Fluid Mechanics Tutorial

Question 4
Oil is flow in a 20 mm pipe. The pipe is split into two pipe which is the first pipe is 10 mm
diameter with velocity 0.3 m/s and the other pipe is 15 mm diameter with velocity 0.6 m/s.
Calculate the flow rate for 20 mm pipe.

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Question 5
Water is flow in 50 cm pipe which is connected from two pipes A and B, which is the diameter
for both pipe are 25 cm and 30 cm. The velocity for both pipes A and B are 0.3 m/s and
0.2 m/s. Calculate the flow rate of pipe A, B and C and also find the velocity for pipe C.

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Bernoulli’s Theorem

Bernoulli’s Theorem states that the total energy of each particle of a
body of fluid is the same provided that no energy enters or leaves
the system at any point. The division of this energy between
potential, pressure and kinetic energy may vary, but the total
remains constant.

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Assumptions
The following are the assumptions made in the derivation of Bernoulli’s
equation:
▪ The fluid is ideal or perfect, that is viscosity is zero.
▪ The flow is steady (The velocity of every liquid particle is uniform).
▪ There is no energy loss while flowing.
▪ The flow is incompressible.
▪ The flow is Irrotational.
▪ There is no external force, except the gravity force, is acting on the liquid.

Application
of

Bernouli’s
Theorem

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Pipe

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Horizontal Venturi Meter
Venturi meter: It is a device used for measuring the rate of flow of a

non-viscous, incompressible fluid in non-rotational and steady-
stream lined flow.

Where:
Cd = coefficient of Discharge
A1 = Area of entrance
v1 = Velocity at entrance
g = gravity (9.81 m/s²)
m = Area ratio
H = Pressure difference expressed as a head of the liquid flowing
in venturi meter (m)
x = Difference of level in U-tube manometer
ωHg = Specific weight of Mercury in manometer
ωsub = Specific weight of fluid entering the venturi meter
P1 – P2 = Difference of pressure in entrance and throat

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Inclined Venturi Meter

Where:
Cd = coefficient of Discharge
A1 = Area of entrance
v1 = Velocity at entrance
g = gravity (9.81 m/s²)
m = Area ratio
H = Pressure difference expressed as a head of the liquid
flowing in venturi meter (m)
x = Difference of level in U-tube manometer
ωHg = Specific weight of Mercury in manometer
ωsub = Specific weight of fluid entering the venturi meter
P1 – P2 = Difference of pressure in entrance and throat
Z1 – Z2 = Difference of height between entrance and throat

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Orifice Meter
An orifice meter is a piece of equipment used to measure the flow rate

of a gas or a fluid.
The Orifice Meter consists of a flat orifice plate with a circular hole
drilled in it. There is a pressure tap upstream from the orifice plate and

another just downstream.
"Vena Contracta" is the minimum jet area that appears just
downstream of the restriction. The viscous effect is usually expressed
in terms of the non-dimensional parameter Reynolds Number - Re.

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Pitot Tube
Pitot tube is a mechanical device which is used to measure veloci‐
ty of flow at any point in a pipe or a channel. It was invented by

French engineer Henri Pitot and modified by French scientist
Henry Darcy.

Pitot Tube works on a basic principal of fluid Mechanics and that
is, if a fluid stops flowing, all its kinetic energy gets converted into
pressure energy. It helps us in measuring that pressure energy of

stopped fluid.
Theoretically = √(2 h) , pitot tubes may require calibration.
The actual velocity is then given by = √(2 h) , where C is the

coefficient of the instrument.

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Tutorial 2.5

Question 1
Water flows through a pipe 36 m from the sea level as shown in figure below. Pressure in the pipe
is 410 kN/m² and the velocity is 4.8 m/s. Calculate total energy of water above the sea level.

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Question 2
A bent pipe labeled MN measures 5 m and 3 m respectively above the datum line. The
diameter M and N are both 20 cm and 5 cm. The water pressure at inlet is 5 kg/cm². If the
velocity at M is 1 m/s, determine the pressure at N in kN/m².

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Question 3
A horizontal venturi meter has a diameter of entrance and throat 0.25 m and 0.18 m
respectively. The pressure at entrance is 280 kN/m² and throat is 100 kN/m²
Determine the actual discharge of oil if Soil = 0.9 and coefficient of discharge is 0.92.

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Question 4
A venture tube tapers from 300 mm in diameter at the entrance to 100 mm in diameter at
the throat; the discharge coefficient is 0.98. A differential mercury U-tube gauge is
connected between pressure tapping at the entrance at throat. If the meter is used to
measure the flow of water and the water fills the leads to the U-tube and is in contact with
the mercury (SHg = 13.6), calculate the actual discharge when the difference of level in the
U-tube is 55 mm.

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Question 5
A horizontal venturi meter has a diameter of throat 150 mm and 250 mm for entrance. This
venturi meter is used to measure the flow rate of fluid that has mass density 900 kg/m³. A
U- tube mercury (SHg = 13.6) is use and show the difference of level 0.15 m. Calculate the
Qactual if Cd = 0.98.

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Question 6
A vertical venturi meter measured the flow of water and has an entrance of 125 mm
diameter and throat of 50 mm diameter. There are pressure gauges at the entrance and at
the throat, which is 250 mm above the entrance. If the coefficient for the meter is 0.97 and
the pressure difference is 50 kN/m², calculate the actual discharge in m³/s.

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Question 7
A vertical venturi meter measures the flow of oil of specific gravity 0.82 and has an
entrance of 125 mm diameter and throat of 50 mm diameter. There are pressure gauges at
the entrance and at the throat, which is 300 mm above the entrance. If the coefficient for
the meter is 0.97 and pressure difference is 27.5 kN/m², calculate the actual discharge in
m³/s.

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Question 8
A meter orifice has a 100 mm diameter circular hole in the pipe. Diameter of the pipe is
250 mm. Coefficient of discharge, Cd = 0.65 and specific gravity of oil in the pipe is
0.9. The difference of level is measured by manometer is 750 mm. Calculate the actual
flow rate of the oil through the pipe.

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