Head loss due to pipe fittings experiment

TIME/DATE OF EXPERIMENT: TIME, DATE

OBJECTIVES The objectives of this lab are to:

a) measure head losses through bends, transitions, and fittings,

and use these measurements to estimate the loss coefficients for

each transition or fitting.

b) illustrate flowrate measurement by measuring the pressure

drop across a gate valve (i.e. orifice plate).

INTRODUCTION Fluids are usually transported through pipes from one location to

another using pumps. In order to size a pump for a given application, it

is necessary to predict the pressure drop which results from friction in

the pipe and fittings. Also, once a pipe system is built,

measurements of the amount of fluid flowing through the pipes

have to be performed, to ensure that the desired flow rate is

delivered by the system.

PRESSURE LOSSES

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 study only

flow through round pipes.

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 (i.e. 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 (hf)

while losses through fittings are called minor losses

(hi). Together they make up the total head losses (hL) for pipe

flows. Hence:

 

 n1i

ifL hhh



(1)

Head losses in pipe flows can be calculated by using a special

form of the energy equation that is discussed in the next section.

Energy Equation for Pipe Flows Consider a steady, incompressible flow through a piping

system. The energy equation between two points, 1 and 2, in the

flow can be written as:

L h

g

V z

p

g

V z

p 

22

2

2 2

2

2

1 1

1

 (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:

 Z - the elevation of the cross section, taken to be positive

upwards.

 V - the average velocity at a cross section.

 hL - the total head loss between cross-sections 1 and 2.

Details on how to calculate the head loss are given in the next

section.

An examination of Equation 2 reveals that for a fixed amount

of mechanical energy available at point 1, a higher head loss will

lead to lower mechanical energy at point 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,

hL = 0, and the energy equation reduces to Bernoulli’s Equation.

Calculation of Head Losses Major Losses

The major head loss in pipe flows is given by the equation:

g

V

D

L fh

f 2

2

 (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. 2, is usually

referred to as the Moody plot, after L. F. Moody who first

published such data in this form.

Flow in a pipe is considered laminar if Reynolds number,

ReD < 2000, in which case the friction factor is only a function of

the Reynolds number and is given as:

e

arla R

f 64

min  (4)

Minor Losses

The minor head losses can be expressed as:

g

V Kh

ii 2

2

 (5)

where K is a loss coefficient that must be determined

experimentally for each situation. In some cases, such as short

pipes with multiple fittings, minor losses are actually a large

percentage of the total head loss.

Another common way to express minor head loss is in terms

of frictional (major) head loss through an equivalent length, Le, of

a straight pipe. In this form, the minor head loss is written as:

g

V

D

L fh

e

f 2

2

 (6)

August 2015 ME495 - Pipe Flow Losses Page 3

The loss coefficients, K, and equivalent lengths, Le, 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 described below. 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

6. The head loss can then be used to determine the pressure drop

between two sections using equation 2. A reliable estimate of the

pressure loss is critical for determining the hardware requirements,

e.g. pump size, for a specific task.

Conversely, if the pressure drop due to frictional losses is

measured, then the friction factor, f, can be calculated using

equation 7 derived from the energy equation.

  

   

  

  



 

  

   

  

  



 

  

 



22

22 V

D

L

hg

V

D

L

p

f 

(7)

Where:

V = velocity of flow, m/s

D = inside diameter of pipe, m

 = kinematic viscosity, m 2 /s

p = friction pressure drop over length L, Pa = kg m -1  s

-2

L = length of pipe generating pressure loss p, m

g = acceleration of gravity, m/ s 2

h = manometer head due to friction pressure drop, m

 = density of manometer fluid

This is the case in the present experiment; the pressure drop

is measured for a range of flow rates corresponding to different

Reynolds number. Hence, the calculated friction factor can be

plotted as a function of Reynolds number on a layout resembling

the standard Moody chart (Equation 8 may be used to plot parts of

the Moody chart).

EXPERIMENTAL APPARATUS — The pipe flow losses test rig consists of an Armfield© Hydraulics Bench and a Losses

in Bends bench top module. Figure 1 shows a schematic of the

bench top module consisting of the following pipe fittings:

 Area enlargement

 Area contraction

 Long bend

 Short bend

 Elbow bend

 Mitre bend  Gate valve (Orifice Plate)

Figure 1—Losses in Bends bench top module.

Technical Data ID of main pipe = 0.0196 m

ID of enlargement outlet and contraction inlet = 0.0240 m

EXPERIMENTAL PROCEDURE 1. Open all valves on the bench top module, then power on the

hydraulic bench.

2. Adjust the flowrate (use valve located on hydraulic bench)

until output flow appears fully developed and non-turbulent

(should be relatively low flow rate)

3. Close the flow control valve located on bench top module,

and ensure that all manometers are leveled with each other.

Consult TA if manometers are not leveled.

4. Open the flow control valve, and ensure that all manometer

readings are stable and read within 0 and 440 mmH2O. If not,

adjust the flowrate accordingly.

5. At a set flowrate, record the manometer readings for all of the

pipe fittings as well as measure the flowrate using the

hydraulic bench volumetric readout and a timer. Record all

these values on the tables provided in Appendix 1, and run

the experiment three times using different flowrate settings

for each run.

Note: The gate valve takes 6 full rotations to close. To

reduce the gate valve to 67% open, simply turn the

handle 2 full rotations from fully open. To reduce the

gate valve to 33% open, turn the handle 4 full rotations

from fully open.

EXPERIMENTAL RESULTS and DISCUSSION

For Pipe Fittings 1. Rank the pressure drops, in order, from highest to lowest for

all of the pipe fittings.

2. Explain the physical meaning of the term “loss coefficient”.

3. Calculate the loss coefficients for all of the pipe fittings.

Tabulate the data and explain why the loss coefficients are

different between the pipe fittings.

4. Discuss the results and comment on whether or not K (loss

coefficient) follows the trends you expect.

5. Calculate the straight length equivalent for each pipe fitting

assuming the same pipe characteristics (ID, internal pipe

roughness, etc.).

6. Estimate the friction factor as a function of the Reynolds

number for all sections of the pipe (including gate valve).

7. Plot the calculated values of the friction factor on the Moody

diagram (use a computer code for this plot). Note that you

will have to plot parts of the Moody diagram using the

equation provided in Figure 2 (below the diagram).

8. Comment on the uncertainty of your results, by answering the

following questions:

a. How accurate are your results?

b. What uncertainty (or resolution) would you assign to the

measurements?

c. Based on the level of uncertainty in your measurements,

how are other quantities (friction factor, Reynolds

number) affected?

August 2015 ME495 - Pipe Flow Losses Page 4

For Orifice Plate (Gate Valve) 1. For the gate valve, using the experimental data, determine the

orifice coefficient, C0. Why do the values of C0 vary with the

gate-position/flowrate?

2. Using the derived equation that relates the velocity to the

pressure drop (as learned in Fluid mechanics), calculate the

flowrate of the fluid through the orifice plate for each

pressure drop. Compare calculated flowrate with the

measured flowrate.

3. What are the advantages of using an orifice meter over other

types of flowmeters? What are the disadvantages?

Figure 2 – Moody diagram.

The function used to plot the curves from Moody diagram (friction factor, f, vs. Re) in the turbulent region is

 





 





 





 



 

 2

9.0

74.5

7.3 log

25.0

e RD

f



(8)

Where:

f = friction factor, dimensionless

Re = Reynolds number, dimensionless

D = Diameter of pipe, m

 = Average roughness of pipe inside wall (asperities are measured root to tip), m.

Note: 1) Use SI units throughout your report.

2) When submitting the report, each team member must also submit a peer evaluation form. The form is in

the appendix of this handout.

10 10 4

10 10 10 10 5 6 7 83

0.008

0.009

0.015

0.025

0.020

0.010

0.030

0.040

0.050

0.060

0.070

0.080

0.090

0.10

Reynolds Number, Re = VD

F ri c ti o n F

a c to

r f =

h f

(L /D

)V /(

2 g )

2

0.00001

0.00005

0.0001

0.0002

0.0004 0.0006 0.0008 0.001

0.05

0.04

0.03

0.02

0.01

0.015

0.008

0.006

0.004

0.002

R e la

ti v e R

o u g h n e s s , /D

Laminar Flow

Critical Zone

Transition Zone

L a

m in

a r F

lo w

f = 6

4 /R

e

/D = 0.000005

/D = 0.000001

Complete Turbulence, Hydraulically Rough

Hydraulically Smooth

k



k

k

August 2015 ME495 - Pipe Flow Losses Page 5

APPENDIX — DATA SHEET FOR PIPE FLOW LOSSES

Time/Date: ___________________

Lab Partners____________________________ ____________________________

____________________________ ____________________________

TEST 1, Part 1

Fitting Manometer

(h1) Manometer

(h2) Total Head Loss

(h1-h2) Volume

(L) Time (s)

Flow Rate (L/min)

MITRE

ELBOW

SHORT

LONG

CONTRACTION

ENLAGEMENT

GATE VALVE (100%)

TEST 1, Part 2

Fitting Manometer

(h1) Manometer

(h2) Total Head Loss

(h1-h2) Volume

(L) Time (s)

Flow Rate (L/min)

GATE VALVE (~67%)

GATE VALVE (~33%)

TEST 2, Part 1

Fitting Manometer

(h1) Manometer

(h2) Total Head Loss

(h1-h2) Volume

(L) Time (s)

Flow Rate (L/min)

MITRE

ELBOW

SHORT

LONG

CONTRACTION

ENLAGEMENT

GATE VALVE (100%)

TEST 2, Part 2

Fitting Manometer

(h1) Manometer

(h2) Total Head Loss

(h1-h2) Volume

(L) Time (s)

Flow Rate (L/min)

GATE VALVE (~67%)

GATE VALVE (~33%)

August 2015 ME495 - Pipe Flow Losses Page 6

TEST 3, Part 1

Fitting Manometer

(h1) Manometer

(h2) Total Head Loss

(h1-h2) Volume

(L) Time (s)

Flow Rate (L/min)

MITRE

ELBOW

SHORT

LONG

CONTRACTION

ENLAGEMENT

GATE VALVE (100%)

TEST 3, Part 2

Fitting Manometer

(h1) Manometer

(h2) Total Head Loss

(h1-h2) Volume

(L) Time (s)

Flow Rate (L/min)

GATE VALVE (~67%)

GATE VALVE (~33%)

Name: ME 495 Lab

Group #:

Peer Evaluation Grade your teammates – be honest: A – Work is exemplary, exciting, engaging. This student made a positive, active, and essential contribution to the team. Outstanding effort

B – Student was a willing participant. Contribution was positive and exactly what was expected. Very good effort and solid work.

C – Fair to average effort. Only worked on tasks when they were assigned. Not much volunteering.

D – Irresponsible and didn’t contribute to the team effort. Hurt team.

F – Who is this person? Were they on our team? Never heard of him/her….. Grade Name