Major and Minor Losses
Sarah Grace Miller
Team 6
Abstract:
A change in pressure and friction within pipes in a piping system can lead to
considerable losses within the system. These losses can come from a variety of
different things including the diameter of the pipes, the length of the pipes and the
types of fittings used. This experiment was designed to compare causes of loss. The
relationship between the slope of head loss (m) versus velocity-squared (m2/s2) and
the minor loss coefficient was found to be directly proportional, as slop increases so
does the minor loss coefficient. The relationship between diameter and the
corresponding friction factor was determined to be inversely proportional, as the
diameter of the pipe increased the friction factor decreased. Although the
relationship between diameter and friction is inversely proportional, it was also
determined that the relationship between diameter and price was directly
proportional. Therefore, an engineer must maximize diameter while minimizing
cost for the most efficient system both functionally and financially.
Introduction:
Major and minor losses in pipes are important pieces of information when
designing a piping system. Expanding the inner diameter of a pipe can reduce the
major losses, but increase the cost of building the ideal system. By evaluating a state
of a piping system, engineers attempt to build a system where major losses are
minimized as well as minimizing the cost of the project. Minor losses become a
concern if the length of pipe being used is short, or if there are a variety of valves or
turns. While minor losses may be negligible for systems with long lengths of pipe, in
smaller piping systems, like in that of a house, the minor losses become a concern.
Minor losses will affect the flow for around 10 times the length of the diameter after the
obstruction (Cengel, Cimbala 2014).
Objectives:
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The purpose of the lab is to measure the effect of pipe diameter on friction factor
(major loss) and the effect of fitting type on minor losses due in pipes.
Methods and Materials:
Using a Technovate fluid circuit system, the major loss through a piping
system was measured. A valve was used to alter the flow rate through the system.
Using Equation (1), pressure drop across the orifice was used to calculate
volumetric flow rate (Fasina, 2015.)
2𝛥𝑃𝑜𝑟𝑖𝑓𝑖𝑐𝑒
𝑄 = 𝐶𝑑 𝐴𝑜 √
𝜌(1−𝛽 4 )
(1)
An Edibon Energy Losses in Bends Module FME05 was used to measure the
minor losses in a system due to various fittings. The orifice pressure drop was used to
calculate volumetric flow rate of the system while pressure drop of the system was used
to calculate the Darcy friction factor. Equation solver was used in the Excel program to
estimate the friction factor, based on Equation (2).
𝐿
𝑉2
ℎ𝐿 = 𝑓 (𝐷)(2𝑔)
(2)
In this experiment, minor losses were calculated for various different
types of fittings, including three types of elbows, sudden contraction, sudden
expansion and a Mitre bend. . The Edibon Energy Losses in Bends Module was used
to control the flow rate throughout the system and measure the pressure drops across each
fitting at it’s respective location. Six flow rates were recorded with the corresponding
pressure readings.
𝑉2
ℎ𝑓 = 𝐾 2𝑔
(3)
Equation (3) was graphed and the slope of the trendline was used to estimate the minor
loss coefficient (K). Theoretical values for the minor loss coefficient were either
calculated or obtained from outside sources, such as Fluid Mechanics Fundamentals and
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Applications by Cengal and Cimbala (2014), and the values were compared to that of the
experimental data.
Results and Discussion:
The theoretical values for the large diameter pipe (Di=0.545 in) decreases
with increasing velocity, though the trend is slightly difficult to see (Figure 1.)
However, this trend cannot be accurately inferred using this data because the theoretical
friction factor is not a completely accurate representation of real pipe systems. The
experimental data seems to have a slightly decreasing trend, but doesn’t show much
consistency across the spectrum of data. The variation in the experimental data
could be attributed to human error throughout the experiment, such as
inconsistency when changing the flow rate with the valve, or when taking data
values.
In the second pipe with a smaller diameter (Di=0.430 in), the difference
between the experimental and the theoretical data was very miniscule, with one
slight outlier value affecting the trend, which in the grand scheme of things isn’t a
major concern (Figure 2.) Both the theoretical data and the experimental data had a
consistent negative trend, with the exception of one point in the experimental data.
This data point can be more than likely be attributed to human error.
The friction factor in the pipe with the smaller diameter is going to be higher
than that of the pipe with a larger diameter. This is due to ratio of surface area to
volume; a higher percentage of the fluid, in this case water, that ran through the
pipes was touching the walls of the pipe with the smaller diameter, creating more
friction in the fluid as a whole. A higher friction force in the system contributes to a
higher energy loss, causing the system to be less efficient, and therefore less
desirable from a design stand point.
The Edibon system was used to analyze the head loss for different
fittings that the fluid ran through. Each fitting has a corresponding minor loss
coefficient; one was determined experimentally and the theoretical value was found
using Fluid Mechanics Fundamentals and Applications by Cengal and Cimbala. The
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slope of each linear regression (Figure 3 and Figure 4) was then plugged in as the m value
in Equation (4), where g is equivalent to the gravity constant.
K=m*2g
(4)
Each experimental minor loss coefficient, K, was obtained and lead to the
understanding that the higher the slope, the higher the coefficient. The higher the minor
loss coefficient, the more energy is lost in the corresponding fitting. In the comparison of
the mitre, short bend and elbow fittings (Figure 3,) the mitre fitting had the highest slope
and therefore the highest minor loss coefficient. This means that in the mitre fitting there
was more energy loss in the face of the turn.
In the comparison of the expansion, contraction and the long bend, the highest
minor loss coefficient would belong to the expansion (Figure 4.) However, it is believed
that this value is due to an error of some kind. It would be more reasonable to have the
contraction fitting to have a higher minor loss coefficient because the surface area to fluid
volume ratio is being affected here, and as found with the major losses, the diameter of a
pipe has a lot of affect on the energy loss.
Conclusions:
The relationship between pipe diameter and fluid friction factor is inversely
proportional, the larger the diameter the lower the friction factor. However, it is
unreasonable to have an oversized pipe to decrease the friction factor due to the
increase in price for larger diameters. An engineer must find a perfect medium that
maximizes diameter while minimizing cost.
When finding a minor loss coefficient, the relationship between the slope and
the coefficient is directly proportional, as the slope increases so does the minor loss
coefficient. To decrease the minor loss coefficient, and in turn the head loss, an
engineer should avoid sharp turns and constricting the flow of a liquid with a
contraction of the pipe. Expanding the pipes in the system and using elbow fittings
will aid in the minimization of head loss.
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Graphs and Tables:
0.021
0.0205
Friction factor (f)
0.02
0.0195
0.019
0.0185
Theoretical
0.018
Experimental
0.0175
0.017
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Velocity squared (m^2/s^2)
Figure 1: Pipe friction factor (f) for Pipe 2 (inner diameter= 0.545 in, outer
diameter= 0.625 in) versus Velocity squared
0.03
Friction factor (f)
0.025
0.02
0.015
Theoretical
0.01
Experimental
0.005
0
0
1
2
3
4
5
6
Velocity squared (m^2/s^2)
Figure 2: Pipe friction factor (f) for Pipe 1 (inner diameter= 0.430 in, outer
diameter= 0.500 in) versus Velocity squared
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0.07
y = 0.0409x
0.06
elbow
Head Loss (m)
0.05
short bend
y = 0.0265x
0.04
mitre
0.03
0.02
y = 0.0106x
0.01
0
0.00
0.20
0.40
0.60
0.80
1.00
Velocity squared (m^2/s^2)
1.20
1.40
1.60
1.80
Figure 3: Head loss versus velocity squared for Elbow, Short Bend and Mitre
0.06
0.05
y = 0.0305x
Long Bend
Head Loss (m)
0.04
Expansion
0.03
Contraction
y = 0.0118x
0.02
0.01
y = 0.0697x
0
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Velocity Squared (m^2/s^2)
Figure 4: Head loss versus velocity squared for Long Bend, Expansion and
Contraction
1.80
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References:
Cengel, Y., & Cimbala, J. (2006). Fluid mechanics: Fundamentals and Applications (3rd
ed., pp. 76-111). Boston: McGraw-Hill Higher Education.
Fasina, O. Lab Handout: “BSEN 3310 Major and Minor Losses” Print. 10 November,
2015.