FLUID DYNAMICS
Engr. Hassan Arshad
Today’s Content
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Different types of heads (or energies) of a
liquid in motion
Bernoulli’s equation
Euler’s equation for motion
Bernoulli’s equation for real fluids
INTRODUCTION

The science which deals with the action of the
forces in producing or changing motion of fluids is
known as “hydrokinetics”.
 The
dynamic equation of fluid motion is obtained by
applying Newton’s second law of motion.
 The fluid is assumed to be incompressible and nonviscous.
DIFFERENT TYPES OF HEADS (OR ENERGIES)
OF A LIQUID IN FLOW

Potential head or potential energy:
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
This is due to configuration or position above some
suitable datum line. It is denoted by z.
Velocity head or kinetic energy:
 This
is due to velocity of flowing liquid and is
measured as V2/2g.

Pressure head or pressure energy:
 This
P/w.
is due to the pressure of liquid and reckoned as
Total head

Total Head

In a pipe of 90 mm diameter water is flowing with
a mean velocity of 2 m/s and at a gauge pressure of
350 kN/m2. Determine the total head, if the pipe is
8 meters above the datum line. Neglect friction.
EULER’S EQUATION OF MOTION FOR
FLOW ALONG A STREAMLINE

This is equation of motion in which the forces due
to gravity and pressure are taken into consideration.
This is derived by considering the motion of a fluid
element along a stream-line.
EULER’S EQUATION
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BERNOULLI’S EQUATION
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BERNOULLI’S EQUATION FOR REAL
FLUIDS
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Some Comments on B.EQ’s
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In 1738 Daniel Bernoulli published his
Hydrodynamics in which an equivalent of this
famous equation first appeared.
To use it correctly we must constantly remember the
basic assumptions used in its derivation:
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viscous effects are assumed negligible,
the flow is assumed to be steady,
the flow is assumed to be incompressible, and
the equation is applicable along a streamline.
Finding Pressure using B.EQ

The water is flowing through a pipe having diameters 20 cm
and 10 cm at sections 1 and 2 respectively. The rate of flow
through pipe is 35 liters/s. The section 1 is 6 m above datum
and section 2 is 4 m above datum. If the pressure at section 1
is 39.24 N/cm2, find the intensity of pressure at section 2.
Any Questions?