Assignment 102

Friction and losses in
Pipes

∆𝑃𝐿 𝑡ℎ= 𝜌𝑔ℎ𝐿

ℎ𝐿 = 𝑓
𝐿

𝐷

𝑣2

2𝑔

𝑣 =
𝑄°
𝜋

4

𝐷2

𝑅𝑒 =
𝜌𝑣𝐷

𝜇

𝑅𝑒 < 2300 𝑙𝑎𝑚𝑖𝑛𝑎𝑟 𝑓 = 64

𝑅𝑒

𝑅𝑒 > 4000 𝑡𝑢𝑟𝑏𝑙𝑒𝑛𝑡
1

𝑓
= −2𝑙𝑜𝑔

𝜀/𝐷

3.7
+

2.51

𝑅𝑒 𝑓

∆𝑃𝐿 𝑒𝑥𝑝= 𝜌𝑔(ℎ1 − ℎ2)

%𝐸 =
𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 − 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙

𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
× 10

0

Theoretical

Experimental

4

𝑄°(L/h) 𝑄°(𝑚3/s) ℎ1-ℎ2 (𝑚) v Re f ℎ𝐿 ∆𝑃𝐿 𝑡ℎ ∆𝑃𝐿 𝑒𝑥𝑝 %𝐸

1000 0.240

1600 0.280

2000

0.48

5

Rough pipe 2

Smooth pipe 5

𝜌 = 1000 𝑘𝑔/𝑚3

𝜇 = 1.002 ∗ 10−3𝑁.𝑠/𝑚

𝜀 = 0.15 𝑚𝑚

𝜀 = 0

𝐿 = 1 𝑚

𝐷 = 17 𝑚𝑚

𝐷 = 16.5𝑚𝑚

𝑄°(L/h) 𝑄°(𝑚3/s) ℎ1-ℎ2 (𝑚) v Re f ℎ𝐿 ∆𝑃𝐿 𝑡ℎ ∆𝑃𝐿 𝑒𝑥𝑝 %𝐸

1000 0.12

6

1600 0.245

2000 0.420

5
Rough pipe 2
0

1000

2000

3000

4000

5000

6000

0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04 5.00E-04 6.00E-04

Δ
P

(
P

a
)

Flow rate (m^3/s)

ΔP Rough pipe

ΔP th (Pa) ΔP Exp (Pa)

0

%

5%

1

0%

15%

20%

25%

30%

0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04 5.00E-04 6.00E-04

E
rr

o
r

%
Flow rate (m^3/s)

%Error Rough pipe

𝑄°(L/h) 𝑄°(𝑚3/s) ℎ1-ℎ2 (𝑚) v Re f ℎ𝐿 ∆𝑃𝐿 𝑡ℎ ∆𝑃𝐿 𝑒𝑥𝑝 %𝐸
1000

1600

2000

6
Smooth pipe 5
0

100

200

300

400

500

0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04 5.00E-04 6.00E-04
Δ
P
(
P
a
)
Flow rate (m^3/s)

ΔP Smooth pipe

ΔP th (Pa) ΔP Exp (Pa)
0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04 5.00E-04 6.00E-04
E
rr
o
r
%
Flow rate (m^3/s)

%Error Smooth pipe

𝑄°(L/h) 𝑄°(𝑚3/s) ℎ1-ℎ2 (𝑚) v Re f ℎ𝐿 ∆𝑃𝐿 𝑡ℎ ∆𝑃𝐿 𝑒𝑥𝑝 %𝐸
1000
1600
2000

Friction and Minor losses in Pipes

ME 309
Fluid Mechanics

Fluid Mechanics ME309

2 | P a g e

SAFETY INSTRUCTIONS

All practical work areas and laboratories should be covered by local safety regulations
which must be followed at all times.

Hot Surfaces and Liquids

The unit incorporates a pumped electric water heater, and is capable of producing
temperatures that could cause skin burns.

Before disconnecting any of the pipes or tubing:

 Stop all the pumps.

 Leave time for the water to cool

 Check that the temperature is at a safe level

 Do not touch any surfaces close to ‘Hot Surfaces’ warning labels, or any of the
interconnecting tubing, whilst the equipment is in use.

General Instructions

 If a spill occurs, turn off the pumps (if possible without injury) and immediately

get in touch with the Laboratory Instructor or Technician.

 Ensure that protective clothing (LAB coat) and gloves are worn when handling
any of the substances used in the reactor.

 Shorts or skirts should not be worn to the lab.

 Sandals, high heels, or open-toe shoes are not acceptable.

 Safety glasses are a required item to be worn in all areas of the laboratories.

 Electrical – Burn / Shock: Care with electrical connections, particularly with
grounding, and not using frayed electrical cords, can reduce hazard.

Fluid Mechanics ME309 3 | P a g e

Contents
Objective …………………………………………………………………………………………………………………………………….. 4

Introduction …………………………………………………………………………………………………………………………………. 5

Theory…………………………………………………………………………………………………………………………………………. 6

Rig Specifications: …………………………………………………………………………………………………………………………. 8

Procedure: …………………………………………………………………………………………………………………………………… 8

Analysis: ………………………………………………………………………………………………………………………………………. 8

Data tables:………………………………………………………………………………………………………………………………….. 9

References …………………………………………………………………………………………………………………………………… 9

List of tables:

Table 1 data calculations regarding smooth pipes …………………………………………………………………………….. 9

Table 2 data calculations regarding rough pipes ……………………………………………………………………………….. 9

Fluid Mechanics ME309 4 | P a g e

Objective

This unit (Figure 1) is designed to study the behavior of internal flows. It makes it possible
to study pressure drops in pipes as well as in different hydraulic accessories. The losses
by friction in straight pipes of different sizes can be studied on a certain range of Reynolds
number. The objective of this experiment is to determine the pressure loss and the
friction factor f for the following:

 Rough pipe (PVC covered in sand) with an internal diameter

of 23 mm (3).

 Smooth pipe (PVC) with an internal diameter of 26.5 mm (6).

The loss coefficient of two valves is determined as well, namely:

 Angle seat valve (7).

 Gate valve (8).


The experimentally determined values will be compared to theoretical and existing
values. Please refer to the schematic sketch (figure. 2) in the appendix section to locate
the different segments and devices according to the numbers given above.

Learning Outcomes & relationship to ABET Student Outcomes (SO)

Experiment Name Learning Outcomes ABET Student Outcomes

Friction and Minor Losses in Pipes

To confirm the head loss

predicted by a pipe friction

equation associated with flow of

water through a smooth pipe.

b, g, i

* b: An ability to design and conduct experiments, as well as to analyze and interpret

data.

* g: An ability to communicate effectively.

* i: Recognition of the need for, and an ability to engage in life-long learning

Performance indicators for SO; Students are expected to be able to

SO (b) 1. Design an experiment plan

2. Identify variables and acquire data related to the experiment

3. Compare obtained data and results to appropriate theoretical models

4. Explain observed differences between model and experiment

SO (g) 1. Deliver an organized written document

Fluid Mechanics ME309 5 | P a g e

Introduction

Energy losses in pipe flows are the result of friction between the fluid and the pipe walls
and internal friction between fluid particles. Minor (secondary) head losses occur at any
location in a pipe system where streamlines are not straight, such as at pipe junctions,
bends, valves, contractions, expansions, and reservoir inlets and outlets. In this
experiment, you will measure minor head losses through a pipe section that has several
bends, transitions, and fittings.

Figure 1 Experimental apparatus.

Figure 2 Schematic sketch of the apparatus.

Fluid Mechanics ME309 6 | P a g e

Theory

A quantity of interest in the analysis of pipe flow is the pressure drop ∆P since it is
directly related to the power requirements of the fan or pump to maintain flow. For
laminar flow, the pressure drop can be
Expressed as:

A pressure drop due to viscous effects represents an irreversible pressure loss, and it is
called pressure
Loss ∆PL to emphasize that it is a loss (just like the head loss hL, which is proportional to
it).

Note from Eq. 1 that the pressure drop is proportional to the viscosity µ of the fluid, and
P would be zero if there were no friction. Therefore, the drop of pressure from P1 to P2
in this case is due entirely to viscous effects, and Eq. 1 represents the pressure loss ∆PL
when a fluid of viscosity flows through a pipe of constant diameter D and length L at
average velocity Vavg.

In practice, it is found convenient to express the pressure loss for all types of fully
developed internal flows (laminar or turbulent flows, circular or noncircular pipes,
smooth or rough surfaces, horizontal or inclined pipes) as:

For fully developed laminar flow in circular pipes, the Darcy-Weisbach friction factor f can
be found using Eq. 3. Where Re in Eq. 3 is the Reynolds number and is given by Eq. 4

Fluid Mechanics ME309 7 | P a g e

The flow can be treated as laminar so long as Reynolds number is less than 2300. For RE
> 2300 (i.e. for transitional and fully turbulent regions) the Colebrook equation is used to
find the friction factor.
Where ε/D is the relative roughness of the pipe (ε/D = 0 for smooth pipes). As seen from
Eq. 5, the friction factor ƒ appears on both sides of the equation; that’s, the equation is
implicit in ƒ and must be solved iteratively. Alternatively, Eq. 7 is an approximate
expression of the Colebrook equation and can be used to solve explicitly for ƒ. The
resulting values are within 2 percent of those obtained using Colebrook equation.

The fluid in a typical piping system passes through various fittings, valves, bends, elbows,
tees, inlets, exits, enlargements, and contractions in addition to the pipes. These
components interrupt the smooth flow of the fluid and cause additional losses because
of the flow separation and mixing they induce. In a typical system with long pipes, these
losses are minor compared to the total head loss in the pipes (the major losses) and are
called minor losses.

Minor losses are usually expressed in terms of the loss coefficient KL (also called the
resistance coefficient), defined as:

The loss coefficient K can be indirectly found by measuring the pressure drop ∆Ptotal across
the whole pipe line (including the fitting/valve) and then subtracting the pressure loss due
to friction yielding the loss due to the fitting only. In Eq. 8, L refers to the pipe length
excluding the fitting in question.

P.S. Please refer to Fluid Mechanics textbook by Fox and McDonald (Chapter 8-
Section 8.1 & 8.2)

Fluid Mechanics ME309 8 | P a g e

Rig Specifications:

The device includes the FME00 hydraulic bench and has a rotameter incorporated (range:
600-6000 ƪ/h).
The experiment offers a multitude of possibilities and the reader is advised to refer to the
schematic drawing (Fig. 2) to acquaint him/herself with them.

The circuits have 7 ball valves (V1-V7), required to distribute the flow through the
different elements tested. The equipment has differential anti-obturant pressure sensors,
located at the beginning and at the end of every element studied. Each one of them
connects easily to Bourdon tube pressure gauges (24) and to differential water
manometers (25). The Bourdon tube will be used to measure large differences of
pressure, while the water manometer will be used to measure small differences of
pressure.

Procedure:

N.B. Make sure to carry out the necessary calibration before performing the
experiment.
The steps of this experiment go as follows:

1. Open only the ball valve that would direct the flow rate through the pipe segment or
the fitting desired (keep the rest closed).
2. Switch on the pump on the hydraulic bench.
3. Carefully open both valves until you reach the desired flow rate (directly read on the
rotameter).
4. Wait until a steady flow is established throughout the pipe line
5. Plug in the pressure probes on both ends of your test segment (use the differential
manometers for small pressure differences).
6. If the manometers go o_-bound in the previous step, unplug them and attach the
Bourdon tube probes in their places.
7. Measure the length of the test segment, excluding the fitting, for use in equations 2
and 8.
8. Take different readings for different Reynolds numbers.
9. Repeat the above steps for a different test segment and/or fitting.

Analysis:

1. Compare the experimental loss-coefficient values for different fittings to those
found in a fluid mechanics text book (or another source). Be sure to cite the source
of the published values.

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2. Does the static pressure increase or decrease for the enlargement and contraction?
Explain the increase or decrease in static pressure.

3. What is the advantage of expressing the friction factor as a function of the Reynolds
number rather than as a function of the flow rate?

4. Why are two different pressure transducers used to measure the head loss? (The
answer isn’t explicitly in the lab manual!)

Data tables:

Table 1 data calculations regarding smooth pipes

Table 2 data calculations regarding rough pipes

References

1. Fluid Mechanics: Fundamentals and Applications, Cengel, Y. and Cimbala, J., Third Edition in. (n.d.).

(Edibon AFT User’s Manual.)

𝑸 (𝒎
𝟑

𝒔⁄ )
∆𝑷 (𝒑𝒂) ∆𝑨 (𝒎𝟐) 𝑽𝒂𝒗𝒈 (

𝒎
𝒔⁄ ) 𝑹𝒆 𝒇𝒕𝒉𝒆𝒐 𝒇𝑬𝒙𝒑 % Error

𝑸 (𝒎
𝟑
𝒔⁄ )
∆𝑷 (𝒑𝒂) ∆𝑨 (𝒎𝟐) 𝑽𝒂𝒗𝒈 (
𝒎
𝒔⁄ ) 𝑹𝒆 𝒇𝒕𝒉𝒆𝒐 𝒇𝑬𝒙𝒑 % Error