Chapter 5
Fluid Mechanics
Pressure in a Fluid
When a fluid ( liquid or gas ) is at rest , it exerts a force
perpendicular to any surface in contact with it ,
such as a container wall or a body immersed in the
fluid .While the fluid as a whole is at rest ; the
molecules that make up the fluid are in motion ;
the force exerted by the fluid is due to molecules
colliding with their surroundings .
The Pressure P on a surface area A is defined as the
net normal force per unit area , i.e
P = F/A
{ Pressure is a scalar quantity }
The SI unit of Pressure is : N / m2 = Pa ( Pascal )
Multiples of Pascal are : kiloPascal
kPa = 103 Pa
MegaPascal MPa = 106 Pa
Atmospheric Pressure Po
Atmospheric pressure is the pressure of the earth’s
atmosphere , the pressure at the bottom of this sea of
air in which we live . Normal atmospheric pressure at
sea level have an average value of :
1 atm = Po = 1.013 x 105 Pa
In Metrology they don’t like SI units .
They invented a unit called : bar = 105 Pa
Therefore , 1 atm = 1.013 bar = 1013 mb (millibar)
This is why the instrument used to measure the
atmospheric pressure in Metrology Stations is
well-known as : Barometer
Pressure , Depth and Pascal’s Law
For a liquid of constant density  , the
pressure P at a depth h is calculated
as :
P=gh
( SI Units )
where g = 9.8 m/s2 is the acceleration
due to gravity .
Pascal’s Principle :
A change in pressure at any point in a confined
fluid is transmitted everywhere throughout
the fluid .
Applications of
Pascal’s Principle
(1) The hydraulic Lift in Car Washing Stations :
Applications of
Pascal’s Principle
(2) Dentist’s Chair : The dentist applies
a small force to lift a heavy patient .
(2) Car Brakes : The brake oil transmits the
pressure applied by the foot of the driver to
the to the disc of the tire .
Absolute Pressure
and Gauge Pressure
Pressure gauges ( called Manometers )
are designed to measure the pressure
without taking the atmospheric pressure
Po into consideration , Therefore the total
( absolute pressure P is always more
than the gauge pressure by Po i.e
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
P
=
Pg
+
Po
Measuring the Atmospheric Pressure Po
{ Mercury Barometer }
Torricelli’s Apparatus
Fluid Flow and
the Continuity Equation
The study of moving fluids is very complex .
The Continuity Equation relates the speed of
flow v to the cross-sectional area A of the
fluid as follows : ( incompressible fluid )
A1 v1 = A2 v2
Applications of
the Continuity Equation
Water flows faster when it comes out from the
small holes of a bathroom hose or from a
garden hose .
Think of the motion of blood in the circulatory
system in humans and animals .
Does the blood move with a constant speed or
with different speeds ?? Explain
What will happen when a patient has high
cholesterol precipitated on the inner walls
of the veins ??