Chapter 2:
Fluid Statics
1. Pressure as a function of depth in a stationary fluid
2. Manometers to measure pressure differential
3. Forces on flat and curved surfaces
4. Buoyancy force and stability of a floating object
Surface and Body Forces
Arbitrary system
Surface forces only act on
the surface of the system.
Examples:
Pressure
Friction
Body forces only act on
volumes.
Examples:
Gravity
Electric field
Pressure is a Scalar Function
Consider a differential prism of stationary fluid at a certain depth:
Weight of the fluid in the prism =
·
=
Surface forces due to
pressuredF = P*dA
Pressure is a Scalar Function
Consider a differential prism of stationary fluid at a certain depth:
Apply Newton’s 2nd Law in y and z directions
= ·= 0
− · = 0
But
·
=
=
Pressure is a Scalar Function
Consider a differential prism of stationary fluid at a certain depth:
Apply Newton’s 2nd Law in y and z directions
= ·= 0
−·−
2= 0
But
·
=
0
=
Pressure is a Scalar Function
Consider a differential prism of stationary fluid at a certain depth:
= = =
Pressure does not depend on the orientation on the plane
upon which the pressure acts. It is a scalar function, and
only depends on space (x, y, z) and time t.
Pressure Variation in a Stagnant Fluid
Again apply Newton’s second
law to this fluid region.
=
=
0
+ = ()+ = ()+#
# Velocity is zero
everywhere for all time t.
Pressure Variation in a Stagnant Fluid
In the y-direction:
−#
#
2− +#
#
2 = 0
#
# = 0
#
# = 0 Pressure can not vary in the y direction
in a stagnant fluid.
In the x-direction:
Same thing #
#
=
0
Pressure can not vary in the x direction
in a stagnant fluid.
Pressure Variation in a Stagnant Fluid
In the z-direction:
−#
#
2− +#
#
2− = 0
−#
# − = 0
#
#
=
= − Pressure can only vary in a stagnant
fluid in the direction of gravity.
Pressure Variation in a Stagnant
Fluid: Incompressible Fluid
x
y
z(x1, y1, z1)
h
po
Pressure at the surface
= −
ρ= constant
If gravity is constant
γ= constant
= −
$
%&
%‘= −$
‘()
‘
*−+= −(++ℎ−+)
+
=
*
+
ℎ
Pressure Variation in a Stagnant
Fluid: Incompressible Fluid
ρ= constant
Pressure Variation in a Stagnant
Fluid: Ideal Gas
negligible radius
