06. Experiment Name: Determination of the Friction Factor for Pipes.

Objective:

To determine the friction factor (f) for pipes of different materials and diameters under
varying flow rate and flow regimes. i.e laminar flow, turbulent flow.

Introduction:

The friction factor is determined by measuring the pressure head deference between two
fixed points in a straight pipe with a circular cross section for a steady flows. The friction
factor can be defined in terms of the pressure drop and the air mass velocity. In engineering
application, it is important to increase pipe productivity, i.e. maximizing head loss per unit
length. The total energy loss in a pipe system is the sum of the major and minor losses. Major
losses are associated with frictional energy loss that is caused by the viscous effects of the
fluid and roughness of the pipe wall. Major losses create a pressure drop along the pipe since
the pressure must work to overcome the frictional resistance. The Darcy-weisbach equation is
the most widely accepted formula fore determining the energy loss in pipe flow. we can
measure friction factor from this formula. In this equation friction factor (1), a dimensionless
quantity is used to described the friction loss in a pipe. In laminar flows, I is only a function
of the Reynolds number and is independent of the surface roughness of the pipe. In Jully
turbulent flows, & depends on both the Reynolds and relative roughness of the pipe wall. In
engineering problem f is determined by using the moody diagram. create a pressure drop
along the pipe since the pressure must work to overcome the frictional resistance. The Darcy-
weisbach equation is the mast widely accepted formula for determining The energy loss in
pipe flow. we can measure friction factor from this formula In this equation friction factor (f),
a dimensionless quantity is used to described the friction loss. in a pipe. In laminar flows, &
is only a function of the Reynolds number and is independent of the surface Roughness of the
pipe. In fully turbulent flows, & depends on both the Reynolds and relative roughness of the
pipe wall. In engineering problem f is determined by using the moody diagram.

Theory:

The friction factor in pipes is a dimensionless quantity that represents the resistance due to
friction in the flow of a fluid through a pipe. For a fully developed flow in a straight, circular
pipe, the Darcy-Weisbach equation is commonly used: In Bernouli’s equation as shown
below, he represents the head loss due to the friction between the fluid and the internal
surface of the constant diameter pipe as well as the friction between the adjacent fluid layers.

P1/ρg +V12 /2g +Z1= P2/ρg +V22 /2g +Z2+hf

This will result in a continuous change of energy from a valuable mechanical form to a less
valuable thermal form that is heat. This change of energy is usually referred to as friction
head lass, which represents the amount of energy converted into heal per unit weight of fluid.
The head loss (hf) in pipe due to friction can be determined using Darcy-Weisbach equation,
hf =(4fLV2 )/(2gD) ; for turbulent flow.

hf = 32fLQ2 /(π2gD5); for Laminar flow.

where:

p= is the pressure drop across a length of pipe,

f= is the friction factor,

l= is the length of the pipe,

D=is the diameter of the pipe,

D=is the density of the fluid,

v=is the velocity of the fluid,

g= gravity.

The friction factor can vary based on the Reynolds number (a dimensionless number
representing the ratio of inertial to viscous forces), which is calculated as:

Re= ρvD/μ

Where,

ρ= density

D = inside diameter

v= velocity

μ= viscosity
Friction factor can be estimated using the following co-relation,

Laminar flow: f=64/Re

Turbulent flow: f= 0.316 x Re-0.25

For turbulent flow (), the friction factor depends on factors such as pipe roughness and is
often determined experimentally or by the Moody chart. Moreover, for turbulent how the
relationship between hf and v takes forms;

hf= kvn

where,

k= loss co-efficient

n= range from 1.7 to 2

this equation can be written as

loghf = logk+ nlogv

In order to find k and n experimentally using graph,

Experimentally, one can obtain the head. loss by applying energy equation between any two

points along a pipe. This is done in Eq-1 and by noticing constants diameter that the pipe is

horizontal and the diameter is constant 1. The of fluid between two pressure heads points h,

and h₂ measured by using piezometer tube. to are total head loss can be determined

experimentally by applying the Bernouli’s equation as follows,

hf = (P1-P2)/ ρg = h1-h₂

Energy losses are proportional to the velocity head of the fluid as it flows around an elbow,

through enlargement or contraction of the flow section. on through a valve. Experimental

values for energy losses usually reported in terms of a resistance or loss co-efficient k as
follows

hL = kv2 /2g

where,
hL is the minor loss, k is the resistance or loss co-efficient and v is the average velocity of
flow in the pipe in the vicinity where the minor occurs. The resistance or loss co-efficient is
dimensionless because it represents a constant of proportionality between the energy loss and
the velocity head. Minor loss of sudden enlargement: when a fluid flow from a smaller pipe
to a larger pipe through a sudden enlargement, its velocity abruptly decreases causing
turbulence which generates energy loss

Where,

P1 = pressure at smaller section

P2= pressure at large section

V1= velocity at smaller section

V2= velocity at large section

D1= Diameter at smaller section

D2= Diameter at large section

The loss of head takes place due to the formation of this eddies.

Bernouli’s equation at small and large section,

P1/ρg +V12 /2g +Z1= P2/ρg +V22 /2g +Z2+hf

Where Z1=Z2 as pipe is horizontal

P1/ρg +V12 /2g = P2/ρg +V2 2 /2g +hf

hf= (P1-P2)/ ρg + (V12 – V22)/2g

considering the control volume of liquid between small and large section. Then the force
acting on the liquid in the control volume in the direction of flow is given by,

Fx= P1A1+ P’(A2 – A1) – P2A2

And P1=P’

As p1=p’,

Fx= P1A1+ P1 (A2 – A1) – P2A2

= P1 A2 - P2A2

= A2(p1-p2)

Momentum of liquid per second at smaller section = mass × velocity

= 𝜌 A1 V1 × V1

= 𝜌 A1 V12

Momentum of liquid per second at large section = 𝜌 A2 V2 × V2

= 𝜌 A2 V22

Change of momentum = 𝜌 A2 V22 − 𝜌 A1 V12……….. (i)

But from continuity equation we have,

A1 V1 = A2 V2

Or, A1 = A2 V2 / V1

So change of momentum per second = 𝜌 A2 V2 2 − 𝜌 (A2 V2 / V1) V1 2

= 𝜌 A2 (V2 2 − V1 V2) ………….. (ii)

Hence equating (i) and (ii),

(p1 - p2) A2 = 𝜌 A2 (V2 2 − V1 V2)

Or, (p1 − p2) / 𝜌 = (V2 2 − V1 V2)

Dividing by g on both side,

(p1 − p2) / 𝜌𝑔 = (V2 2 − V1 V2) /g

We get,

Loss of head due to sudden enlargement.

Loss of head due to sudden contraction:

Loss of head due to Entrance of a pipe:

This loss is denoted by h1,

h1=0.5(V12/2g)

Loss of head at the exit of a pipe:

This loss is denoted by h0,
ho=V12/2g
where, V1= velocity at outlet of pipe.

Loss of head due to bend in pipe:

hb=kv2 /2g
where,

hb=loss of bend due to bend

V= velocity of flow

K=co-efficient of bend

The value of k depends on,

1.Angle of bend

2.Radius of curvature of bend

Loss of head due to obstruction in pipe:

where, a=Maximum area of obstruction

A=Area of pipe

v=Velocity of liquid in pipe

(A-a) =Area of flow of liquid at section 1-1

Vc=Velocity of liquid at vena-contraction

Cc=ac/(A-a)

So, aa=cc*(A-a)

And, head loss due to obstruction:

=(vc-v)2 /2g

={Av/cc(A-a) -v}/2g

=v2 /2g{A/∑(A-a) -1}2

Equipment:

1.Pipe setup (various materials and diameters)

2.Flow rate measurement device

3.Pressure sensors or manometer

4.Water or another fluid of known viscosity

5. Stopwatch

Procedure:

1. Setting up the pipe apparatus and ensuring it is free from leaks.

2. Measuring and record the diameter and length of the pipe.

3. Starting the fluid flow and adjusting to a known, steady rate.

4. Recording the flow rate , pressure drop , and any other necessary parameters (e.g.,

temperature for viscosity calculations).

5. Calculating the fluid velocity , where .

6. Calculating the Reynolds number for each flow rate.

7. Calculating the friction factor for each trial using the Dercy-Weisbach equation.

8. Repeated for different flow rates to analyze the effect on .

 Graph and Calculations:

Part 1: loss due to friction in pipe

Observati Flow Tube Tube Tube Tube Tube Tube Tube Tube Tube Tube 10
on rate 1 2 3 4 5 6 7 8 9 mm

(m3/s) mm mm mm mm mm mm mm mm mm

1 0.2174 550 548 536 472 314 388 510 282 260 108

2 0.2632 530 492 478 330 275 419 454 432 430 82

3 0.3704 570 515 484 388 294 438 450 407 400 68

4 0.08333 435 430 425 448 308 419 410 408 406 98

5 0.2174 462 438 427 435 308 290 420 400 395 83

Part 2: Minor loss due to fittings (Mitre)

Fitting N Volume Time( Flow rate Velocity M1 h1 M2 Head V2/2g k Re

o (m3) s) (Q) (V) m h2 m loss
(h1
-h2)

Miitre 1 0.005 23 0.000217 0.343 0.55 0.548 0.002 0.006 1.4 12161.298
2 0.005 19 0.000263 0.415 0.53 0.492 0.038 0.0087 14714.107
3 0.005 13.5 0.000370 0.5845 0.57 0.515 0.055 0.0174 20723.845
4 0.005 24 0.000833 0.1314 0.435 0.43 0.005 0.00088 4658.87
5 0.005 23 0.000217 0.343 0.462 0.438 0.024 0.006 12161.298
 Part-2: Minor loss due to fittings (Elbow)

Fittin N Volum Time( Flow rate Velocit M1 h1 M2 Head V2/2g k Re

o e s) (Q) y (V) m h2 m loss
g
(m )3
(h1
-h2)

Elbow 1 0.005 23 0.000217 1.41 0.536 0.472 0.064 0.101 0.652 24644.19
2 0.005 19 0.000263 1.709 0.478 0.33 0.148 0.149 29870.16
3 0.005 13.5 0.000370 2.405 0.484 0.388 0.096 0.295 42034.95
4 0.005 24 0.000833 0.541 0.448 0.425 0.023 0.014 9455.68
9
5 0.005 23 0.000217 1.41 0.435 0.427 0.008 0.101 24644.19

Part-2: Minor loss due to fittings (Expansion)

Fitting N Volum Time( Flow rate Veloci M1 h1 M2 Head V2/2g k Re

o e s) (Q) ty (V) m h2 m loss
(m )3
(h1
-h2)

Expansio 1 0.00 23 0.00021 0.571 0.38 0.31 0.07 0.016 0.92 15682.8
n 5 7 8 4 4 6 8 9
2 0.00 19 0.00026 0.692 0.41 0.27 0.14 0.024 19006.2
5 3 9 5 4 4 4
3 0.00 13.5 0.00037 0.974 0.43 0.29 0.14 0.048 26751.5
 5 0 8 4 4 4 6
4 0.00 24 0.00083 0.219 0.41 0.30 0.11 .0024 6014.98
5 3 9 8 1 4
5 0.00 23 0.00021 0.571 0.30 0.29 0.01 0.016 15682.8
5 7 8 8 6 9

Part-2: Minor loss due to fittings (Contraction)

Fitting N Volum Time( Flow rate Velocit M1 h1 M2 Head V2/2g k Re

o e s) (Q) y (V) m h2 m loss
(m )3
(h1
-h2)

Contractio 1 0.005 23 0.00021 0.571 0.51 0.282 0.22 0.0166 0.1 15682.89
n 7 0 8 68
2 0.005 19 0.00026 0.692 0.45 0.432 0.02 0.0244 19006.24
3 4 2
3 0.005 13.5 0.00037 0.974 0.40 0.407 0.04 0.0484 26751.56
0 5 3
4 0.005 24 0.00083 0.219 0.41 0.408 0.00 .00244 6014.98
3 0 2
5 0.005 23 0.00021 0.571 0.42 .400 0.02 0.0166 15682.89
7 0

Part 2: Minor loss due to fittings (Large bend)

Fitting No Volum Time( Flow rate Velocity M1 h1 M2 Head V2/2g k Re

e s) (Q) (V) m h2 m loss
(m )3
(h1
 -h2)

Large 1 0.005 23 0.000217 0.11 0.26 0.108 0.152 0.00061 0.6 6866.41
Bend 2 0.005 19 0.000263 0.133 0.43 0.082 0.348 0.00090 42 8302.12
3 0.005 13.5 0.000370 0.188 0.40 0.068 0.332 0.0018 11735.3
3
4 0.005 24 0.000833 0.0424 0.060 0.098 0.308 0.000009 2646.69
5 0.005 23 0.000217 0.1106 0.395 0.083 0.312 0.00061 6903.87

Discussion:

1. Comparing the experimental friction factor values to theoretical or standard values (e.g.,
from the Moody chart).

2. Analyzing how the friction factor changes with Reynolds number, pipe material, and pipe
roughness.

3. Discussing any sources of error (instrumental, procedural) and how they could affect the
results.

4. Describing any deviations from expected values and potential reasons.

Conclusion:

Summarizing the main findings of the experiment, including how well the experimental
results matched theoretical values. We discussed the importance of understanding the friction
factor in engineering applications, especially in pipe design and fluid transport system.