐿 𝑣2𝜌
∆P=4𝑓 ( 𝐷 ) +4𝑓 (𝐷)
2 2

(0.022028)2 (1000) 1 (0.022028)2 (1000)

266.6447 =4𝑓(75) +4𝑓 (17×10−3 )
2 2

Making f the subject,

𝒇 =2.053081

At Q=10 cm3/s ,∆P=0.8 cmHg ,L=1m, D=17mm=10× 𝟏𝟎−𝟑 m

𝟏𝟎𝟑
∆P2(Pa)=𝟎. 𝟖 × (𝟏𝟎 × 𝟏𝟎𝟏. 𝟑𝟐𝟓 × 𝟕𝟔𝟎) =666.6118
(𝟏𝟕×𝟏𝟎−𝟑 )𝟐
A=𝝅 × =0.000227
𝟒
Q(m3/s) =10× 10−6

10×10−6
V=0.000227 = 0.044057
The presence of a wide-open globe valve contributed to the minor loss. For this type of valve, Le=300

16
 (0.044057)2 (1000) 1 (0.044057)2 (1000)
666.6118 =4𝑓(75) +4𝑓 (17×10−3 )
2 2
Making f the subject,

𝒇 = 1.283175

Pipe 5
At Q=5 cm3/s ,∆P=0.4 cmHg ,L=1m, D=17mm=10× 𝟏𝟎−𝟑 m

𝟏𝟎𝟑
∆P2(Pa)=𝟎. 𝟒 × (𝟏𝟎 × 𝟏𝟎𝟏. 𝟑𝟐𝟓 × 𝟕𝟔𝟎) = 533.2895
(𝟏𝟕×𝟏𝟎−𝟑 )𝟐
A=𝝅 × =0.000227
𝟒
−𝟔
Q(m3/s) =5× 𝟏𝟎

𝟓×𝟏𝟎−𝟔
V=0.000227 =0.022028
The presence of a returned bend and globe valve contributed to minor losses, Le/D both are 75 and 300 respectively

𝐿𝑒1 𝑣 2 𝜌 𝐿 𝑣2𝜌 𝐿𝑒2 𝑣 2 𝜌

∆P=4𝑓 ( ) +4𝑓 (𝐷) +4𝑓 ( )
𝐷 2 2 𝐷 2

(0.022028)2 (1000) 1 (0.022028)2 (1000) (0.022028)2 (1000)

266.6447 =4𝑓(75) +4𝑓 (17×10−3 ) +4𝑓(300)
2 2 2

Making f the subject,

𝒇 =1.266646

At Q=10 cm3/s ,∆P=0.9 cmHg ,L=1m, D=17mm=10× 𝟏𝟎−𝟑 m

𝟏𝟎𝟑
∆P2(Pa)=𝟎. 𝟖 × (𝟏𝟎 × 𝟏𝟎𝟏. 𝟑𝟐𝟓 × 𝟕𝟔𝟎) =1199.901
(𝟏𝟕×𝟏𝟎−𝟑 )𝟐
A=𝝅 × =0.000227
𝟒
−6
Q(m3/s) =10× 10

10×10−6
V= = 0.044057
0.000227
The presence of a wide-open globe valve contributed to the minor loss. For this type of valve, Le=300

(0.044057)2 (1000) 1 (0.044057)2 (1000) (0.044057)2 (1000)

1199.901=4𝑓(75) +4𝑓 (17×10−3 ) +4𝑓(300) +
2 2 2
Making f the subject,

𝒇 = 0.712489

17
12. DECLARATION

I declare that:

• This report is my unaided work and is a true reflection of the lab I participated in.

• Large portions of it have not been submitted by another student for assessment.

• A significant portion of it was not copied from an internet source or a book (Daboo).

• A significant portion of it was not written using ChatGPT or any other AI tool.

• If any of the above statements turn out to be false, I forfeit the marks awarded to this report.

GROUP MEMBERS

NAME SIGNATURE

BERCHIE BRIGHT AMOAH

AMOATEY JOEL KWAO

OKAI MARK NII KOTEY

ADJAH RICHMOND ELIKEM

18