Environmental assignment -science
Pipe and Fitting Losses Lab Report
Contents
Abstract 2
Objectives 3
Section2.0Theory 4
Section3.0MaterialsandMethods 6
Section4.0 Results 8
Calculations carried out 10
17 mm pipe(smooth) 10
13.6 mm pipe(smooth) 11
26.2 mm pipe(smooth) 12
17 mm pipe(rough) 13
100mm bend, 13.6mm diameter 14
Gate Valve 13.6mm Diameter Fully open 15
Gate Valve half open 13.6mm Diameter 16
Gate Valve quarter way open 13.6mm Diameter 16
Globe valve 13.6mm diameter 17
Section 5: Discussion 19
Section6.0Conclusions 20
Appendix A 21
List of Figures and Tables
Figure 1: Moody chart
Figure 2: Graph of loss coefficient against flow rate
Table1: Smooth and Rough Pipes, & Bend
Table 2: Gate Valve 13.6mm Diameter
Table 3: Globe valves 13.6 mm diameter
Table 4: Table for graph of loss coefficient against flow rate
Abstract
The basic flow of fluids in pipes is affected by frictional forces between the fluid molecules and the internal diameter of the pipe it is flowing through. These losses affect the flow rate of the fluid. The characteristics of the duct play a major role in determining the dynamics of flow within it.
The diameter of the pipe affects the cross-section area of the pipe, which is a critical factor in determining flow rate within the pipe. The area of a circular cross-section pipe is as per the equation below:
Area of pipe= (πd^2)/4
The Dracy-Weisbach formula relates the loss of pressure head by a fluid to the properties of the pipe and the fluid characteristics. The equation aids in the calculations of major losses. This formula is represented below;
S= F_D 1/2g V^2/D
Minor losses are calculated from the effect of valves and bends in the flow of a fluid. Equation of head loss around a bend is used for the calculations.
h=k v^2/2g
The value of Darcy’s friction factor (0.016) is different from the Moody diagram extracted value of (0.035). This difference in values obtained through different methods proves that the pipes are not perfectly smooth, as theoretical data would suggest
The gate valve has the highest values of K. Its values are higher that the globe valve when it is fully opened. The globe valve has the lowest value as per the calculations.
Objectives
The purpose of this experiment is to determine experimental values for loss coefficientsfor pipes and fittings, and tocompare themto commonly acceptedvalues. This involves conducting tests on pipes of varying diameters and using equations governing the flow to calculate the factors that lead to energy losses.
Section2.0Theory
The basic flow of fluids in pipes is affected by frictional forces between the fluid molecules and the internal diameter of the pipe it is flowing through. These losses affect the flow rate of the fluid. The characteristics of the duct play a major role in determining the dynamics of flow within it. These parameters of the duct are its size, in terms of length and diameter, the texture of the internal diameter that is in contact with the fluid, and, the material that the pipe is made of.
The diameter of the pipe affects the cross-section area of the pipe, which is a critical factor in determining flow rate within the pipe. The area of a circular cross-section pipe is as per the equation below:
Area of pipe= (πd^2)/4
The losses experienced in a fluid flowing through a pipe can be classified into major and minor losses. The losses are explained to be the resistance that the fluid experiences which cause it to lose some of its energy.Major losses are those frictional losses that are exerted on the fluid along the entire length of the pipe. Minor losses are named so because they are losses experienced over short instances due to instances like fittings, bends, sudden or gradual increases and decreases on the pipe cross-section.
The Dracy Weisbach formula relates the loss of pressure head by a fluid to the properties of the pipe and the fluid characteristics. The equation aids in the calculations of major losses. This formula is represented below;
S= F_D 1/2g V^2/D
S is the head loss; F_Dis Darcy’s friction factor; V is velocity; D is the diameter and g is the acceleration due to gravity.
S can be calculated from:
S=∆h/L=1/ρg ∆p/L
∆h is due to the head loss because of the friction experienced over the length of the pipe.
In terms of fluid flow rate, the Darcy-Weisbach equation can be expressed as:
S=F_D 8/(π^2 g) Q^2/D^5
This formula is then used to determine the friction loss coefficient for the flow.
A moody diagram is also used in the calculations of major losses in fluid mechanics. It relates surface roughness, Reynold’s number which in turn give the reading for the energy loss coefficient.
F
Figure 1: Moody chart
Minor losses are calculated from the effect of valves and bends in the flow of a fluid. Different valves have different friction factors. The radius of bends and their geometry determine the energy loss coefficient. Equation of head loss around a bend is used for the calculations.
h=k v^2/2g
This experiment, therefore, investigates the different factors that affect the amount of energy lost from the fluid flowing through the pipes. Both the minor losses and the major losses are investigated for their effect in the pressure head.
Section3.0MaterialsandMethods
Materials
The equipment used in this experimentare:
Pipe and fitting frame withmanometers.
Pipes with nominal diameters of13.6, 17 and 26.2 mm.
Pipe with radius bend of 100 mm.
Graduated cylinder.
Piezometer
Bucket
Valves: Gate and globe valves
Procedure
The recirculating tank is plugged in to the electrical connection to maximum flow. The outlet valve is opened and a short period is allowed to elapse to allow any trapped air to leave the circuit. The outlet valve is closed on the circuit being tested. Suitable lengths of connecting tube are selected. One end is placed into the bucket while the other end is connected to the tapping points to be used.
At first, all the air in the connecting pipes is forced out of the connecting pipes. The free ends of the pipes from out of the bucket are then quickly connected to the pair of tapping on the piezometers. The valve in the cap at the manifold, which is at the top of the piezometer, is opened and the piezometer is allowed to fill up. Once the piezometer tubes are full of water, the valve is released.
The cold water supply is then reduced to a low flow rate and the outlet valve on the circuit being tested is opened. The valve cap on the piezometer manifold is opened again and pressure is allowed to equalize in the tubes. The valve cap is then closed after the equalization.
Losses in Straight Pipes (for each diameter pipe)
The valve on the pipe circuit is fully opened. The globe valve is positioned on the light blue line. The ball valve is the grey circuit while the gate valve is the dark blue circuit. The valve to be used is opened first before closing the other 2 valves in the circuit.
The flow gauge isused to time how long one gallon of water takes to flow through the system. The value obtained is recorded.
Tubing is connected to the ports on the circuit being tested while the other end is connected to the piezometer. The readings on the piezometer are read and recorded.
The flow rate is adjusted two more times and the pressure readings recorded each time.
This procedure is repeated for the other smooth pipes and the rough pipe.
This section of the procedure is repeated for the bend radius of 100mm using the globe valve instead of the gate valve.
Losses in Valves
The gate valve is carefully opened and closed. The number of turns made by the hand-wheel is counted and each turn is converted into a percentage figure.
The gate valve is fully opened and the head loss and flow rate values obtained are recorded.
The valve opening is carefully reduced to 50% opening then to 25% opening. The head loss and flow rate readings on each of the percentage openings are recorded.
The experiment is then repeated for a fully opened globe valve.
Section4.0 Results
Table1: Smooth and Rough Pipes, & Bend
Pipe
Size or
Fitting
Type
Trial
No. Graduated
Cylinder
Volume
(mL)
Elapsed
Time
(seconds)
Flowrate
(L/sec)
Velocity
Manometer Readings
17 mm pipe
(smooth) 1 1000 6.25 0.160 404 400
17 mm pipe
(smooth) 2 1000 7.14 0.140 415 406
17 mm pipe
(smooth) 3 1000 7.69 0.130 421 416
17 mm pipe
(rough) 1 1000 6.66 0.150 371 410
17 mm pipe
(rough) 2 1000 8.40 0.119 475 421
17 mm pipe
(rough) 3 1000 8.55 0.117 448 421
13.6 mm pipe
(smooth) 1 1000 14.08 0.071 445 419
13.6 mm pipe
(smooth) 2 1000 25.64 0.039 442 423
13.6 mm pipe
(smooth) 3 1000 47.62 0.021 425 419
26.2 mm pipe
(smooth) 1 1000 6.37 0.157 456 382
26.2 mm pipe
(smooth) 2 1000 6.54 0.153 386 352
26.2 mm pipe
(smooth) 3 1000 6.41 0.156 392 360
100 mm bend, 13.6 mm diam. 1 1000 6.04 0.166 390 355
100 mm bend, 13.6 mm diam. 2 1000 6.26 0.160 385 349
100 mm bend, 13.6 mm diam. 3 1000 5.77 0.173 379 343
Valve Type: Globe Valve 13.6mm Diameter
Valve Position Volume Collected Time to Collect Volume
Flowrate, Q Piezometer Readings
Upstream Tapping (mm) Downstream Tapping (mm)
Difference, h (mm) Flow Velocity, m/s
K
Re
100% (Fully Open) 1000 6.38 0.157 378 320 58
100% (Fully Open) 1000 6.11 0.163 374 314 60
Valve Type: Gate Valve 13.6mm Diameter
Valve Position Volume Collected Time to Collect Volume
Flowrate, Q Piezometer Readings
Upstream Tapping (mm) Downstream Tapping (mm)
Difference, h (mm) Flow Velocity, m/s
K
Re
100% (Fully Open) 1000 6.63 0.151 609 151 458
100% (Fully Open) 1000 6.21 0.161 583 177 406
50% 1000 6.25 0.160 582 170 412
25% 1000 6.17 0.161 500 169 421
Table 2: Gate Valve 13.6mm Diameter
Table 3: Globe valves 13.6 mm diameter
Calculations carried out
Fluid flow velocity in a circular pipe is calculated using the fluid flow rate and the pipe’s inside diameter.
Fluid flow velocity(m/s)=flow rate(m^3/s)×Pipe inside diameter(m)
17 mm pipe(smooth)
Area of pipe= (πd^2)/4
17mm=17/1000 m=0.017m
Area=(π 〖0.017〗^2)/4=2.270×〖10〗^(-4) m^2
Trial 1
Flow rate=(Volume(L))/(Elapsed time(s))=1/6.25=0.16ls^(-1)
0.16ls^(-1)=0.16×〖10〗^(-3)=0.00016m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(0.00016m^3 s^(-1))/(2.270×〖10〗^(-4) m^2 )=0.705ms^(-1)
Trial 2
Flow rate=1/7.14=0.14ls^(-1)
0.14ls^(-1)=0.14×〖10〗^(-3)=0.00014m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(0.00014m^3 s^(-1))/(2.270×〖10〗^(-4) m^2 )=0.617ms^(-1)
Trial 3
Flow rate=1/7.69=0.13ls^(-1)
0.13ls^(-1)=0.13×〖10〗^(-3)=0.00013m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(0.00013m^3 s^(-1))/(2.270×〖10〗^(-4) m^2 )=0.573ms^(-1)
Average value for velocity is calculated.
Average velocity=(0.705+0.617+0.573)/3=0.632ms^(-1)
Calculating the Reynold’s number
Re=ρVD/μ=(1000×0.632×0.017)/(8.90×〖10〗^(-4) )=1.207×〖10〗^4
Calculating the friction factor using the Blasius Equation
f=0.079(Re)^(-1/4)=0.079〖(1.207×〖10〗^4)〗^(-0.25)=7.537×〖10〗^(-3)
13.6 mm pipe(smooth)
Area of pipe= (πd^2)/4
13.6mm=13.6/1000 m=0.0136m
Area=(π 〖0.0136〗^2)/4=1.453×〖10〗^(-4) m^2
Trial 1
Flow rate=(Volume(L))/(Elapsed time(s))=1/14.08=0.071ls^(-1)
0.071ls^(-1)=0.071×〖10〗^(-3)=7.1×〖10〗^(-5) m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(7.1×〖10〗^(-5) m^3 s^(-1))/(1.453×〖10〗^(-4) m^2 )=0.489ms^(-1)
Trial 2
Flow rate=1/25.64=0.039ls^(-1)
0.039ls^(-1)=0.039×〖10〗^(-3)=3.9×〖10〗^(-5) m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(3.9×〖10〗^(-5) m^3 s^(-1))/(1.453×〖10〗^(-4) m^2 )=0.268ms^(-1)
Trial 3
Flow rate=1/47.62=0.021ls^(-1)
0.021ls^(-1)=0.021×〖10〗^(-3)=2.1×〖10〗^(-5) m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(2.1×〖10〗^(-5) m^3 s^(-1))/(1.453×〖10〗^(-4) m^2 )=0.145ms^(-1)
Average value for velocity is calculated.
Average velocity=(0.489+0.268+0.145)/3=0.301ms^(-1)
Calculating the Reynold’s number
Re=ρVD/μ=(1000×0.301×0.0136)/(8.90×〖10〗^(-4) )=0.460×〖10〗^4
Calculating the friction factor using the Blasius Equation
f=0.079(Re)^(-1/4)=0.079〖(0.460×〖10〗^4)〗^(-0.25)=9.593×〖10〗^(-3)
26.2 mm pipe(smooth)
Area of pipe= (πd^2)/4
26.2mm=26.2/1000 m=0.0262m
Area=(π 〖0.0262〗^2)/4=5.391×〖10〗^(-4) m^2
Trial 1
Flow rate=(Volume(L))/(Elapsed time(s))=1/6.37=0.157ls^(-1)
0.157ls^(-1)=0.157×〖10〗^(-3)=1.57×〖10〗^(-4) m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(1.57×〖10〗^(-4) m^3 s^(-1))/(5.391×〖10〗^(-4) m^2 )=0.291ms^(-1)
Trial 2
Flow rate=1/6.54=0.153ls^(-1)
0.153ls^(-1)=0.153×〖10〗^(-3)=1.53×〖10〗^(-4) m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(1.53×〖10〗^(-4) m^3 s^(-1))/(5.391×〖10〗^(-4) m^2 )=0.284ms^(-1)
Trial 3
Flow rate=1/6.41=0.156ls^(-1)
0.156ls^(-1)=0.156×〖10〗^(-3)=1.56×〖10〗^(-4) m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(1.56×〖10〗^(-4) m^3 s^(-1))/(5.391×〖10〗^(-4) m^2 )=0.289ms^(-1)
Average value for velocity is calculated.
Average velocity=(0.291+0.284+0.289)/3=0.288ms^(-1)
Calculating the Reynold’s number
Re=ρVD/μ=(1000×0.288×0.0262)/(8.90×〖10〗^(-4) )=0.848×〖10〗^4
Calculating the friction factor using the Blasius Equation
f=0.079(Re)^(-1/4)=0.079〖(0.848×〖10〗^4)〗^(-0.25)=8.232×〖10〗^(-3)
17 mm pipe(rough)
Trial 1
Flow rate=1/6.66=0.15ls^(-1)
0.15ls^(-1)=0.15×〖10〗^(-3)=0.00015m^3 s^(-1)
Area considers a pipe with effective diameter of 14 mm and the pipe is coated internally with sand that has an average grain size of 0.5 mm
Calculating relative roughness
Relative roughness=Average pipe wall roughness/(internal diameter)=(0.5×〖10〗^(-3))/0.014=0.036
Area=(π 〖0.014〗^2)/4=1.539×〖10〗^(-4) m^2
Calculating velocity
velocity=(flow rate)/area=(0.00015m^3 s^(-1))/(1.539×〖10〗^(-4) m^2 )=0.975ms^(-1)
Trial 2
Flow rate=1/8.40=0.11ls^(-1)
0.11ls^(-1)=0.11×〖10〗^(-3)=0.00011m^3 s^(-1)
Calculating velocity
velocity=(flow rate)/area=(0.00011m^3 s^(-1))/(1.539×〖10〗^(-4) m^2 )=0.715ms^(-1)
Trial 3
Flow rate=1/8.55=0.117ls^(-1)
0.117ls^(-1)=0.117×〖10〗^(-3)=1.17×〖10〗^(-4) m^3 s^(-1)
Calculating velocity
velocity=(flow rate)/area=(1.17×〖10〗^(-4) m^3 s^(-1))/(1.539×〖10〗^(-4) m^2 )=0.760ms^(-1)
Calculating the average velocity
Average velocity=(0.975+0.715+0.760)/3=0.817ms^(-1)
Calculating the Reynold’s number
Re=ρVD/μ=(1000×0.817×0.014)/(8.90×〖10〗^(-4) )=1.285×〖10〗^4
From the Moody diagram, the friction factor is 0.035
Calculating the friction factor from the Darcy-Weisbach equation.
S= F_D 1/2g V^2/D
S is the head loss; F_Dis Darcy’s friction factor; V is velocity; D is the diameter and g is the acceleration due to gravity.
S can be calculated from:
S=∆h/L=1/ρg ∆p/L
∆h is due to the head loss because of the friction experienced over the length of the pipe.
In terms of fluid flow rate, the Darcy-Weisbach equation can be expressed as:
S=F_D 8/(π^2 g) Q^2/D^5
Head loss calculations
Trial 1;
S=410-371=39mm
Trial 2;
S=475-421=54mm
Trial 3;
S=448-421=27mm
Average head loss=(39+54+27)/3=40mm=0.04m
Calculating Darcy’s friction factor
0.04=F_D 1/(2×9.81) 〖0.817〗^2/0.014=2.430F_D
F_D=0.04/2.430=0.016
The value of Darcy’s friction factor from the Moody diagram is different from the calculated value that uses the Darcy-Weisbach equation.
100mm bend, 13.6mm diameter
Equation of head loss around a bend is used.
h=k v^2/2g
K is the bend coefficient.
In this case, D=13.6mm.
13.6mm=13.6/1000 m=0.0136m
Area=(π 〖0.0136〗^2)/4=1.453×〖10〗^(-4) m^2
Average flow rate
(0.166+0.160+0.173)/3=0.166l/s=1.663×〖10〗^(-4)
Velocity
velocity=(flow rate)/area=(1.663×〖10〗^(-4) m^3 s^(-1))/(1.453×〖10〗^(-4) m^2 )=1.145ms^(-1)
Head loss
Trial 1
390-355=35
Trial 2
379-343=36
Trial 3
379-343=36
Average head loss
(35+36+36)/3=35.67mm=0.036m
Calculating the bend coefficient
0.036=k〖1.145〗^2/(2×9.81)=0.067k
k=0.036/0.067=0.537
The value of K from theoretical values is obtained from a chart.
The chart presents the K values in terms of the ratio of r/d.
In this case:
r/d=100mm/13.6mm=7.35
Reading from the chart, the value of K for 7.35 r/d ratio is not available. It is interpolated from the ratio values 6 and 8.
For 6, r/d=0.39 while for 8, r/d=0.55
0.55-0.39=0.16
8-6=2
0.16/2=0.08
7.35-6=1.35
1.35×0.08=0.12
0.39+0.12=0.51
This is the theoretical value of the bending coefficient.
Gate Valve 13.6mm Diameter Fully open
Cross-sectional Area
Area=(π 〖0.0136〗^2)/4=1.453×〖10〗^(-4) m^2
Total head= head loss from pipe + head loss from fitting
This is because both pipe friction and minor losses contribute to the total loss in the piping system.
The total head loss
(458+406)/2=432mm=0.432m
Equation of minor losses
Minor losses are the losses due to exits, fittings and valves although they account for a significant value of the total loss.
∆h=∑▒〖k v^2/2g〗
This is because both pipe friction and minor losses contribute to the total loss in the piping system.
Calculating average flow rate
(0.151+0.161)/2=0.156l/s=1.56×〖10〗^(-4) m^3 s^(-1)
Calculating velocity
velocity=(flow rate)/area=(1.56×〖10〗^(-4) m^3 s^(-1))/(1.453×〖10〗^(-4) m^2 )=1.074ms^(-1)
0.432=(k) 〖1.074〗^2/(2×9.81)=0.0588k
k=0.432/0.0588=7.348
Gate Valve half open 13.6mm Diameter
flow rate=1/6.25=0.16l/s=1.6×〖10〗^(-4) m^3 s^(-1)
Calculating velocity
velocity=(flow rate)/area=(1.6×〖10〗^(-4) m^3 s^(-1))/(1.453×〖10〗^(-4) m^2 )=1.101ms^(-1)
∆h=∑▒〖k v^2/2g〗
∆h=412mm=0.412m
0.412=(k) 〖1.101〗^2/(2×9.81)=0.0618k
k=0.412/0.0618=6.669
Gate Valve quarter way open 13.6mm Diameter
flow rate=1/6.17=0.162l/s=1.62×〖10〗^(-4) m^3 s^(-1)
Calculating velocity
velocity=(flow rate)/area=(1.62×〖10〗^(-4) m^3 s^(-1))/(1.453×〖10〗^(-4) m^2 )=1.115ms^(-1)
∆h=∑▒〖k v^2/2g〗
∆h=421mm=0.421m
0.421=(k) 〖1.115〗^2/(2×9.81)=0.0633k
k=0.412/0.0633=6.644
Globe valve 13.6mm diameter
Cross-sectional Area
Area=(π 〖0.0136〗^2)/4=1.453×〖10〗^(-4) m^2
Total head loss
(58+60)/2=59mm=0.059m
Flow rate average
(0.157+0.163)/2=0.16l/s=1.6×〖10〗^(-4) m^3/s
velocity=(flow rate)/area=(1.6×〖10〗^(-4) m^3 s^(-1))/(1.453×〖10〗^(-4) m^2 )=1.101ms^(-1)
∆h=∑▒〖k v^2/2g〗
0.059=(k) 〖1.101〗^2/(2×9.81)=0.0633k
k=0.955
A graph is plotted:
Independent Variable
(X-axis) Dependent Variable
(Y-axis)
Flow Rate, Q Loss coefficient
0.143×〖10〗^(-3) 0.7537×〖10〗^(-3)
0.043×〖10〗^(-3) 0.9593×〖10〗^(-3)
0.155×〖10〗^(-3) 0.8232×〖10〗^(-3)
0.126×〖10〗^(-3) 0.016×〖10〗^(-3)
0.1663×〖10〗^(-3) 0.537×〖10〗^(-3)
Table 4: Table for graph of loss coefficient against flow rate
Figure 2: Graph of loss coefficient against flow rate
Section 5: Discussion
The value of Darcy’s friction factor(0.016) is different from the Moody diagram extracted value of (0.035). This difference in values obtained through different methods proves that the pipes are not perfectly smooth, as theoretical data would suggest.
The analysis conducted also shows that an increase in pipe diameter decreases the factor that causes energy losses in fluids flowing through pipes. The 0.017m diameter gives a coefficient of 0.7537×〖10〗^(-4), the 0.0316m diameter gives 0.9593×〖10〗^(-4) and the 0.0262m diameter gives 0.8232×〖10〗^(-4).
The value of K from theoretical values is obtained from a chart.
The chart presents the K values in terms of the ratio of r/d.
In this case:
r/d=100mm/13.6mm=7.35
Reading from the chart, the value of K for 7.35 r/d ratio is not available. It is interpolated from the ratio values 6 and 8.
For 6, r/d=0.39 while for 8, r/d=0.55
0.55-0.39=0.16
8-6=2
0.16/2=0.08
7.35-6=1.35
1.35×0.08=0.12
0.39+0.12=0.51
This is the theoretical value of the bending coefficient. It is close to the value calculated from the experimental results (0.537).
For the valves, the K coefficient for each valve using the minor loss equation is compared to literature values. Globe valve value of K when fully open is 10.0 as per theory while the value from the experiment is 0.955. Gate valve, fully open theoretical value is 0.12 while the calculated value is 7.348. Gate valve, half open theoretical value is 6.0 while the calculated value is 6.669. Gate valve, 25% open theoretical value is 24.0 while the calculated value is 6.644.
These figures depict a great discrepancy between the theoretical values and the figures obtained from the data after conducting the experiment.
The gate valve has the highest values of K. Its values are higher that the globe valve when it is fully opened. The globe valve has the lowest value as per the calculations.
The value of K changes with variability in flow rate. Different values of flow rate provide different values of K. Flow rate affects the velocity hence a change in flow rate causes a subsequent change in velocity which, in turn, causes a change in the value of K.
Section6.0Conclusions
The basic flow of fluids in pipes is affected by frictional forces between the fluid molecules and the internal diameter of the pipe it is flowing through. Minor losses are the losses due to exits, fittings and valves although they account for a significant value of the total loss. The losses experienced in a fluid flowing through a pipe can be classified into major and minor losses. There is difference in values obtained through different methods which proves that the pipes are not perfectly smooth, as theoretical data would suggest. The value of K changes with variability in flow rate. Different values of flow rate provide different values of K. Flow rate affects the velocity hence a change in flow rate causes a subsequent change in velocity which, in turn, causes a change in the value of K.
Appendix A
Sample calculations
Fluid flow velocity(m/s)=flow rate(m^3/s)×Pipe inside diameter(m)
17 mm pipe(smooth)
Area of pipe= (πd^2)/4
17mm=17/1000 m=0.017m
Area=(π 〖0.017〗^2)/4=2.270×〖10〗^(-4) m^2
Trial 1
Flow rate=(Volume(L))/(Elapsed time(s))=1/6.25=0.16ls^(-1)
0.16ls^(-1)=0.16×〖10〗^(-3)=0.00016m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(0.00016m^3 s^(-1))/(2.270×〖10〗^(-4) m^2 )=0.705ms^(-1)
Trial 2
Flow rate=1/7.14=0.14ls^(-1)
0.14ls^(-1)=0.14×〖10〗^(-3)=0.00014m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(0.00014m^3 s^(-1))/(2.270×〖10〗^(-4) m^2 )=0.617ms^(-1)
Trial 3
Flow rate=1/7.69=0.13ls^(-1)
0.13ls^(-1)=0.13×〖10〗^(-3)=0.00013m^3 s^(-1)
Calculating velocity
velocity=flow rate/area=(0.00013m^3 s^(-1))/(2.270×〖10〗^(-4) m^2 )=0.573ms^(-1)
Average value for velocity is calculated.
Average velocity=(0.705+0.617+0.573)/3=0.632ms^(-1)
Calculating the Reynold’s number
Re=ρVD/μ=(1000×0.632×0.017)/(8.90×〖10〗^(-4) )=1.207×〖10〗^4
Calculating the friction factor using the Blasius Equation
f=0.079(Re)^(-1/4)=0.079〖(1.207×〖10〗^4)〗^(-0.25)=7.537×〖10〗^(-3)
