http://www.eng.fsu.edu/~alvi/EML4304L/webpage/experiment_5.htm
Experiment 5
Pipe Flow: Major and Minor Losses
Objectives
The goal of this laboratory is to study pressure losses due to viscous (frictional) effects in fluid flows through pipes. These pressure losses are a function of various geometric and flow parameters including pipe diameter, length, internal surface roughness and type of fitting. In this experiment, the influence of some these parameters on pressure losses in pipe flows will be evaluated by measuring flow rates through different types of pipes.
Theoretical Background
Head Loss in Pipe Flows
Pipe flows belong to a broader class of flows, called internal flows, where the fluid is completely bounded by solid surfaces. In contrast, in external flows, such as flow over a flat plate or an airplane wing, only part of the flow is bounded by a solid surface. The term pipe flow is generally used to describe flow through round pipes, ducts, nozzles, sudden expansions and contractions, valves and other fittings. In this experiment we will limit our study to flow through round pipes and pipe fittings, such as elbows and valves.
When a gas or a liquid flows through a pipe, there is a loss of pressure in the fluid, because energy is required to overcome the viscous or frictional forces exerted by the walls of the pipe on the moving fluid. In addition to the energy lost due to frictional forces, the flow also loses energy (or pressure) as it goes through fittings, such as valves, elbows, contractions and expansions. This loss in pressure is mainly due to the fact that flow separates locally as it moves through such fittings. The pressure loss in pipe flows is commonly referred to as head loss. The frictional losses are referred to as major losses (hl) while losses through fittings, etc, are called minor losses (hlm). Together they make up the total head losses (hlT) for pipe flows. Hence:
hlT = hl +hlm (1)
Head losses in pipe flows can be calculated by using a special form of the energy equation discussed in the next section.
Energy Equation for Pipe Flows
Consider steady, incompressible flow through a piping system. The energy equation between points 1 and 2 for this flow can be written as:
(2)
In the above equation, the terms in the parenthesis represent the mechanical energy per unit mass at a particular cross-section in the pipe. Hence, the difference between the mechanical energy at two locations, i.e. the total head loss, is a result of the conversion of mechanical energy to thermal energy due to frictional effects.
The significant parameters in equation 2 are described below:
· z, is the elevation of the cross section, taken to be positive upwards.
· a is called the kinetic energy factor. For laminar flow a = 2, for turbulent flow a = 1.
· Flow in a pipe is considered laminar if Reynolds number, ReD < 2000, where ReD = rV/n.
· V is the average velocity at a cross section.
· hlT, as discussed earlier, is the total head loss between cross-sections 1 and 2. Details of calculating the head loss are discussed in the next section.
An examination of equation 2 reveals that for a fixed amount of mechanical energy available at station 1, a higher head loss will lead to lower mechanical energy at station 2. The lower mechanical energy can be manifested as a lower pressure, lower velocity (i.e. lower volumetric flow rate), a lower elevation or any combination of all three. It should also be noted that for flow without losses, hlT = 0 and the energy equation reduces to Bernoulli’s Equation.
Calculation of Head Loss
Major Losses
The major head loss in pipe flows is given by equation 3.
(3)
where L and D are the length and diameter of the pipe, respectively, V is the average fluid velocity through the pipe and f is the friction factor for the section of the pipe. In general, the friction factor is a function of the Reynolds number and the non-dimensional surface roughness, e/D. The friction factor is determined experimentally and is usually published in graphical form as a function of Reynolds number and surface roughness. The friction factor plot, shown in Fig. 1,(attached) is usually referred to as the Moody Plot, after L. F. Moody who first published this data in this form.
When the Reynolds number is below 2000 and the flow can be assumed to be laminar, the friction factor is only a function of the Reynolds number and is given as:
(4)
Minor Losses
The minor head losses which for some cases, such as short pipes with multiple fittings, are actually a large percentage of the total head loss - hence, not really ‘minor’ - can be expressed as:
(5)
where K is the Loss Coefficient and must be determined experimentally for each situation. Another common way to express minor head loss is in terms of frictional (major) head loss through an equivalent length, Le, of a straight pipe. In this form, the minor head loss is written as:
(6)
Loss coefficients, K and equivalent lengths can be found in a variety of handbooks; representative data for limited fittings is available in most undergraduate Fluid Mechanics texts.
The calculation of head loss for flow through a pipe with known conditions is generally carried out as follows. If the fluid velocity and the pipe diameter are known, the Reynolds number can be calculated. The Reynolds number and the pipe roughness are used to determine the friction factor, f, from the Moody plot using the appropriate curve. Once, the friction factor is known, the major head loss can be calculated from equation 3. The head loss can then be used to determine the pressure drop between two sections from equation 2. A reliable estimate of the pressure loss is critical for determining the hardware requirements, e.g. pump size, for a specific task.
Conversely, if the head loss, i.e. the pressure drop due to frictional losses, is measured then the friction factor, f, can be calculated using the energy equation. This is the case in the present experiment; the pressure drop is measured for a range of flow rates corresponding to different Reynolds number, hence the friction factor can be calculated as a function of Reynolds number. These values can then be compared to the standard Moody chart.
Apparatus
The following apparatus will be used for this experiment:
1. The pipe flow rig with pipes of different diameters and lengths.
2. A digital flow meter to measure the volumetric flow rate.
3. A digital differential pressure gage to measure the pressure drop between two locations in a pipe.
4. A digital pressure gage to measure the pressure at the bottom of the water reservoir.
5. A bucket to collect the water flowing out of the pipes.
6. A pump for refilling the water reservoir.
NOTE: Please be careful and avoid spilling water while conducting this experiment.
PLEASE CLEAN UP IMMEDIATELY ANY SPILLS THAT OCCUR.
Experimental Procedure
In performing this experiment, please proceed carefully to minimize any water spills, especially on the electronics. Wipe any spills immediately. Always keep paper towels handy.
1. Measure and record the relevant dimensions and distances listed on the data sheet.
1.1. These include: the height of the reservoir base, distances between the pressure ports on the pipes, among others. Also, record any other dimensions you think you may need even if they are not specified in the data sheet.
1.2. Record the total length of the pipe with elbows and the number and types of elbows in this configuration.
2. Start with the reservoir filled approximately to the highest level indicated in the data sheet for the pipe you are examining.
3. Ensure that all manual valves to all the pipes are closed.
4. Record the initial height of water in the reservoir.
5. Place a bucket or another collection device at the exit of the pipe you are examining. The bucket will have to be tilted to avoid spillage.
6. Open the manual valve only to the pipe under study.
7. Wait for steady flow to be established. This should only take a few seconds.
8. Once the flow is steady, the following readings should be recorded simultaneously.
8.1. The pressure drop across the pipe.
8.2. The volumetric flow rate.
8.3. The pressure at the base of the reservoir.
8.4. The water level in the reservoir.
Note: Since the readings must be simultaneous, designate members of the group for recording specific parameters. You will also need to establish a way to synchronize your measurements. The first two parameters (8.1 and 8.2) are the most critical and should be recorded with due diligence. It will be difficult to record the exact height of the water level at each reading, approximate values for this parameter are sufficient. However you need to know the uncertainty in your measurement.
9. Take 8-10 readings at roughly the water levels indicated in the data table (the levels indicated are only a guideline) as the water drains from the tank.
10. Shut off the valve and keep the bucket under the pipe until all the water flowing through the piping system has been collected.
11. Measure and record the height to which the water level has dropped in the reservoir.
12. Repeat steps 4 – 11 for the various pipe systems specified by the lab instructor.
Questions to be answered
1. Calculate average flow velocities (m/s) at each reservoir height. Plot the average flow velocities as a function of the difference in heights between the water in the reservoir and the pipe exit for (Dz) for all straight pipe configurations.
2. For same configurations as in question 1, calculate the average velocities you would obtain for Dz’s used in your measurements, if you assumed that the flow was frictionless, i.e. without any losses.
3. Compare the actual measured velocities (question 1), with the velocities predicted assuming frictionless flow (see question 2), on a plot as a function of Dz for all straight pipe configurations. Are the actual velocities higher or lower? Discuss the physical significance of your results.
4. Estimate and plot the friction factors as a function of the Reynolds numbers for all straight pipes; use a separate plot for each pipe. The plots should be on log-log scale similar to the Moody plot.
5. Graphically compare the trends in the above plots (question 4) with the Moody plot to estimate the relative roughness of each pipe. Comment on this comparison, including reasons for any discrepancies.
6. Calculate the loss coefficient, K for each elbow in the pipe with elbows, as a function of the average Reynolds number. Discuss the results; does K follow the trends you expect?
7. Using the frictions factor estimated in question 3, determine the equivalent length of a straight pipe required to produce the same head losses as the pipe with elbows.
8. Compare this length with the actual length of the pipe with elbows (if it were ‘straightened’ out). Comment on this comparison, including reasons for any discrepancies.