Experiment
5
Pipe
Flow: Major and Minor Losses
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Experiment 5 Description
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 (h_{l}) while
losses through fittings, etc, are called minor losses (h_{lm}).
Together they make up the total head losses (h_{lT})
for
pipe flows. Hence:
h_{lT}
= h_{l} +h_{lm
}(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, Re_{D }<
2000, where Re_{D} = r V/ n
·
V is the average velocity at a cross section.
·
h_{lT}, 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, h_{lT }= 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, 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,
L_{e}, 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.
NOTE:
Please
be careful and avoid spilling water while conducting this experiment.
PLEASE
CLEAN UP IMMEDIATELY ANY SPILLS THAT OCCUR.
Figure 2 – Pipe flow
Hardware
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.
Questions
to be answered
1.
Plot the measured average flow velocities (m/s) as a function of the difference
in heights between the water in reservoir and the pipe exit for (Dz) all
six configurations, i.e. 6 mm (short), 15 mm (long and short), 20 mm (long
& short) and 15 mm (with elbows) pipes.
2.
For all six configurations, 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 (see question 1), with the velocities
predicted assuming frictionless flow (see question 2), on a plot as a function
of Dz for all configurations. Are the actual velocities higher or
lower? Discuss the physical significance of your results.
4.
Assuming that total head loss for the short pipes and the 15mm pipe with
elbows is due to minor losses only, calculate the minor head losses for
the short pipes and the pipe with elbows for all flow rates measured.
Plot the loss coefficient, K, as a function of the average Reynolds number.
Discuss the results; does K follow the trends you expect?
5.
Using the loss coefficients determined in question 4; calculate the friction
factor for the two long pipes as a function of Reynolds number. Display
this trend graphically and discuss its significance.
6.
Graphically compare the friction factors measured experimentally to those
for obtained from the Moody Chart for a smooth pipe. Comment on this
comparison.