Physical properties of fluid and fluid transport in piping system
Laminar and turbulent flow in pipe
Static, dynamic and total pressure
Flow in pipes and valves theory - full content
Static pressure is pressure of fluid in flow stream. Total pressure is pressure of fluid when it is brought to rest,
i.e. velocity is reduced to 0.
Total pressure can be calculated using Bernoulli theorem. Imagining that flow is in one point of stream line stopped
without any energy loss Bernoulli theorem can be written as:
If velocity at point 2 v2=0, pressure at point 2 is than total p2=pt:
where is:
- p - pressure
- pt - total pressure
- v - velocity
- &rho - density
The difference between total and static pressure represents fluid kinetic energy and it is called dynamic pressure.
Dynamic pressure for liquids and incompressible flow where the density is constant can be calculated as:
where is:
- p - pressure
- pt - total pressure
- pd - dynamic pressure
- v - velocity
- &rho - density
If dynamic pressure is measured using instruments like Prandtl probe or Pitot tube velocity can be calculated in
one point of stream line as:
where is:
- p - pressure
- pt - total pressure
- pd - dynamic pressure
- v - velocity
- &rho - density
For gases and larger Mach numbers than 0.1 effects of compressibility are not negligible.
For compressible flow calculation gas state equation can be used. For ideal gases, velocity for Mach number M < 1
is calculated using following equation:
where is:
- M - Mach number M=v/c - relation between local fluid and local sound velocity
- &gamma - isentropic coefficient
It should be said that for M > 0.7 given equation is not totally accurate.
If Mach number M > 1, than normal shock wave will occur. Equation for velocity in front of the wave is given bellow:
where is:
- p - pressure
- pti - total pressure
- v - velocity
- M - Mach number
- &gamma - isentropic coefficient
Note: You can download complete derivation of given equations
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