Objective of the Lab
We need to experimentally study the pipe flow in both laminar and turbulent flow regime.
Objective is to arrive at pipe roughness numbers and compare them with literature.
Formulation
Head loss “ hL” is directly proportional to the Pipe frictional constant “f” , Length of the pipe ( L) in m, Square of flow velocity.
Head loss “ hL” is inversely proportional to the Pipe diameter (D) in m , acceleration due to gravity (g) in m/s*s
Taking Log of above equation, we get
Log(hL)= log(f) + Log(L)- log(D)+ 2*Log(V) – log(2*g)
So plot of Log(hL) vs Log(V) must have linear behaviour and must have slope of 2.
Same phenomenon gets checked out we plot hL vs f*V2 , and verify if we get linear trend in laminar and turbulent flow regimes.
The friction factor is function of
, where e is the average wall roughness height
The Data of test setup
Pipe diameter is 3mm and pipe length 524 mm.
Specific gravity of water is 1000 kg/m3, and Hg 13594 kg/m3
Data collected
Procedure for data analysis
From the collected data an analysis program is made in MATLAB and the same is used for data analysis.
The programs codes are attached in appendix.
The Moody chart defines the variation of pipe friction coefficient for pipes of different roughness coefficients.
Moody’s diagram relates friction factor with Reynolds number and relative pipe rough ness (
Figure 1 : Gives the Moody Diagram taken from Wikipedia
Results
The water flow results plot is shown in figure 2
‘Figure 2 : Water flow head loss coefficient multiplied by V*V Vs Reynolds number
Laminar flow, turbulent flow and transition zones are clearly seen.
We see laminar flow where plot has lower slope from Re number 1000 to 1700
From Reynolds number 2500 and beyond we can see higher slope, and now flow is turbulent.
Between Re number 1700 to 2500 we see slowly rising slope signifying transition zone.
Velocity in m/s for 9 test runs are
0.2947 0.345 0.404 0.491 0.606 0.707 0.7736 0.8842 1.0268
f*[V*V] is 0.00562 0.007 0.00876 0.01097 0.0137 0.0171 0.0214 0.0322 0.0483
The f varies from
| 0.064656 |
| 0.058966 |
| 0.053627 |
| 0.045458 |
| 0.037279 |
| 0.034254 |
| 0.035787 |
| 0.041164 |
| 0.045785 |
For Re Number range
| 884.1949 |
| 1035.155 |
| 1212.61 |
| 1473.658 |
| 1818.915 |
| 2122.068 |
| 2321.012 |
| 2652.585 |
| 3080.421 |
Figure 3 shows the plots of experimental points for water flow experiments.
When we place the experimental points on Moody Diagram we see that Friction Factor Vs Re number follows Laminar flow path up to Re Number 2000.
| Re | f | 64/Re | RE*f |
| 1000*V*0.003/0.001 | |||
| 884.1949 | 0.064656 | 0.072382 | 57.16806 |
| 1035.155 | 0.058966 | 0.061826 | 61.03882 |
| 1212.61 | 0.053627 | 0.052779 | 65.02867 |
| 1473.658 | 0.045458 | 0.043429 | 66.98954 |
| 1818.915 | 0.037279 | 0.035186 | 67.80768 |
| 2122.068 | 0.034254 | 0.030159 | 72.68919 |
| 2321.012 | 0.035787 | 0.027574 | 83.06248 |
| 2652.585 | 0.041164 | 0.024127 | 109.191 |
| 3080.421 | 0.045785 | 0.020776 | 141.0384 |
Mean of First 5 points is = 63.6, so Laminar flow region formulation of 64/Re gets validated.
Figure 3 shows the plots of experimental points for water flow experiments.
At Re Number of 3080 point crosses transition zone, and relative pipe rough ness is predicted as 0.002.
Since pie diameter is 3 mm, the surface roughness is 0.006mm or 6 microns.
As only one data point is present in turbulent zone, the pipe surface rough ness may be get predicted with accuracy.
So further experiments are performed using Hg
For flow of Hg, 6 experimental data points are generated.
RE Number varies from 3000 to 8000, and data falls in turbulent zone.
‘Figure4: Hg flow head loss coefficient multiplied by V*V Vs Reynolds number
Results from MATLAB code
Volume_flow_Hg_cum_p_s = 1.0e-04 *[ 0.0758 0.0946 0.1154 0.1471 0.1818 0.2333]
V_mps =[ 1.0718 1.3382 1.6324 2.0805 2.5722 3.3010]
Re_nos = 1.0e+04 *[ 2.7310 3.4100 4.1595 5.3013 6.5543 8.4113]
f_Vmps_Vmps = [ 0.0039 0.0058 0.0087 0.0130 0.0195 0.0293]
Actual RE Numbers are
27310 34100 41595 53013 65543 84113
V in m/s is
1.071 1.338 1.632 2.08 2.572 3.30
f*V*V is
0.00386 0.0058 0.00869 0.0130 0.0195 0.0293
Giving f as
0.0034 0.00324 0.00326 0.0030 0.00295 0.0269
The points are plotted on the Moody chart as shown in figure
Figure 5 shows the plots of experimental points for Hg flow experiments.
The flow is in turbulent regime.
Relative pipe roughness in in range 0.003 and 0.004. With 0.004, the roughness is 3mm*0.004=0.012 mm or 12 microns. From literature (ref1) it is
| Surface Material | Absolute Roughness Coefficient – ε in mm |
| Drawn Brass, Drawn Copper | 0.0015 |
| PVC, Plastic Pipes | 0.0015 |
| Fiberglass | 0.005 |
| Stainless steel | 0.015 |
So surface roughness of 12 micron is reasonable.
Plot of log(hL) vs log( V) is shown in figure 6
Figure 6: Log(velocity) vs Log(hL) plot
We can see that behaviour is liner as expected.
The slope is = (5.6-3.5)/ (1.2-0.1) = 2.1 / 1.1, Close to 2 which is theoretical value.
Figure 7 demonstrates low RE region covered by water flow experiments, which falls in Laminar flow region, and Re number moves to turbulent flow region with Hg flow experiments.
Figure 7 : Friction factor for both water flow and Hg flow experiments
Conclusions
Nine sets of experiments were performed using water, which covered laminar flow region and transitory flow region. First 5 test points validated friction factor of 64/Re formulation.
During transition region this factor keep rising from 64 to 141. The last point falls beyond transition zone.
For data of flow of Hg, re no varies from 1.0e+04 *[ 2.7310 3.4100 4.1595 5.3013 6.5543 8.4113] and from Moody chart, we could predict surface roughness as 12 microns, which looks reasonable.
References
1: https://www.enggcyclopedia.com/2011/09/absolute-roughness/
Appendix A
MATLAB codes
Exp 1 with water flow
Dia_m=0.003;Length_m= 0.524;viscocity= 0.001;
Area_sq_m= (3.14159/4)*(0.003*0.003);
H2O_Head_loss=[50 62.5 78 97.65 122 152.58 190.7 286.5 429.75];
H2O_Head_loss_m=0.001*H2O_Head_loss;
Volume_flow_H2O_cum_p_s=[75/36 100/41 100/35 125/36 150/35 150/30 175/32 200/32 225/31]*0.000001
V_mps=Volume_flow_H2O_cum_p_s/Area_sq_m;
Re_nos=1000*V_mps*Dia_m/viscocity;
f_by_Vmps_Vmps=H2O_Head_loss_m*(Dia_m/Length_m)*(2*9.81)
plot(Re_nos, f_by_Vmps_Vmps)
Results
>> Lab_code_H2O
Volume_flow_H2O_cum_p_s =
1.0e-05 *
0.2083 0.2439 0.2857 0.3472 0.4286 0.5000 0.5469 0.6250 0.7258
V_mps =
0.2947 0.3451 0.4042 0.4912 0.6063 0.7074 0.7737 0.8842 1.0268
Re_nos = 1.0e+03 *[ 0.8842 1.0352 1.2126 1.4737 1.8189 2.1221 2.3210 2.6526 3.0804]
f_by_Vmps_Vmps =[ 0.0056 0.0070 0.0088 0.0110 0.0137 0.0171 0.0214 0.0322 0.0483]
Exp 2 with Hg
Dia_m=0.003;Length_m= 0.524;viscocity= 0.0016;
Area_sq_m= (3.14159/4)*(0.003*0.003);
Hg_Head_loss=[34.38 51.57 77.35 116 174 261];next=6;
Hg_Head_loss_m=0.001*Hg_Head_loss
Volume_flow_Hg_cum_p_s=[250/33 350/37 450/39 500/34 600/33 700/30]*0.000001
V_mps=Volume_flow_Hg_cum_p_s/Area_sq_m
Re_nos=13590*V_mps*Dia_m/viscocity
f_Vmps_Vmps=Hg_Head_loss_m*(Dia_m/Length_m)*(2*9.81)
%plot(Re_nos, f_Vmps_Vmps)
for i = 1:next
friction_coef(i)= f_Vmps_Vmps(i)/(V_mps(i)*V_mps(i));
end
friction_coef
plot(log(V_mps), log(Hg_Head_loss))
% plot(Re_nos, friction_coef)
Results
>> Lab_code_Hg
Hg_Head_loss_m = 0.0344 0.0516 0.0774 0.1160 0.1740 0.2610
Volume_flow_Hg_cum_p_s = 1.0e-04 *
0.0758 0.0946 0.1154 0.1471 0.1818 0.2333
V_mps = 1.0718 1.3382 1.6324 2.0805 2.5722 3.3010
Re_nos = 1.0e+04 *
2.7310 3.4100 4.1595 5.3013 6.5543 8.4113
f_Vmps_Vmps = 0.0039 0.0058 0.0087 0.0130 0.0195 0.0293
friction_coef = 0.0034 0.0032 0.0033 0.0030 0.0030 0.0027
>>
Combined code
Dia_m=0.003;Length_m= 0.524;viscocity_Hg= 0.0016;
Area_sq_m= (3.14159/4)*(0.003*0.003);
Hg_Head_loss=[34.38 51.57 77.35 116 174 261];nexp_Hg=6;
Hg_Head_loss_m=0.001*Hg_Head_loss
Volume_flow_Hg_cum_p_s=[250/33 350/37 450/39 500/34 600/33 700/30]*0.000001
V_mps=Volume_flow_Hg_cum_p_s/Area_sq_m
Re_nos=13590*V_mps*Dia_m/viscocity_Hg
f_Vmps_Vmps=Hg_Head_loss_m*(Dia_m/Length_m)*(2*9.81)
for i = 1:nexp_Hg
friction_coef_Hg(i)= f_Vmps_Vmps(i)/(V_mps(i)*V_mps(i));
end
friction_coef_Hg
figure
subplot(2,2,1);
plot(log(V_mps), log(Hg_Head_loss))
subplot(2,2,2);
plot(Re_nos, friction_coef_Hg)
hold on
Dia_m=0.003;Length_m= 0.524;viscocity_H2O= 0.001;nexp_H2O=9;
Area_sq_m= (3.14159/4)*(0.003*0.003);
H2O_Head_loss=[50 62.5 78 97.65 122 152.58 190.7 286.5 429.75];
H2O_Head_loss_m=0.001*H2O_Head_loss;
Volume_flow_H2O_cum_p_s=[75/36 100/41 100/35 125/36 150/35 150/30 175/32 200/32 225/31]*0.000001
V_mps_H2O=Volume_flow_H2O_cum_p_s/Area_sq_m
Re_nos_H2O=1000*V_mps_H2O*Dia_m/viscocity_H2O
f_by_Vmps_Vmps=H2O_Head_loss_m*(Dia_m/Length_m)*(2*9.81)
for i = 1:nexp_H2O
friction_coef_H2O(i)= f_by_Vmps_Vmps(i)/(V_mps_H2O(i)*V_mps_H2O(i));
end
friction_coef_H2O
subplot(2,2,1);
plot(log(V_mps_H2O), log(H2O_Head_loss))
hold on
subplot(2,2,2);
plot(Re_nos_H2O, friction_coef_H2O)
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