Abstract

The experiment was to examine the pressure losses in turbulent pipe flow due to frictional forces present at the boundaries of the pipe’s flow area

Introduction

In this experiment you will investigate the frictional forces inherent in laminar and turbulent pipe flow. By measuring the pressure drop and flow rate through a pipe, an estimate of the coefficient of friction (friction factor) will be obtained. Two different flow situations will be studied, laminar flow and turbulent flow. The experimentally obtained values of the coefficient of friction will then be compared with established results by plotting them on the Moody chart provided.

1

In order to generate a dimensionless group to describe the frictional losses experienced by a pipe flow, the Bernoulli energy equation is used generate an expression that describes the pressure losses due to friction

P1/ρ +V12 /2 +gz1-Ws +q =P2/ ρ + V2

2/2 + gz2+gh2 (eq.1)

Where ρ is the density of the fluid, P1 is the pressure of the fluid upstream, V1 is the upstream velocity of the flow, z1 is the upstream height, W s is shaft work done by the flow, q is heat addition to the flow, P2 is the downstream pressure, V2 is the downstream velocity, z2 is the downstream height of the flow, and gh L is the head loss.

Assume the pipe flow is fully developed, therefore the velocity at states one and two are equal and can be neglected. It will also be assumed that the heights of state one and two are equal and negligible, that there is no shaft work being done by the flow and that there is no heat addition to the flow. Therefore, Equation 1 can be simplified to produce the following equation.

P2-P1/ ρ =ghL (eq. 2)

2

The head loss component of Equations 1 and 2 can also be represented as a pressure drop Δh, multiplying both sides of the equation by the fluid’s density, ρ, yields the hydrostatic equation.

ΔP = ρgΔh (eq.3)

Another equation used to represent pressure losses in pipe flow is the Darcy-Weisbach equation. The equation is written as follows

ΔP = f (L/D) (ρV2/2) (eq.4)

Where ΔP is the pressure difference over a segment of conduit, f is the friction factor of the flow, L is the length over which the pressure drop is measured, D is the diameter of the conduit, ρ is the fluid’s density and V is the average velocity of the flow. Setting the hydrostatic equation equal to the Darcy-Weisbach equation yields the following expression.

ρgΔh =f(L/D)( ρV2/2) (eq.5)

Rearranging Equation 5 to solve for the dimensionless friction factor of the flow yields the following equation.

f = (2gΔh)/ (V2 (L/D)) (eq.6)

3

It is common to generate a log-log graph of the friction factor plotted against the Reynolds number for a series of volume flow rates. This diagram is known as the Moody diagram (Figure 2) and is useful to determine the characteristics of pipe flow. To calculate the Reynolds number, employ the following equation.

Re = (VD)/ν (eq.7)

Where V is the average velocity of the pipe flow, D is the diameter of the conduit and ν is the kinematic viscosity of the fluid.

4

Experimental equipment and methods

1- Ensure that the sump tank is full and engage the pump(s) specific to the pipe(s) that will be used for the experiment.

2- Open and close the appropriate valves on the apparatus (left and right side of Figure 3) to obtain the desired flow path.

3- Use the valve closest to the pump(s) on the downstream side of the apparatus to obtain a desired flow rate.

4- With the pump still running, record the pressure drop that occurs from the manometer board and record the indicated flow rate from the flow meter.

5- Using the valve closest to the pump(s), increase the flow rate and again record the pressure drops from the manometer board and the indicated flow rate from the flow meter.

6- Repeat Step 5 until separate pressure drops and flow rates have been recorded.

5

Conclusions

Results

A comparison of the Moody diagram generated from the experimental data (Figure 4) to the diagram shown in

(Figure 2) indicates that the data gathered in this experiment

is flawed. The curve in (Figure 4) shows a momentary increase in the frictional factor as the Reynolds number increases. The curve should be a decreasing exponential function as seen in the Moody diagram of (Figure 2)

6

A possible cause of the discrepancy between the generated Moody diagram and Figure 4 would be a sudden expansion of the fluid in the testing apparatus. It was noted during the experiment that the line that returns fluid back to the sump tank was exhibiting vibration. This vibration was likely due to an interference with the flow, there by interrupting the fully developed flow.

The assumptions used to derive the dimensionless friction factor of Equation 6 rely on the flow being fully developed, turbulent and steady .A sudden expansion in the line would

cause the flow to be unsteady and would skew the data.

Other sources of error were present in this experiment. One source of error was due to the measurement of the head loss, Δh, from the manometer board. Due to unsteady flow in the testing apparatus, the air over water manometer did not give a steady reading.

In order to compensate for this discrepancy, the lowest value the fluctuating fluid took was the recorded value. Another source of error was due to the flow meter of the testing apparatus. The indicated flow rates would fluctuate over a range of five to ten GPM, preventing an accurate reading of the flow rate and therefore further skewing the data

7

References

Introduction to Fluid Mechanics, 3 rd Edition William S. Janna (1993)

A Manual for the Mechanics of Fluid LaboratoryWilliam S. Janna (2008)

White, F. M. 2003, Fluid Mechanics, 5th Edition, McGraw-Hill, Chapter 6;

8