Hydrostatic, Hydrodynamic, Static and Total Pressure
- Let us consider a fluid flowing through
a pipe of varying cross sectional area. Considering two
points A and B as shown in Figure 16.1(c), such that A and B
are at a height ZA and ZB respectively from the datum.
![](images/image001.gif)
Figure 16.1 (c)
- If we consider the fluid to be
stationary, then,
where
the subscript hs represents the hydrostatic case.
So, pAhs - pBhs = ρg( ZBZA)
|
(16.1) |
where pAhs is the hydrostatic
pressure at A and pBhs is the hydrostatic pressure
at B.
- Thus, from above we can conclude
that the Hydrostatic pressure at a point in a fluid is the
pressure acting at the point when the fluid is at rest or
pressure at the point due to weight of the fluid above it.
- Now if we consider the fluid to
be moving, the pressure at a point can be written as a sum
of two components, Hydrodynamic and Hydrostatic.
where pAhs is the hydrostatic
pressure at A and pAhd is the hydrodynamic pressure at A.
- Using equation (16.2) in Bernoulli's
equation between points A and B.
![](images/image006.gif) |
(16.3) |
From equation (16.1),
the terms within the square bracket cancel each other.
Hence,
![](images/image008.gif) |
(16.4) |
![](images/image010.gif) |
(16.5) |
-
Equations (16.4) and (16.5) convey
the following. The pressure at a location has both hydrostatic
and hydrodynamic components. The difference in kinetic energy
arises due to hydrodynamic components only.
-
In a frictionless flow, the sum
of flow work due to hydrodynamic pressure and the kinetic
energy is conserved. Such conservation shall apply to the
entire flow field if the flow is irrotational.
- The hydrodynamic component is often
called static pressure and the velocity term, dynamic pressure.
The sum of two, p0 is known as total pressure. This is conserved
in isentropic, irrotational flow.
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