DISCUSSION Decrease of pressure represents the energy losses due to friction resistance of fluid flow within the pipe system

DISCUSSION
Decrease of pressure represents the energy losses due to friction resistance of fluid flow within the pipe system. Vertical pipe difference or elevation and changes of kinetic energy will also cause the pressure loss in pipe. In this experiment, we determined the pressure loss within the pipe system by using the Darcy-Weisbach equation. According to the Darcy-Weisbach equation, the pressure loss and head loss is related with the length of pipe (l), coefficient of pipe friction (f), density of flowing medium (?) and square of the flow speed (v). The Darcy-Weisbach equation is stated as below:
Pv=f.l2.D?v2hv=f.lv22D.gWhere,
Pv=Pressure loss due to friction in the pipe
hv=Head loss due to friction in the pipe
f= Coefficient of pipe friction factor
l=Length of pipe
D=Diameter of pipe
v= Velocity pf flow
g=Acceleration due to gravity
?=density of fluid
Reynolds number (Re) is defined as the ratio of the inertial forces to the viscous forces. Inertial forces are the forces of the motion of the liquid while the viscous forces are the forces that caused by the intermolecular forces and the shape of the molecules. We can predict the pattern of the flow whether the flow is laminar, transition or turbulent through the Reynolds number. Laminar(Re?2300) is the flow that characterize by smooth streamlines and highly ordered motion while Turbulent(Re?4000) is the flow that characterize by velocity fluctuations and highly disordered motion. The transitional flow(2300?Re?4000) is the flow that always switches between laminar and turbulent in a disorderly fashion. Reynolds number is a dimensionless quantity and it is related with the pipe diameter(D), flow speed(v) and kinematic viscosity (v). Viscosity is the measure of the fluid’s resistance to gradual deformation by tensile or shear stress. The Reynolds equation is given as below:
Re=vDv=vD??Where,
?=flow velocity
D=diameter of pipe
v=??=kinematic viscosity
?= density of fluid
?= viscosity of fluid
In this experiment, we apply the Blassius formula, Colebrook equation and Moody’s formula to determine the coefficient of pipe friction factor. We apply the Blassius formula to calculate the pipe friction coefficient of the smooth pipesRe<65?D while we apply the Colebrook equation or Moody’s formula to calculate the pipe friction coefficient of the pipe in the transition range to rough pipe (65dk ;Re;1300dk). Blassius formula is expressed as below:
f=0.3164/4ReAs stated in “Fluid Mechanics Fundamentals and Applications”,Yunus A. Cengel and John M.Cimbala (2014), the Colebrook equation is implicit in f since f appears on both sides of the equation. Thus, it must be solved iteratively. The Colebrook equation is shown as below:
1f= -2log?(?D3.7+2.51Ref)
The Moody’s formula is stated as below:
f=0.0013751+200ksd+106Re1/3According to “Modification of Setup for Major Losses in Pipes to Determine the Exact Value of Friction Factor”, Shubham Ghadge et al.(2017),the exact solution of Darcy friction factor in turbulent flow is determined by using Moody diagram or by using Colebrook equation. This had explained that there are many method can be used to find the coefficient of pipe friction factor. In this experiment, we had apply the Blassius formula, Colebrook equation, Moody’s formula and Moody chart to determine the coefficient of pipe friction. Moody’s chart shows the relationship between Reynolds number (Re), coefficient of pipe friction factor (f)and relative roughness ( ?/D). Relative roughness means the ratio of roughness of the pipe to the pipe diameter.

There are different in the values of pressure loss and head loss between the theoretical data and experimental data. We determined the theoretical pressure loss and head loss by using the Moody Chart, Blassius formula, Colebrook equation and Moody’s formula. According to the “Major and Minor Losses”, BSEN 3310 by Christina Richard (November 18, 2014 ), the large percent errors for the pipe does not show that the experimental data was wrong, but shows that the calculated values of the friction factor do not take into effect of all of the losses coming from the pipe. The experimental values are much more accurate than the theoretical for real life applications. Besides, the roughness values given in the Moody chart are for the new pipes while the pipes that we used in this experiment is no the new pipes and the pipes had been used many times. Thus, the relative roughness of pipes may increase due to corrosion, scale build up and precipitation. As a result, the coefficient of pipe friction factor that we get in this experiment will increase and this had caused the experimental data different with the theoretical data. As mentioned in “Fluid Mechanics Fundamentals and Applications”,Yunus A. Cengel and John M.Cimbala (2014), the Moody chart and its equivalent Colebrook equation involve several uncertainties(the roughness size, experimental error, curve fitting of data, etc), and thus the results obtained should not treated as “exact.” They are is usually considered to be accurate to ±15 percent over entire range.

There are different in values for the coefficient of pipe friction factor by using different formula (Blassius formula, Colebrook equation and Moody’s formula). Since the Colebrook equation is implicit in f, thus iteration is needed in the determination of the coefficient of pipe friction factor(f). However, the equation that we apply in this experiment is no under iteration, thus this may be affected the accuracy of the results. There are some distinct difference in the values by using the Colebrook equation and Moody’s formula. For Moody’s formula, the accuracy for the smooth pipe is about±5% while for the rough pipe is about±10%. Since the Blasius equation do not requires the pipe roughness, thus it is the most simple equation for solving the coefficient of pipe friction factor. According to “Darcy Friction Factor Formulae in Turbulent Pipe Flow”, Jukka Kiijärvi (2011), because the Blasius equation has no term for pipe roughness, it is valid only to smooth pipes. However, the Blasius equation is sometimes used in rough pipes because of its simplicity. The Blasius equation is valid up to the Reynolds number105. As a results, this may cause the difference of values for the coefficient of pipe friction factor when we apply different formula in the calculation of coefficient of pipe friction factor.

From the experimental results, PVC 32X1.9 gives the least head loss. According to the Darcy-Weisbach equation, the pressure loss or head loss of pipe is inversely proportional to the diameter of pipe and directly proportional to the coefficient of pipe friction factor. The coefficient of pipe friction factor decreased as the velocity increased. This shows that there is less friction in the pipes as the velocity increases. PVC 32X1.9 has the biggest diameter compare to the other pipes such as copper (18X1). Thus, PVC 32X1.9 had the least head loss compare to others pipes.
There are several factors contributing to errors or inaccuracy in experiment. Presence of the air bubbles in the connecting tube that connect between the manometer and pipes will cause the increased in the pressure and affect the accuracy of the experimental data. Leak in the connecting pipe section will also cause error to the experiment and affect the accuracy of the result. Besides, we carried out this experiment in the open environment. It is very difficult for us to conduct the experiment at constant temperature. Thus, this may be one of the factors that contributing to error or inaccuracy in experimental data. Furthermore, the unstable flow rate that result in the fluctuation of the height in the manometer may affect the observer during taking the accurate reading of the manometer. Presence of parallax error during taking the reading of manometer will also causes the errors and inaccuracy in this experiment.
We must make sure that there is no any air bubbles presence in the connecting tube. We can done this through open the valve to allow over flow of the water to avoid any presence of air bubbles in the tubes before the beginning of the experiment. We must carry out the leak test before starting up the experiment in order to prevent any leaking in the connecting pipe section. It is advised to carry out the experiment in the closed environment. Thus, this allow our experiment do not easily affect by any external factor such as temperature. The unstable flow rate in the experiment can be solved by taking several reading and then take the average reading through calculation. Beside, we can avoid the parallax error by ensure the observer’s eyes is parallel with the water level during taking the reading. Thus, this can improve the accuracy of our results and avoid any error in this experiment.

ANSWER TO THE QUESTIONS
Calculate the Reynolds number,Re and head loss, hv. Determine the coefficient of friction,f for each of the pipes.

Pipe section Volumetric flow
(m3/h) Reynolds number,Rehead loss, hv(mm) Coefficient of friction,fMoody ‘s
Formula Blasius’s
Formula
Colebrook
Equation Moody
Chart
Galvanized steel,1/2″ 0.50 24655.6447 363.6537 0.0194 0.0252 0.0424
0.0424
0.55 27121.2091 438.1632 0.0189 0.0247 0.0422 0.0422
0.60 29586.7736 519.5918 0.0184 0.0241 0.0421 0.0421
0.70 34517.9025 703.2051 0.0175 0.0232 0.0419 0.0419
0.80 39449.0315 914.4919 0.0168 0.0225 0.0417 0.0417
Copper, 18X1 0.80 24360.9243
67.4862
0.0191
0.0253 0.0249 0.0249
1.00 30451.1554 100.1544 0.0178 0.0240 0.0236 0.0236
1.20 36541.3865 138.4326 0.0168 0.0229 0.0227 0.0227
1.40 42631.6176 182.1476 0.0160 0.0220 0.0219 0.0219
1.60 48721.8487 231.1618 0.0153 0.0213 0.0213 0.0213
PVC
20X1.5 0.80 23304.0683 65.6110
0.0194 0.0256 0.0251 0.0251
1.00 29130.0853 97.3342 0.0180 0.0242 0.0238 0.0238
1.20 34956.1024 134.4911 0.0170 0.0231 0.0229 0.0229
1.40 40782.1195 176.9113 0.0162 0.0223 0.0221 0.0221
1.60 46608.1365 224.4596 0.0155 0.0215 0.0215 0.0215
PVC
16X1.8 0.50 18266.1329 97.9535 0.0210 0.0272 0.0267 0.0267
0.55 20092.7462 115.8347 0.0204 0.0266 0.0261 0.0260
0.60 21919.3595 135.0278 0.0198 0.0260 0.0255 0.0255
0.70 25572.5861 177.2691 0.0188 0.0250 0.0246 0.0246
0.80 29225.8126 224.5360 0.0180 0.0242 0.0239 0.0239
PVC
32X1.9 0.50 8803.2333 2.9145 0.0267 0.0327 0.0320 0.0320
1.00 17606.4665 9.7611 0.0213 0.0275 0.0268 0.0268
1.50 26409.6998 19.9272 0.0186 0.0248 0.0243 0.0243
2.00 35212.9330 33.1576 0.0170 0.0231 0.0228 0.0228
2.50 44016.1663 49.2941 0.0158 0.0218 0.0217 0.0217
Compare the calculated value with the measured value by using different formula (Moody, Colebrook and Blasius) and discuss the possible reasons for different values.

The values of coefficient of pipe friction factor that we get from the Moody chart and Colebrook equation is match at a great extent. This is because the Colebrook and Moody both are based on Reynolds number and relative roughness, thus, there is not much difference seen in the results. The Colebrook equation is implicit in f and iteration is needed in the determination of the coefficient of pipe friction factor (f). However, the equation that we apply in this experiment is no under iteration, thus this may be caused the results different with others. For Moody’s formula, the accuracy for the smooth pipe is about±5% while for the rough pipe is about±10%. This few factors had caused some distinct difference in the values by using the Colebrook equation and Moody’s formula. Furthermore, the coefficient of pipe friction factor that we get from the Blasius formula has also some distinct difference of results compare to other formula. Blasius equation is the most simple equation for solving the coefficient of pipe friction factor. Since the Blasius equation do not requires the pipe roughness, thus it had caused the different in results compare to the Moody and Colebrook equation. According to “Darcy Friction Factor Formulae in Turbulent Pipe Flow”, Jukka Kiijärvi (2011), because the Blasius equation has no term for pipe roughness, it is valid only to smooth pipes. However, the Blasius equation is sometimes used in rough pipes because of its simplicity. The Blasius equation is valid up to the Reynolds number105. As a results, this may cause the difference of values for the coefficient of pipe friction factor when we apply different formula in the calculation of coefficient of pipe friction factor.

Based on the experimental results, which pipes gives less head loss? Briefly explain your choice.

Based on the experimental results, PVC 32X1.9 gives the least head loss. According to the Darcy-Weisbach equation, the pressure loss or head loss of pipe is inversely proportional to the diameter of pipe and directly proportional to the coefficient of pipe friction factor. PVC 32X1.9 has the biggest diameter compare to the other pipes such as copper (18X1). Thus, PVC 32X1.9 had the least head loss compare to others pipes. PVC 32X1.9 has the smallest relative roughness that implies that it had the smallest coefficient of pipe friction factor and pressure or head loss. Besides, PVC 32X1.9 had the smallest kinetic viscosity which means that it is less resistance for the liquid to flow through the pipe, thus, the friction factor for PVC 32X1.9 is the lowest.

Briefly discuss factors contributing to errors or inaccuracy in experimental data and propose recommendation to improve the results.

Presence of the air bubbles in the connecting tube that connect between the manometer and pipes will cause the increased in the pressure and affect the accuracy of the experimental data. We must make sure that there is no any air bubbles presence in the connecting tube. We can done this through open the valve to allow over flow of the water to avoid any presence of air bubbles in the tubes before the beginning of the experiment. Leak in the connecting pipe section will also cause error to the experiment and affect the accuracy of the result. We must carry out the leak test before starting up the experiment in order to prevent any leaking in the connecting pipe section. Besides, we had carried out this experiment in the open environment and this had made us difficult to conduct the experiment at constant temperature. It is advised to carry out the experiment in the closed environment. Thus, this allow our experiment do not easily affect by any external factor such as temperature. Furthermore, the unstable flow rate that result in the fluctuation of the height in the manometer may affect the observer during taking the accurate reading of the manometer. As a results, this may cause the error and inaccuracy in our experimental data. The unstable flow rate in the experiment can be solved by taking several reading and then take the average reading through calculation. Presence of parallax error during taking the reading of manometer will also causes the errors and inaccuracy in this experiment. We can avoid the parallax error by ensure the observer’s eyes is parallel with the water level during taking the reading
References
Yunus A Cengel, John M Cmbala, “Fluid Mechanics Fundamental and Applications”, McGRAW-HILL publication., 20142. Shubham Ghadge et.al (2017)”Modification of Setup for Major Losses in Pipes to Determine the Exact Value of Friction Factor”, International Journal for Scientific Research & Development.

3 Jukka Kiijärvi (July 2011)” Darcy Friction Factor Formulae in Turbulent Pipe Flow” Lunowa*Fluid Mechanics Paper 110727.

4. Christina Richard (November 18, 2014 ), “Major and Minor Losses”, BSEN 3310