UNIT 1 .

FLOW OF FLUIDS
 Therefore, the pressure difference
between any two points can be
measured by the distance between
those points in a fluid.
 If the density of fluid varies with
variation of pressure , an average
density could be used.
 The variation in densities is quite
negligible for liquids and gases.
 Since the difference in the heights is
necessary for the measurement ,
height can be measured from the
4
bottom of the stationary column.
REYNOLD’S EXPERIMENT

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Https://www.youtube.com/watch?v=CxqM_kkwgU4&list=PLagszcJQfPU3yUodnZQsgD_YDVvtE-jJD&ind
ex=5

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 Friction Losses
During the flow of fluids, frictional forces causes a loss in pressure. The type of fluid flow also
influences the losses.

In general, pressure drop due to friction in a fluid is: α Velocity (U)

α Density of fluid (ρ)

α Length of the pipe (L)
α 1 / diameter of the pipe (D)

These relationships are proposed in Fanning equation for

calculating friction losses, irrespective of type of flow (viscous/turbulent)

Fanning equation ∆p = 2fu2Lρ / D
F = friction factor
For viscous flow, Hagen –Poiseuille equation for calculating pressure drop due to friction.
∆p = 32 Luη / D2
 Losses in Fitting
Fanning equation is applicable for the losses in straight pipe. When fitting are introduced into
a straight pipe, They cause disturbance in the flow, Which result in the additional loss of
energy
losses in fitting may be due to
 Change in direction
 Change in the type of fittings

Tee fitting
Equivalent length = 90 Globe valve, equivalent length = 300

Equivalent length of this fitting = Equivalent length x internal diameter

For globe valve = 300 x 50

= 15 meter
That means globe valve is equal to 15 meters of a straight pipe towards the losses. so
this length is substituted in fanning equation to obtain energy losses due to fittings.
 Enlargement Loss
If the cross section of the pipe enlarges gradually, the fluid adapts itself to the
changed section without any disturbance. So no loss of energy

u2 u1 u2
u1

Gradual enlargement, No loss of energy Sudden enlargement, Loss

of energy

If the cross section of the pipe changes suddenly then loss in energy is observed due
to eddies. These are greater at this point than straight line Pipe. 2
(u1  u 2 )
ΔH e 
2g
Then u2< u1 ,
For sudden enlargement losses ;
∆ H = loss of head due to sudden enlargement
 Contraction Losses

If the cross section of the pipe is reduced suddenly the fluid flow is
Disturbed.
Normally, the diameter of the fluid stream is less than the initial value of the
diameter. This point of minimum cross section is known as vena contracta.
The velocity of fluid at smaller cross-section will be far GT that at larger cross-
section i.e.,
Ku 2
u1< u2. The losses due to additionalΔH
eddying
 2are observed. Such contraction
C 2g
losses can be expressed as:
Sudden contraction losses:
Manometers https://www.youtube.com/watch?v=MpXhXVF9-HM&list=PLagszcJQfPU3yUodnZ
QsgD_YDVvtE-jJD&index=8

Turbulent flow https://www.youtube.com/watch?v=bw_WC-EVs_g

Venturi meter https://www.youtube.com/watch?v=_bfcdRhY7Rw

Bernoulli's https://www.youtube.com/watch?v=DW4rItB20h4&list=PLEYqyyrm-
hQ09B9JWzypjjTMAITgUItVh&index=2

Pitot tube https://www.youtube.com/watch?v=wBXqF2Z3L7g

Orifice meter https://www.youtube.com/watch?v=oUd4WxjoHKY

Rotameter https://instrumentationtools.com/rotameter-working-principle-animat
ion/

15
 Manometers
Manometers are the devices used for measuring the pressure
difference.

Three different manometers are available. These are

1) Simple manometer
2) Differential manometer
3) Inclined manometer
 SIMPLE MANOMETER
 This manometer is the most commonly used.
 It consists of a glass U shaped tube filled with a liquid A of
density ρA kg /meter cube and above A the arms are filled with liquid B
of density ρB
 The liquid A and B are immiscible and the interference can be seen
clearly
 If two different pressures are applied on the two arms the
meniscus of the liquid A will be higher in one arm than the other.
 Let pressure at point 1 is P1 Pascal's in left-hand side of the
limb.
 Let pressure at point 5 is P2 Pascal's in right-hand side of the
limb.
From the principles of fluid statics, the pressure at point
2 can be written as:

Pressure at point 2 = P1+ (m + R ) ρ B g

(m + R ) = distance from 3 to 5
 Since the points 2 and 3 are at the same level, the pressure at point 3 may be written as

Pressure at point 3 =P1+ (m + R ) ρ B g

Pressure at point 4 can be written as (from the right hand-side of the limb) as:

Pressure at point 4 = P2 + gm ρ B

In another manner, Pressure at point 4 can be written from point 3 (i.e from the left hand-side
of the limb) as:

Pressure at point 4 = P1+ ρ B ( m + R ) g- ρ a R g

Both the equations should be equal

P2 + gm ρ B = P1+ ρ B ( m + R ) g- ρ a R g
P1 – P2 = gm ρ B - ρ B ( m + R) g + ρ A R g
∆P = gm ρ B - gm ρ B - R ρ B g + R ρ A

=R (ρ A- ρ B )g
Applications:
 It helps in measuring the consumption of gases in the chemical reaction.
 Manometers are used in conjugation with flow meters for the measurement of flow of fluids.
 DIFFERENTIAL MANOMETERS
 These manometers are suitable for measurement of
small pressure differences.
 It is also known as two – Fluid U- tube manometer
 It contains two immiscible liquids A and B having nearly
same densities.
 The U tube contains of enlarged chambers on both
limbs. Hence the meniscus of the liquid in these
enlarged chambers does not change appreciably with
changes in the reading R.

Using the principle of simple manometers, the

pressure difference can be written as:

∆P =P1 –P2 =R (ρc – ρA) g

 INCLINED TUBE MANOMETERS
 Many applications require
accurate(minute) measurement of low
pressure such as drafts and very low
differentials, primarily in air and gas
installations.
 In these applications the manometer is
arranged with the indicating tube inclined, with
vertical leg enlarged as in Figure, therefore
providing an expanded scale.

This enables the measurement of small pressure

changes with increased accuracy .

P1 –P2 = g R (ρ A - ρ B) sin α
21
MEASUREMENT OF RATE OF FLOW OF FLUIDS
When ever fluid are used in a process it is necessary to
measure the
rate at which the fluid is flowing through the pipe,
Methods of measurement are
 Direct weighing or measuring
 Hydrodynamic methods
 Orifice meter
 Venturi meter
 Pitot meter
 Rotameter

 Direct displacement meter

 DIRECT WEIGHING OR MEASURING
The liquid flowing through a pipe is collected for specific
period at any point and weighed or measured, and the rate of flow can be determined.
Gases can not be determined by this method. Impracticable.
ORIFICE METER
Principle:
Orifice meter is a thin plate containing a narrow and sharp aperture.
When a fluid stream is allowed to pass through a narrow constriction the velocity of the
fluid increase compared to up stream
This results in decrease in pressure drop and the difference in the pressure may be read
from a manometer

The velocity of the fluid at thin constriction may be written as

U0 =C 0 √ 2g ∆H
 ∆H = can be measured by manometer

C0 = constant

U0 = velocity of fluid at the point of orifice meter

CONSTRUCTION
 It is consider to be a thin plate containing a sharp
aperture through which fluid flows
 Normally it is placed between long straight pipes
 For present discussion plate is introduced into
pipe and manometer is connected at points A and
B

WORKING
 Orifice meter is referred as the variable head
meter, i.e. it measure the variation in the
pressure across a fixed construction placed in the
path of flow
 When fluid is allowed to pass through the orifice the velocity of the
fluid at point B increase, as a result at point A pressure will be
increased.
 Difference in the pressure is measured by manometer
 Bernoulli's equation is applied to point A and point B for
experimental conditions

√U02 – UA2 =C0 √2g. ∆H

U0 = velocity of fluid at orifice

UA = velocity of fluid at point A

C0 = constant
 If the diameter of the orifice is 1/5 or less of the pipe diameter then
UA is neglected

Applications
 Velocity at either of the point A and B can be measured
 Volume of liquid flowing per hour can be determined
VENTURI METER

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3/1/20XX SAMPLE FOOTER TEXT 27
 U v =C v √ 2g .
∆H
DISADVANTAGES
 Expensive

 Need technical expert

 Not flexible, it is permanent
Advantages
 Power loss is less
 Head loss is negligible
3/1/20XX SAMPLE FOOTER TEXT 29
PITOT TUBE
Working
 Tube are inserted in the flow shown is the figure
U2 = Cv √2g. ∆H
 coefficient of Pitot tube
32
ROTAMETER
3/1/20XX SAMPLE FOOTER TEXT 34
 DIRECT DISPLACEMENT METER
Used for the measurement of domestic water supply
PRINCIPLE
In this a stream of water enters meter and strikes
the moving meter,
the rate of rotation of the moving membrane is
proportional to the velocity
of the fluid.