Pipe Friction

Pipe Friction

Summary

The purpose of this lab is to find the friction factor and Reynolds number for laminar and turbulent flow and also for values in the critical zone. Results were taken recorded and used to calculate the friction factor and Reynolds number. They were then compared with the Moody diagram.

Aim

This lab could be used in industry when dealing with a pipe line containing any type of liquid to calculate the Reynolds number and friction factor. It would also help in pipe and pump selection. It will allow for pipe diameter to be chosen for a required pressure and flow rate if the pipe friction is known. This lab reinforces the usefulness of the Moody diagram.

The aim of this experiment is to investigate the pressure drop in a pipe due to surface roughness. This is to be done using a range of flow rates that are laminar, turbulent and in the critical zone.

Theory

The Reynolds number represents the ratio of inertial forces to viscous forces within a fluid flow. This number is calculated using the diameter (D measured in metres) as the length parameter, with the viscosity of the liquid (µ in kgm.s), the density (ρ in kgm3) and the flow rate (U in ms):

Re = ρUDμ

If the Reynolds number is less than 2000 then the flow is laminar, if it is greater than 2000 it is turbulent. When the Reynolds number is approximately 2000 the flow transitions from laminar to turbulent and this is known as the critical zone.

When flow is in the laminar flow range the pressure drop (Δp) over a length (l) is proportional to the velocity:

∆pl∝U

At a higher Reynolds number, during the critical zone it is not possible to define a relationship between the pressure drop and velocity. At a higher Reynolds number again the flow is fully turbulent and the relationship between the pressure drop and velocity becomes exponential:

∆pl∝U2

When the flow rate becomes unstable the critical Reynolds number can be calculated. Normally this number is taken to be 2000.

Equipment * Stainless steel pipe (2m), internal diameter, D=6mm * Two pressure tappings on opposite ends of a manometer; these will indicate the pressure drop * Stop watch * Cylinder

Procedure

* Measure the pressure drop for a range of pipe flow rates that include turbulent flow, laminar flow and flow in the critical zone. Measure the volume flow rate at these same pressure drops using a cylinder and a stopwatch. * At each pressure drop calculate the Reynolds number (Re) and the head loss due to friction (hf):

hf=∆Pρg

* Then calculate the friction factor (f) using the Darcy-Weisbach equation:

hf=4flD U22g

* Plot a graph of log (f) against log (Re) for all flow rates. * Find the critical or transitional Reynolds number, compare with the Moody diagram.

Results

First, the velocity for laminar and turbulent flow must be found so the reading for the pressure drop can be located in either the laminar, turbulent or critical zone.

By using a Reynolds number of 2000 we can get a maximum velocity for laminar flow:

Ul=Re μρ D
Ul=2000×(1.02555×10-3)1000×(6×10-3)
Ul=0.3419 m/s

And by using a Reynolds number of 4000 we can get a minimum velocity for turbulent flow:

Ut=Re μρ D
Ut=4000×(1.02555×10-3)1000×(6×10-3)
Ut=0.6838 m/s

Also the head loss must be found for laminar and turbulent flow so the readings can be taken above and below that head loss. The friction factor (f) is read from the Moody diagram at the point where flow would change from laminar to the critical zone and from the critical zone to turbulent flow.

For laminar flow the Moody diagram shows that the friction factor should be 0.008:

Hfl=4flDU22g
Hfl=4×0.008×26×10-30.341922×9.81
Hfl=64 mm

For turbulent flow the Moody diagram shows the friction factor to be 0.0095:

Hft=4flDU22g
Hft=4×0.0095×26×10-30.683822×9.81
Hft=304 mm

4 readings are then taken below a velocity of 0.3419 m/s and with a pressure drop of under 64mm, this will indicate laminar flow. Then 4 readings are taken with a velocity above 0.6838 m/s and with a pressure drop of over 304mm, this indicates turbulent flow. Two readings are then taken between these values in the critical zone.

ρ = 1000 kgm3 g = 9.81 ms2 D = 6x10-3 m µ = 1.03x10-3 kgs.m L = 2 m

| hin (mm) | hout (mm) | hf (m) | l | m3 | Time (s) | 1. | 782 | 755 | 0.027 | 0.15 | 0.00015 | 30 | 2. | 784 | 748 | 0.036 | 0.2 | 0.0002 | 30 | 3. | 784 | 731 | 0.053 | 0.256 | 0.000256 | 30 | 4. | 788 | 729 | 0.059 | 0.3 | 0.0003 | 31.5 | 5. | 842 | 596 | 0.246 | 0.56 | 0.00056 | 30 | 6. | 846 | 553 | 0.293 | 0.65 | 0.00065 | 30 | 7. | 856 | 516 | 0.34 | 0.71 | 0.00071 | 30 | 8. | 889 | 466 | 0.423 | 0.825 | 0.000825 | 30 | 9. | 908 | 421 | 0.487 | 0.85 | 0.00085 | 30 | 10. | 908 | 406 | 0.502 | 0.86 | 0.00086 | 30 |

Using results from the 1st set:

Q=lt×1000

Q=0.1530×1000

Q=5×10-6 m3/s

U=QA

U=5×10-6π×3×10-32

U=0.18 m/s

Re=ρUDμ

Re=1000×0.18×6×10-31.03×10-3

Re=1034.60

f=hf×D×g2×L×U2

f=0.027×6×10-3×9.812×2×0.182

f=0.0127

Using results from the 7th set:

Q=lt×1000

Q=0.7130×1000

Q=2.367×10-5 m3/s

U=QA

U=2.367×10-7π×3×10-32

U=0.84 m/s

Re=ρUDμ

Re=1000×0.84×6×10-31.03×10-3

Re=4897.10

f=hf×D×g2×L×U2

f=0.34×6×10-3×9.812×2×0.842

f=0.00714

| Q (m3/s) | U (m/s) | Re | f | 1. | 0.000005 | 0.18 | 1034.60 | 0.01270 | 2. | 6.66667E-06 | 0.24 | 1379.47 | 0.00953 | 3. | 8.53333E-06 | 0.30 | 1765.72 | 0.00856 | 4. | 9.52381E-06 | 0.34 | 1970.66 | 0.00765 | 5. | 1.86667E-05 | 0.66 | 3862.50 | 0.00831 | 6. | 2.16667E-05 | 0.77 | 4483.26 | 0.00734 | 7. | 2.36667E-05 | 0.84 | 4897.10 | 0.00714 | 8. | 0.0000275 | 0.97 | 5690.29 | 0.00658 | 9. | 2.83333E-05 | 1.00 | 5862.73 | 0.00714 | 10. | 2.86667E-05 | 1.01 | 5931.70 | 0.00719 |

Discussion of Results

The results from this lab show the clear difference between laminar flow and turbulent flow. The results found compared to the Moody diagram are consistent. The Moody diagram shows that the minimum friction factor for turbulent flow would be 0.01 and the results found show it would be 0.0095. Whereas the maximum friction factor found for laminar flow would be 0.008 on the Moody diagram and the results found show it would also be 0.008.

The graph shows a clear difference in the laminar flow and turbulent flow, this was expected. The values found that should be in the critical zone are actually in the turbulent flow area, this was not expected.

Although the results found are rather accurate compared to the Moody diagram errors could have occurred in this experiment, human error is the most prominent one. It can be improved by using a more accurate way of measuring the time also a more accurate way of collecting the water and how much is collected. There could also be errors with the equipment, with how it is set up or recording data.

Conclusion

In conclusion, this lab shows that the larger the Reynolds number the higher the flow rate. It also shows how important the Moody diagram is and how useful it can be. The results prove that there is a clear difference between laminar and turbulent flow. They also show that the values taken that were thought to be in the critical zone are more likely to be classed as turbulent. Overall the aim of this experiment has been achieved.

Reference

* Mechanics of Fluids – B. S. Massey * Fundamentals of Heat and Mass Transfer – Frank P. Incropera and David P. DeWitt

Bibliography

* http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation * http://en.wikipedia.org/wiki/Reynolds_number

Bibliography: * http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation * http://en.wikipedia.org/wiki/Reynolds_number