Fluid flow is the bulk movement of particles of a fluid (liquid & gases).

While studying fluid flow two assumptions are made:

i) The viscosity of the fluid is negligible.
ii) The fluid is incompressible

Types of fluid flow

i) Streamline flow (steady flow)
ii) Turbulent flow
STREAMLINE FLOW
This is a flow that at a given point each particle of the fluid travels in
the same direction and with the same velocity. This flow is smooth and
steady ie no disturbance.

TURBULENT FLOW
This is a flow that is disorderly and in which the speed and direction
of the fluid particles passing any point is not uniform.
It occurs when an object is moved in opposite direction to a flowing fluid.
Object

Eddies

Eddies are formed and the object requires more effort to move. However if the
object is shaped flat, then no eddies are formed and the flow is streamline.

There are bodies and shapes designed for streamline flow eg cars, aeroplanes,
birds, fish etc. these shapes easily cut through fluids without resistance.
FLOW RATE (VOLUME FLUX)
The rate of flow of a fluid is the volume of the fluid flowing through any section in
one second ie
𝑽𝒐𝒍𝒖𝒎𝒆
𝐅𝐥𝐨𝐰 𝐫𝐚𝐭𝐞 = 𝒕𝒊𝒎𝒆
Am2 at a velocity of Vm/s
If a fluid is flowing thru a pipe of cross-section area of
then Flow rate (volume flux) = A x V
The SI units are cubic meter per second (𝒎𝟑 /𝐬)

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EQUATION OF CONTINUITY
Consider a fluid flowing through a horizontal pipe of varying cross – section area.
V1
V2
A1 A2

The volume of fluid flowing across any section must same ie flow rate is constant.
At the wider section flow rate = A1V1
At the narrow section flow rate = A2V2
When a fluid flows from the big cross – section area to a small cross – section area
its velocity increases ie the bigger the area the lower the velocity and the smaller
the area the higher the velocity.
At any one time the volume flux (flow rate) is the same ie
A1V1 = A2V2
If mass flux is considered instead of volume flux the results are still the same ie
Mass flux = volume flux x density
A1V1 x density = A2V2 x density
But since the fluid is the same hence the density is equal thus
A1V1 = A2V2
EXAMPLE
1. Water is flowing in a horizontal pipe of CSA 36cm2 at a speed of 6m/s. The
water enters into a constriction of area 9cm2. Find its speed in the
constriction. (ANS 24m/s)
2. Water flows along a horizontal pipe of cross – sectional area 30cm2 at a
speed of 40ms-1. It reaches a section where the speed is 7.5ms-1. Find the
area of this section of the pipe. (ANS 160cm2)
3. Water flows steadily through a pipe of diameter 30 cm at 20 ms-1. The
pipes narrows at some point and its diameter reduces to 20 cm. What is the
speed of water at this point? (ANS 45m/s)
4. Water flowing at a speed of 15m/s in a wide pipe enters into a narrower
pipe of CSA 25cm2 and moves at a speed of 48m/s.
i) Determine the area of the wider pipe. (ANS 80cm2)
ii) If the density of water is 1000kg/m . Find the mass flux. (ANS 120kg/s)
3

5. Water flows steadily in a horizontal pipe of CSA 40cm2 at a flow rate of

8 x 10-3 m3/s, calculate its velocity. (ANS 2m/s)
6. A hose pipe of CSA 4cm2 is connected to a sprinkler that has 20 holes each
of CSA 0.05cm2. If the speed of water in the hose pipe is 2.5m/s
determine
i) The flow rate in the hose pipe. (ANS 0.001m3/s)
ii) The speed at which the water emerges from the sprinkler holes. (2m/s)
7. A garden sprinkler has small holes each of area 2mm2 if the water is
supplied at a flow rate of 3x10-3m3/s and the average velocity of the spray
is 10m/s. calculate the no of holes. (ANS 150 Holes)
8. A lawn sprinkler has 20 holes each of cross-sectional area 2 x 10-2 cm2 is
connected to a hose pipe of cross-sectional area 2.4cm2. if the speed of
water in the hose pipe is 1.5 m/s.
(i) Calculate the flow rate in the hose pipe. (ANS 0.00036m3/s)
(ii) The speed of water as it emerges from the holes. (9m/s)
(iii) The mass flux in the hose pipe if density of water 1000kg/m . (0.36kg/s
3

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 BERNOULLI’S PRINCIPLE
It states that “For a fluid that is incompressible, non-viscous and of
streamline flow an increase in its velocity results to a decrease in its
pressure”.
Water is passed through a horizontal tube of varying CSA and the water level is
found to vary as shown.
A C
B

Since the CSA is bigger at A & C, the water flows at a lower velocity and hence
the pressure is high making the water to climb higher in tube A & C.
At section B the CSA is smaller, the velocity is high and hence the pressure is low
making the water to climb just a little in tube B.
This shows that pressure is maximum when velocity is minimum.

CASE EXAMPLES OF BERNOULLI’S EFFECTS

(i) When two papers are held vertically and air blown between them, they
move towards each other

Blow Air

The pressure between the papers reduces due to high velocity of air and hence the
higher atmospheric pressure outside pushes the paper towards each other.
(ii) When a single paper is held from one end and air blown above it, the
paper is raised.

Blow Air

(iii) Two pith balls are held vertically with a string and air blown between
them.

Blow Air
The pith balls moves towards each other as pressure between them is
reduced due to high air velocity. The higher atmospheric pressure pushes
the balls towards where the pressure is lower.

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 (iv) Lifting a ball using a funnel.

When air is blown through the narrow section, it moves at a very high velocity and
therefore low pressure. However as it emerges into the wide section its velocity
reduces making the below the ball (atm pressure) lift the ball upto the neck of the
funnel.
APPLICATION OF BERNOULLI’S EFFECT
(i) Aerofoil (wings of aircraft)
The wings have a curved upper surface and a flat bottom.
Dynamic lift
Wing

The air flowing above the wings moves with at a higher velocity than that flowing
underneath. This makes the air moving over the top to travel a longer distance
resulting in a higher velocity than the one at the bottom.
Due to high velocity at the top surface the pressure above is lowered than at the
bottom. The pressure different between above and below the wings produces a
large lifting force and the aircraft rises thru dynamic lift.

(ii) The spray gun

Piston
Spray

Tube
Liquid

Spray guns are used to spray pesticides or oil paints.

When the piston is pushed forward, air passes past the opening of the tube at a
very high velocity and goes to the nozzle. This reduces the pressure at the
opening. The liquid is forced to move up the tube and it is blown by the moving air
to the nozzle where it emerges as fine spray because of the reduced CSA of the
nozzle.

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 (iii) Bunsen burner.

Barrel

Nozzle
Air drawn in
Gas
Base

The gas is made to escape with a high velocity through a fine nozzle. The pressure
near the nozzle is reduced and air from outside is pushed in by atm pressure and
is mixed with the gas for combustion.

(iv) The carburetor

Venturi
Air petrol
Float Air sucked mixture
chamber in

Petrol

A fast moving air is made to flow above the petrol pipe in the venturi.
Petrol is drawn into the venturi due to low pressure in the venturi and the high
atmospheric pressure in the float chamber. Petrol vapour is produced which mixes
with air and is ready for combustion.

HAZARDS OF BERNOULLI’S EFFECT

i) Blowing off of roof – tops
When wind passes over a roof top at a high velocity, the pressure above the roof
is reduced. The pressure acting on the roof from underneath will be higher and
hence the roof is blown off.

ii) Road accidents.

A small car travelling at a high speed is likely to be pulled towards a long track
travelling in the opposite direction. The air in btn the two vehicles moves at a very
high speed reducing the pressure btn them. The higher atm pressure acting from
the sides pushes them closer which cause accident.

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