Major and Minor Losses BSEN 3310

Christina Richard November 18, 2014

Abstract:

In this experiment, major and minor losses of a pipe were found. These losses were

computed by using a technovate fluid circuit system for the major losses and an Edibon Energy

Losses in Bends Module FME05 for the minor losses. For the major losses, the water flow was

pushed through a small diameter pipe and a large diameter pipe. This was to show how

diameter effects losses. For the minor losses, the effect of different fitting types were

calculated. The module contained a long elbow, a sudden enlargement, and sudden

contraction, a medium elbow, a short elbow and a right angle fitting. The K values were found

to show the amount of loss at each fitting. From the pressure drops recorded by each device,

the pressure drops, friction factors, velocity and K values were computed. For the major losses,

the large pipe friction factor versus velocity squared for the theoretical values and experimental

values were close. This shows that the calculated values are accurate for the large diameter

pipe. For the small diameter pipe, the percent error between the theoretical and experimental

values were high. The theoretical values were much higher than the experimental because they

did not take everything in the pipe into effect. When comparing the large and small pipes, the

theoretical data is much more accurate in the large pipe than in the small pipe. In the minor

losses, the pressure drop versus the velocity squared values were plotted. As the velocity

increases, the pressure drop increases. The right angle fitting had the highest head loss, while

the enlargement fitting had the smallest head loss. From the slope of each fitting, the

experimental K value was found. These experimental values were compared to by theoretical

fitting values. The highest percent error of the fitting was from the contraction, while the

lowest percent error was from the right angle fitting. The errors come from the theoretical

(calculated) values do not take everything from the pipe into account when being calculated.

Introduction:

The major and minor losses in pipes is due to the friction in the pipes and the fitting

type of each pipe and the connection. These losses effect the volumetric flow rate of the fluid

through the system. The volumetric flow rate is the velocity of the fluid multiplied by the cross-

sectional area. Major losses are due to friction while, minor losses are due to the velocity

change in bends, valves and changes in area. Major losses are formed in long length pipes and

are due to the head loss in the straight sections. A head loss is a pressure drop in the pipes. If

there were no friction in the pipe, the head loss would be zero. The smoother the material of

the pipes, the less friction against the walls of the pipe that is formed. In minor losses, the

components such as valves and bends interrupt the flow of fluid and cause additional losses to

the system due to flow separation and mixing. (Cengel, Cimbala, 2014) The loss coefficient for

these head losses is 𝐾𝐿. The loss coefficient is found by the pressure loss divided by the

dynamic pressure. The pressure drop for the minor losses can be found by using equation 1

(Cengel, Cimbala, 2014).

ℎ𝑓 = 𝐾𝑉2

2𝑔 (1)

The loss is almost negligible for well-rounded inlets while, for sharp-edged piping, the loss

increases significantly. This is because fluids cannot make sharp-edged turns very well which

causes about half of the velocity head to be lost. The fluids flowing off of the sharp edges are

constricted into the vena contracta area. This is where velocity increases then decreases across

the pipe. The loss when using gradual expansion of pipes compared to using sudden expansion

is minimal. Minor losses in pipes can turn into major losses in pipes, such as leaving a valve half

way closed.

The friction formed in the pipes can be found by using the Colebrook equation (Cengel,

Cimbala, 2014) and solving for the friction factor, 𝑓.

1

√𝑓= −2.0 log (

𝜀

𝐷

3.7+

2.51

𝑅𝑒√𝑓) (2)

When a fluid is a fully developed turbulent flow, the friction factor depends on the Reynolds

number and the relative roughness. The Reynolds number determines if a flow is laminar,

turbulent, or transient. The relative roughness is the ratio of the mean height of roughness of

the pipe to the pipe diameter. When solving for the friction factor using the Colebrook

equation, it must be solved iteratively. An approximate equation was formed by S. E. Haaland

(Haaland 1983) as

1

√𝑓≅ −1.8 log[

6.9

𝑅𝑒+ (

𝜀

𝐷

3.7)1.11] (3)

The results receive from this equation were within 2 percent of the results from the Colebrook

equation. (BOOK reference) Another way to obtain the friction factor is to use the Moody chart.

It uses the relationship of Reynolds number and the relative roughness to find the friction

factor. The friction factor is used for finding major losses in piping systems. The Hazen-Williams

equation is used by many engineers in order to accurately estimate the friction factor because

it is much easier to calculate. However, it has limitations especially in irrigation systems. This

equation requires constant temperature which irrigation systems cannot use accurately. (Allen,

1996) This shows that there are many ways to calculate the friction factor.

Objective:

The objective of this experiment was to measure the major and minor losses in piping

systems due to the friction factor and the fitting type of the pipes.

Methods and Materials:

In order to measure the major and minor loses, a technovate fluid circuit was used to

measure major losses and an Edibon Energy Losses in Bends Modules FME05 was used to

measure minor losses. For the major losses, the pressure drop due to the pipe and the orifice.

The pressure drop from the pipe was measured from a smaller pipe (0.625 inches) and a larger

pipe (1.25 inches). For both pipes, the flow rate was changed in 6 increments by valve 52 which

controlled the flow rate through the system. The pressure drop for each increment was

recorded for the loss due to the pipe and the loss due to the orifice. The volumetric flow rate

for each pipe was calculated by using the pressure drop across the orifice. The pressure drop

across the orifice was used to calculate the friction factor. The theoretical friction factor values

were calculated using the Colebrook equations.

For the minor losses, the fittings included a long elbow, a sudden enlargement from 20

mm to 40 mm, a sudden contraction from 40 mm to 20 mm, a medium elbow, a short angle,

and a right angle fitting. The valves controlled the flow rate of the water let into the system.

Seven increments of data were recorded for this system. Each pipe fitting had two tubes

showing the height of the fluid. The flow rate was changed until the last tube (tap 12) measured

to about 0 inches of water. The volumetric flow rate was found by letting water into the

reservoir for one minute after each increment and measuring the height of the amount of

water in the reservoir. The pressure drop and the velocity was calculated and plotted against

each other. 𝐾𝐿 was estimated using the trendline in excel. The theoretical values were

calculated and used in a table to compare those results to the experimental values.

Results and Discussion:

The major and minor losses of pipes are computed for the technovate fluid circuit

system and an Edibon Energy Losses in Bends Module FME05. For the major losses, the

volumetric flow rate was computed by using the equation

𝑄 = 𝐴𝐶𝑑√2∆𝑃

𝜌(1−𝛽4) (4)

The velocity of the fluid was computed by Q/A. The experimental friction factor was computed

by

ℎ𝐿 = 𝑓𝐿

𝐷

𝑉2

2𝑔 (5)

The theoretical values were for the friction factor were calculated by the Colebrook equation.

The experimental and theoretical friction factors versus velocity squared were plotted for the

large pipe and the small pipe. The large pipe graph (Figure 1) shows the values computed for

the theoretical and experimental friction factor values. For the large diameter piping, the

percent errors (Table 1) between the two values were small. This is compared to Figure 2,

which is the small diameter piping system. This graph shows that there was a large difference in

the theoretical values and the experimental values (Table 2). The large percent errors for this

pipe does not show that the experimental data was wrong, but shows that the calculated

values of the friction factor do not take into effect of all of the losses coming from the pipe. The

experimental values are much more accurate than the theoretical for real life applications.

From the data that was taken, it shows that the friction increased when the data was taken

from the small pipe compared to the large pipe. The data also shows that the friction factor

decreased as the velocity increased. This shows that there is less friction in the pipes as the

velocity increases. When comparing the theoretical and experimental values for the large and

small pipes, it shows that they theoretical data is much more accurate with a larger pipe than

with a smaller pipe.

Figure 1. Friction factor of the large pipe versus the velocity squared of major losses

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Fric

tio

n F

acto

r (f

)

Velocity Squared (m^2/s^2)

Theoretical Experimental

Figure 2. Friction factor of the small pipe versus the velocity squared for major losses

Table 1. Percent errors of the large pipe for each flow rate reading

Readings 1 2 3 4 5 6

% Error 3.09 12.34 6.21 4.87 12.14 27.66

Table 2. Percent errors of the small pipe for each flow rate reading

Readings 1 2 3 4 5 6 7

% Error 98.73 98.70 98.68 98.74 98.65 98.81 99.05

For the minor losses, the module had 6 different fittings being tested in order to

estimate the K values for each fitting. The pressure drop across each fitting was found by

subtracting the differences in height of the two tubes. The velocity was found by using the total

volume of the reservoir for each reading and the area of the pipe. The area of the pipe was

0.000314 m^2. This area was used constantly across the pipe because even for the expansion

and contraction, the smallest volume was used because it causes the greatest velocity. The

pressure drop for each fitting versus the velocity squared was graphed on Figure 3. This graph

shows that the pressure drop increased as the velocity increased for each fitting. The lowest

pressure drop across a fitting was for the enlargement fitting while the largest pressure drop

was across the right angle. The pressure drop for the elbows was increasing order from the long

elbow, medium elbow, and short elbow. This could be because the pressure had more time to

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 1 2 3 4 5 6

Fric

tio

n F

acto

r (f

)

Velocity Squared (m^2/s^2)

Theoretical Experimental

adjust to the fitting change with the long elbow compared to the short elbow. The experimental

K values for each fitting were calculated by using the respective slopes of each fitting. The slope

was multiplied by 2 times gravity from the equation

ℎ𝑓 = 𝐾𝑉2

2𝑔 (6)

These experimental K values were found to compare these values to theoretical values on Table

3. The contraction and enlargement fittings had the highest percent error with values of 88.84%

and 70.10% respectively. This could be because the experimental values do not take into

account the change of area over the fittings. For the elbow fittings, the percent error decreased

in the order of long elbow, medium elbow, and short elbow. This could be because of the

decreasing distance the fluid went through. The right angle had the least amount of percent

error. This shows that the theoretical values were close to the experimental values. The highest

K value was for the right angle for both the theoretical and experimental values. This shows

that it will have the highest head loss of the fittings. According to the experimental data, the

contraction then, short elbow, medium elbow, long elbow, and then enlargement fittings had

the highest to lowest K values. While, according to the theoretical data, the short elbow,

enlargement, medium elbow, contraction, and the long elbow fittings had the highest to lowest

K values. This difference is because the theoretical data does not take into account everything

about the pipe and the fitting, making the experimental data more accurate to use. The K value

is directly proportional to the pressure drop.

Figure 3. Pressure drop versus the velocity squared of the Edibon system for minor losses

y = 0.0171x

y = 0.009x

y = 0.0385x

y = 0.0214x

y = 0.0368x

y = 0.0563x

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Pre

ssu

re D

rop

(m)

Velocity Squared (m^2/s^2)

Long Elbow

Enlargement

Contraction

Medium Elbow

Short Elbow

Right Angle

Table 3. Theoretical and Experimental K values for the fittings comparison for minor losses

Long

Elbow

Enlargement

20 to 40 mm

Contraction

40 to 20mm

Medium

Elbow

Short

Elbow

Right

Angle

Theoretical 0.25 0.5906 0.4 0.5 0.74 1.1

Experimental 0.335 0.176 0.755 0.419 0.722 1.104

Percent error 34.20% 70.10% 88.84% 16.02% 2.43% 0.42%

Conclusion:

In this experiment, the major and minor losses were computed. For the major losses,

the flow was pushed through a long pipe; one with a large diameter and one with a small

diameter. For these, the fraction factor was plotted against the velocity squared of the fluid.

The graph showed that for the large pipe, the theoretical and experimental friction factor

values were close. This shows that the calculated values are close to the actual friction factor

values of the large diameter pipe. For the small diameter pipe, the percent error was around

98% for each flow reading. This shows that the calculated values are not close to the actual

experimental values. The theoretical values do not take everything into account when

calculating the value. This causes a high percent error of the small pipe. For the minor losses,

the pipe had 6 different fittings that have different losses based on the type of fitting. A graph

that compared pressure drop for each fitting versus the velocity squared was made for the

minor losses. The graph shows that the pressure drop increased as the velocity increased. The

highest pressure drop came from a right angle fitting, while the lowest pressure drop came

from an enlargement fitting. The K values were found by the slope of each fitting on the graph.

These experimental values were compared to theoretical values. The highest percent error

came from a contraction fitting and the lowest percent error came from the right angle fitting.

The differences in the fittings came from the theoretical values not taking everything about the

pipe into effect. The experimental K value was found to be directly proportional to the pressure

drop. This relates the loss coefficient (K) to the head loss of the system.

References:

R. G. Allen (1996). Relating the Hazen-Williams and Darcy-Weisbach Friction Loss Equations for Pressurized Irrigation

Yunus A. Cengel & John M. Cimbala (2014). Fluid Mechanics: Fundamentals and Applications 3rd Edition

Haaland, SE (1983). Simple and Explicit Formulas for the Friction Factor in Turbulent Flow. Journal of Fluids Engineering