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

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.

· ais 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 =  r V/ 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.

### 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, is usually referred to as the  Moody Plot , after L. F. Moody who first published this data in this form.

Figure 1  – Friction factor for flow through round pipes, (Moody Plot)

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.

### Apparatus

The following apparatus will be used for this experiment:
1. The pipe flow rig  with pipes of different diameters and lengths.
2. A large graduated cylinder used to measure the volume of water flowing out of the system.
3. A stop watch used to measure the time required to collect the water.
4. A pump for refilling the water reservoir.

## Experimental Procedure

1.Measure and record the heights of the base of the reservoir and the center of the pipes in the table in the data sheet.
2.Start with the reservoir filled to the highest level indicated in the data sheet for the pipe you are examining.
3.Record the exact, initial height of water in the reservoir.
4.Ensure that all manual valves to all the pipes are closed.
5.Place a graduated cylinder at the exit of the pipe you are examining.The graduated cylinder will have to be tilted to avoid spillage.
6.Open the manual valve only to the pipe under study.

7.One person should operate the stop-watch and the solenoid switch, which starts the flow.

8.Open the solenoid valve and start the stop-watch simultaneously.

9.Shut off the valve and the stop-watch simultaneously when the water level drops to the next height on the table in the data sheet for this pipe.Collect all the water flowing through the piping system in the graduated cylinder.

10.Measure and record the actual height to which the water level has dropped.

11.Measure and record the volume of water collected in the graduated cylinder.

12.Record the time taken to collect the water.

13.Empty the water from the measuring cylinder into the bucket provided

14.Repeat steps 7 – 14 for all other reservoir levels indicated in the Table for this pipe.

15.Close the manual valve for this pipe.

16.Repeat steps 2 –16 for the various pipe systems specified by the lab instructor.

NOTE:For accurate measurements, the solenoid and the stop watch must be turned on and off at the same time.If there is a time lag between the two, repeat the measurement.