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fluid mechanics lecture notesTRANSCRIPT
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Fluid Statics
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Pressure
In general, fluids are subject to both normal and
shearing forces.
However, only fluids with velocity gradients
produce shearing forces.
For fluids at rest, only normal forces exist.
These normal forces in fluids are called pressure
forces
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Pressure
It is defined as
where F is the normal force acting over the area A.
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In a wedge shaped stationary fluid element,
there are pressure forces acting normal to
the surfaces and the weight force:
pnA
A
x
y
z
Weight
l
z= l sin
x= l cos
y
pxA sin
pzA cos
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The equation of equilibrium in the x-direction:
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Or the equation of equilibrium in the z-direction:
As l goes to zero at a point:
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We conclude that the pressure at a point in
a static fluid acts with the same magnitude
in all directions.
Pressure is a scalar quantity,
not a vector; the pressure at a
point in a fluid is the same in
all directions.
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In the outer space which is virtually void of
gases, the pressure is zero.
Pressures measured relative to a perfect
vacuum (absolute zero) are termed
absolute pressure.
The atmospheric pressure at sea level is
taken as 101325 Pa
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Many pressure measuring devices measure
the differences in pressure relative to the
atmospheric pressure.
This type of pressure reading is called gage
pressure.
Therefore, a gage pressure can be
negative, which is referred as suction or
vacuum pressure.
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Absolute pressure: The actual pressure at a given position. It is measured relative to absolute vacuum (i.e., absolute zero pressure).
Gage pressure: The difference between the absolute pressure and the local atmospheric pressure. Most pressure-measuring devices are calibrated to read zero in the atmosphere, and so they indicate gage pressure.
Vacuum pressures: Pressures below atmospheric pressure.
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EQUATION FOR PRESSURE FIELD
Consider a stationary fluid element.
There are two types of forces acting on this
element:
Surface forces due to pressure
and a body force due to the weight of the
element (we observed that pressure changes in z
direction)
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y
x
zy
x
z
xyz
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Pressure on the surfaces can be expressed in terms of p
given at the center of the element.
The resultant surface force in the y direction is:
The weight of the fluid is:
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The total force on the element then becomes:
or in component form:
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Since p only depends on z:
The weight per unit volume g is defined as
specific weight
The ratio of the specific weight of a given liquid to
the specific weight of water is defined as specific
gravity, S
For incompressible fluid: the above equation may be
integrated to yield:
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For h=z1-z2>0 the pressure between two points can be
specified in terms of the distance h:
h is called the pressure head.
The pressure p at any depth h below a reference surface, where
pressure is p0, is then given by
In an incompressible fluid at rest the pressure varies linearly
with depth.
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Pressure in a liquid at
rest increases linearly
with distance from the
free surface.
The pressure of a fluid at rest
increases with depth (as a
result of added weight).
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The pressure is the same at all points on a horizontal plane in a
given fluid regardless of geometry, provided that the points are
interconnected by the same fluid.
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A manometer can contain one or more fluids such as mercury, water, alcohol,
or oil.
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Example