Cover Page for Precalculations – Individual Portion
Head Losses in Pipes
Prepared by Professor J. M. Cimbala, Penn State University
Latest revision: 11 January 2012
Name:
________________________________________
Date:
________________________________________
Section number:
ME 325._____
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Precalculations
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Precalculations
Start with the quasi-steady-flow energy equation for flow between the two static pressure taps in the test specimen, as
sketched below in Figure 1. Assume that the control volume surrounds the pipe, and cuts through sections 1 and 2 where the
static pressure taps are located.
Test specimen (section of pipe)
L
Pipe wall
Control volume
V
d
V
Static pressure taps
1
2
Figure 1. Schematic diagram of the test specimen, with control volume from 1 to 2 (not to scale).
The term “quasi-steady” refers to the assumption that the volume flow rate is essentially constant, thereby eliminating
all of the time-dependent terms in the full form of the energy equation. We use the average velocity V over the cross-sectional
area for convenience, with kinetic energy correction factor  included to account for the non-uniformity of the velocity
profile. For the case of flow with one inlet and one outlet, the steady, incompressible energy equation in head form is given
as follows:
P1
g

1
V12
2g

z1

Wpump
mg

Wviscous
mg

P2
g

2
V2 2
2g
 z2

Wturbine
mg
 hL, total (4)
(3)
1.
Assuming that the flow is fully developed in the pipe, and that the pipe is horizontal, simplify Eq. (4) as much as
possible. Specifically, cross off terms in the above equation, justifying each simplification in the space below the
equation.
(2)
2.
Obtain a final expression, as Eq. (5) below, for the head loss between static taps 1 and 2 as a function of pressures
P1 and P2, along with any other necessary constants and fluid properties. Note that for this example case, there are
no minor losses, so hL , total  hmajor .
hL , total 
(5)
3.
(5)
The goal of the present experiment is to obtain values of friction factor f as a function of Reynolds number Red
through pipe sections of various diameters and surface roughnesses. In the space below, generate an equation for
friction factor f in terms of measured values of volume flow rate and irreversible head loss.
f=
(6)
(3)
4.
In the space below, generate an equation for Reynolds number Red as a function of volume flow rate.
Red =
(2)
5.
(7)
Major losses will be measured through long straight sections of various pipes. One test specimen is a section of
3/4-inch commercial galvanized iron pipe. Estimate the average roughness height for this type of pipe, and
indicate the source of your information. (Reference, page number, equation number or table number, etc.)
=
mm
Source of information:
(3)
6.
Assuming an inner diameter of 0.75 inches (the actual pipe diameter will not be exactly this), and a volume flow
rate of 8.0 gallons per minute, calculate the Reynolds number. Be careful with your units, and show all your
calculations in the space below. Note: Always include the units along with any numerical values that you write
down in your calculations.
Red = _______________________________
(2)
7.
Is the flow in this example pipe laminar or turbulent? Explain.
(5)
8.
Estimate the irreversible head loss (in inches of water) through the 3/4-inch commercial galvanized iron pipe
discussed above. Assume that the length of the pipe is L = 84.0 inches. Show all your calculations in the space
below.
hmajor =
inches of water column
(3)
9.
Assuming that the flow starts off with a uniform velocity distribution across the pipe cross section (plug flow),
how much entrance length is required to achieve fully developed pipe flow conditions in this example? (Be sure to
give a reference for any equations you use, and show all your calculations in the space below.)
Le, required =
inches
Source of information:
(2)
10. The Moody chart is sometimes difficult to read accurately because of the logarithmic scales. Fortunately, the
Moody chart is generated by using the Colebrook equation. Write the Colebrook equation in the space below, and
indicate your source of information.
Colebrook equation:
Source of information:
Experimental Objectives
a.
b.
c.
Calibrate a Venturi meter (along with a second electronic pressure transducer), so that volume flow rate can be
measured through computer data acquisition.
Measure the head loss through various kinds of pipe sections and over a range of flow rates.
Normalize the data to generate a plot of Darcy friction factor versus Reynolds number, and compare to the
published Moody Chart values (as obtained from the Colebrook equation).