1
Major & Minor Losses
Lucas White
Group 4
Abstract
The Modules used in this lab were the Technovate fluid circuit and the Edibon Energy Loss in
Bends Module. From the gathered data using the Technovate fluid circuit, the friction coefficients for the
two pipes of different diameters were calculated to confirm the benefit of using a pipe with a greater
diameter to reduce head loss over the length of the pipe. These values were compared to the theoretical
values calculated using the Colebrook Equation. The experimental error was greater for pipe 3 (25%)
than pipe 4 (11.4%). This indicates the slower velocity makes for more consistent data. The data
gathered using the Edibon Energy Loss in Bends Module was used to calculate and plot the minor loss in
each fitting versus the squared velocity. The slopes of each trendline was obtained from the plots to
calculate the experimental loss coefficient, K, and was compared to the theoretical K obtained from the
textbook. When compared, the K values for the elbows fall within 10% experimental error, and the K
values for the expanding and contracting fittings exceed 50%. This high error is somewhat due to human
and systematic error, but is ultimately due to the method used in the calculation of the experimental K.
Introduction
Fluids flowing through a pipe carry a
certain amount of energy. Some of that
energy is lost due to friction.
The roughness of pipes varies with material,
even new pipes have an interior roughness.
A higher roughness can cause
Figure 1: Major Loss
𝑃1 𝑉1
+
+ 𝑧1 + ℎ𝑝𝑢𝑚𝑝
𝜌𝑔 2𝑔
𝑃2 𝑉2
=
+
+ 𝑧2 + ℎ𝑇 + ℎ𝐿
𝜌𝑔 2𝑔
In the above equation, hL is the measure of
energy lost in the form of pressure drops
between two points in the flow.
The total energy lost can be
categorized as major loss or minor loss. The
major loss (head loss) is the energy lost due
to friction in the straight section of the pipe
(Cengel & Cimbala, 2014). The friction
acting on the fluid is created from contact
with the surface of the pipe (Spellman,
2008).
𝐿 𝑉2
ℎ𝐿 = 𝑓
𝐷 2𝑔
(Image Source: Spiraxsarco, 2010)
more turbulence in a flow, which leads to
more head loss across the length of the
pipe due to swirling and friction. The
roughness is subject to change as a result of
age and corrosion (Spellman, 2008). The
length and diameter of the pipe are factors
in the frictional contact with the flowing
fluid. A pipe with shorter length has a loss
due to friction. However, the larger the
diameter of the pipe, the less head loss. A
large diameter means less contact with the
fluid per unit volume passing through the
pipe. Also, a pipe with a smaller diameter
2
has a higher velocity than a larger diamerter
pipe with the same volumetric flow rate. A
higher velocity leads to a higher turbulence
and head loss (Cengel & Cimbala, 2014).
In addition to the losses due to the
friction of the interior surface of the pipe,
there are losses due to the flow through
valves and fittings. There are several types
of fittings: elbows of varying angles,
expansions and contractions of diameter,
Methods & Materials
Materials
The Techovate fluid circuit system consists
of several flowmeters and copper pipes.
Four manometers were used to take
readings from two copper pipes of differing
diameters and an orifice flowmeter. There
Figure 3: Technovate Circuit System
Figure 2: Minor Loss
(Image Source: L. White)
(Image Source: Slidesharecdn, 2013)
and valves. The losses in these fittings and
valves are rather minor when compared to
the head loss, therefore, it’s referred to as
minor loss (Cengel & Cimbala, 2014).
𝑉2
ℎ𝑓 = 𝐾
2𝑔
Each fitting and valve has a varying loss
coefficient, K. For sudden enlargements in a
pipe from a smaller diameter to a larger
diameter, the K value is found to be:
𝐷1 2
𝐾 = [1 − ( ) ]
𝐷2
2
(Pope, 1997). For most fittings and valves,
the manufacturers provide this value.
were several connection points at specific
locations on the pipes and flowmeters. Two
pairs of clear tubes were used to get
readings at theses connection points, which
was taken from the manometers.
The Edibon Energy Loss in Bends
Module consisted of six fittings: a long
elbow, expanding section, contracting
section, medium elbow, short elbow, and a
right angle fitting. Figure 4: Edibon Module
All fittings were
connected by
pipes with an
inner diameter of
20mm (excluding
the 40 mm
expansion and
contraction pipe).
Manometers were (Image Source: L. White)
connected to
3
specific points along the module to
measure the pressure drop at each fitting.
additional trials. The clear tubes connected
to both ends of pipe 3 were disconnected
and connected to both ends of pipe 4. The
process for pipe 3 was repeated for pipe 4.
Methods
The Techovate fluid circuit system
was used to find the major loss on water
flowing through two pipes of differing
diameters and an orifice manometer. The
clear tubes were connected to the specified
pipe (Pipe #3) and the orifice flowmeter.
The flow rate was adjusted until the
maximum Pdrop across the orifice was
obtained. The Pdrop across the orifice and
pipe were recorded from the manometers.
The flow rate was adjusted to be lower and
the above process was repeated for 5
The Edibon Energy Losses in Bends
Module was used to measure the minor
losses in several types of fittings. The flow
rate was adjusted until a Pdrop near 60mm
could be observed in the right angle fitting
manometers. The Pdrop of each fitting was
recorded and the flow rate was determined
by closing the drain of the dump tank and
observing the rate of volume change in the
tank. The flow rate was lowered and the
process was repeated for 5 additional trials.
Calculations
The energy equation represents the constant amount of energy in a system. Whether
the energy is transformed or transferred, it is neither created nor destroyed.
𝑃1
𝑉
𝑃
𝑉
+ 2𝑔1 + 𝑧1 + ℎ𝑝𝑢𝑚𝑝 = 𝜌𝑔2 + 2𝑔2 + 𝑧2 + ℎ𝑇 + ℎ𝐿 (m)
𝜌𝑔
The head loss, hL, is obtained from the sum of head loss from the pipe and minor loss
from any valves or fittings attached to the system, or from the simplified energy equation.
𝑃
𝑃
ℎ𝐿 = ℎ𝑚𝑎𝑗𝑜𝑟 + ℎ𝑚𝑖𝑛𝑜𝑟 = 𝜌𝑔2 − 𝜌𝑔1
(EQ. 1)
The major loss was calculated from the pressure drop data taken from the manometers
and the below equation was used to solve for the experimental friction coefficient, f.
𝐿 𝑉2
ℎ𝐿,𝑚𝑎𝑗𝑜𝑟 = 𝑓 𝐷 2𝑔
(EQ. 2)
f = friction coefficient (no unit)
L = length of section of pipe (m)
D = inner diameter of pipe (m)
V = velocity of fluid flow (m/s)
The theoretical friction coefficient was calculated using the Colebrook Equation and the
Goal Seek function in Microsoft Excel.
1
√𝑓
𝜀
𝐷
= −2.0 log( 3.7
+
2.51
𝑅𝑒√𝑓
) (EQ. 3)
4
The minor losses were calculated from the pressure drop data taken from the
manometers and the below equation was used to solve for the experimental loss coefficient, K.
K= (slope of trendline) x 2g
(EQ. 4)
The theoretical loss coefficient for the expanding section (EQ. 4) and contracting section
(EQ. 5) of the pipe was calculated using the following equation.
𝐷
2 2
𝐾 = [1 − (𝐷1) ]
(EQ. 5)
2
Results & Discussion
After the calculations of the velocity,
head loss, and friction coefficient, the
calculated data was plotted in the graph
below. Figure 3 is a graph of the calculated
friction coefficient values versus the
squared velocity for two pipes of different
diameters. According to the graph, the
experimental friction coefficient values are
slightly larger than the theoretical values.
The average difference in theoretical and
experimental friction coefficient values for
pipe 3 is 0.00565 with an average
experimental error of 25%. The error is due
to human error in the gathering of data.
Despite the large experimental error, the
experimental and theoretical values were
consistently within a 0.01 range.
The average difference in theoretical
and experimental data for pipe 4 was
0.00237 with an average experimental error
was 11.4%. The data gathered from pipe 4
was more accurate and consistent with the
theoretical values. The larger diameter of
pipe 4 causes a lower velocity than pipe 3
when similar volumetric flow rates are
applied. The lower friction coefficient
values for pipe 4 confirms that a pipe with a
larger diameter will have less head loss due
to friction. The length of the pipe is a factor
in the loss due to friction, however, both
pipes are the same length. A longer pipe
would mean more exposure to the interior
surface which leads to more head loss.
0.035
0.030
f values
0.025
0.020
0.015
0.010
0.005
0.000
0
0.5
1
1.5
2
2.5
V squared
Theoretical f (Pipe 3)
Experimental f (Pipe 3)
Experimental f (Pipe 4)
Theoretical f (Pipe 4)
Figure 4: Friction Coefficient values versus the squared velocity
3
5
Figure 4 is a plot of the minor loss of
each fitting versus the squared velocity.
From the plotted trendlines with a set zero
intercept, the slope was used in Equation 4
to calculate the experimental loss
coefficients of each fitting. According to the
graph, the right angle fitting has the highest
head loss at all velocities. This is due to the
sharp 90 degree turn without any flanges or
threads to cushion the fluid as it changes
direction abruptly, which lead to more loss.
The sudden expansion fitting has the least
minor loss because of its sudden increase in
diameter. The flowing fluid expands to fill
the pipe and experiences less loss because
of its limited contact with the interior of the
pipe. The long elbow has more loss than the
medium elbow but less loss than the short
elbow. This is due to the long elbow slowing
the direction change of the fluid. The
medium elbow changes the fluids direction
quicker with less head loss. The short elbow
transitions quicker than the long and
medium elbow and that causes more head
loss than the other two elbows. The only
notable difference between the right angle
fitting and the short elbow is the flanges of
the short elbow that lowers the loss.
0.06
y = 0.052x
R² = 0.9751
0.05
y = 0.0385x
R² = 0.9859
hL (m)
0.04
y = 0.0349x
R² = 0.9545
0.03
y = 0.0166x
R² = 0.9656
0.02
y = 0.0142x
R² = 0.9464
0.01
y = 0.0084x
R² = 0.9239
0
0.0
0.2
0.4
0.6
0.8
1.0
V squared
Long Elbow
Expansion
Compression
Medium Elbow
Short Elbow
Figure 6: Calculated minor loss versus squared velocity
Right Angle
1.2
6
The theoretical and experimental
loss coefficient values and their
experimental errors are displayed in Table
1. The theoretical loss coefficients were
calculated or found in the tables of the
textbook. The experimental errors for the
elbow fittings were within 10% error.
However, the errors of the expansion and
compression fittings exceeds 50%. This
indicates the method used to calculate the
experimental loss coefficients is not as valid
for these two fittings as it is for the elbow
fittings.
Long Elbow Expansion Contraction
Medium
Short
Right Angle
K (Exp)
0.326
0.165
0.755
0.279
0.685
1.02
K (Theo)
0.300
0.563
0.500
0.300
0.700
1.10
% Exp Error
8.56
70.7
51.1
7.13
2.18
7.25
Table 1: Experimental K values, theoretical K values, and percent experimental error
Conclusion
After gathering data and calculating
the friction coefficients for the two copper
pipes of different diameters on the
Technovate fluid circuit and the theoretical
friction coefficients using the Colebrook
equation, it’s noticeable that a pipe of
larger diameter has less loss due to friction.
A larger diameter would have less contact
with the interior surface of the pipe per unit
volume flowing through the pipe. The larger
diameter would also have a lower velocity
which made for more accurate data, a
difference in experimental error of 13.6%.
The lengths of both pipes were equal and
did not change so the group was not able to
observe the effect of length on the head
loss. According to Cengel & Cimbala, a
greater length would cause more head loss
because of a longer contact to the interior
of the pipe (Cengel & Cimbala, 2014).
The data gathered from the Edibon
energy losses in bends module was used to
calculate and plot the head loss and
squared velocity. This plot showed the right
angle fitting to have the highest loss of all
fittings used. This relatively high loss is due
to the abrupt change in the direction of the
fluid flow. From the trendlines of each plot,
the slope was used to calculate the
experimental K. The theoretical K was
obtained from the textbook depending on
the fitting. After comparison of the two K
values for each fitting, it was found that the
method used for calculating the
experimental K was accurate within 10%
experimental error of the theoretical K for
the elbow fittings. However, it was less
accurate for the sudden expansion and
contraction fittings with an experimental
error greater than 50%. Some of the error is
due to systematic and human error but
ultimately to the method used in
calculation.
7
References
Text
Cengel, Y. A. & Cimbala, J. M., 2014, Fluid Mechanics: Fundamentals and Applications. New York
City, New York: McGraw-Hill.
Spellman, F. R., 2008, The Science of Water. Boca Raton, Florida: Taylor & Francis Group.
Pope, J. E., 1997, Rules of Thumb For Mechanical Engineers. Houston, Texas: Gulf Publishing
Company.
Images
Spiraxsarco, http://www2.spiraxsarco.com/images/resources/steam-engineeringtutorials/10/2/Fig_10_2_3.gif
Slidesharecdn, http://image.slidesharecdn.com/8-fm9flowinpipesmajorlosesco3-copy130328071733-phpapp02/95/8-fm-9-flow-in-pipes-major-loses-co-3-copy-35638.jpg?cb=1364455131