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Old May 4th 2018, 10:19 AM   #1
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Bernoulli equation

I am confused about the application of Bernoulli's equation in aerodynamics:

p0+1/2rho v^2=constant.

Strictly speaking this equation is only valid for incompressible fluids without viscosity.
So possibly for water, but not for an ideal gas like air.

But I find this equation used frequently when the basics of aerodynamics are discussed.

Take for instant a pitot-valve:

In an ideal gas rho is a function of p and temperature.

So if p increases in the pitot-valve with respect to the upstream value so does rho.
So which rho do I use to calculate the speed to be measured?

How about temperature? At very low speed I would except the process to be isothermal, but as speed increaeses we probably get adiabatic. So what temperature to use when converting p to rho?

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Old May 4th 2018, 03:38 PM   #2
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Bernoulli's equation is an approximation.
For many situations the quantities involved due to compressibility & viscosity & temperature (etc.) will be small enough compared to Bernoulli's equation that the approximation is good enough.

If the process being modelled includes significant compressibility or viscosity or ...
then you have to bite the bullet and use more complex models.
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Old May 5th 2018, 09:00 AM   #3
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Bernoulli is an energy equation, in fact the conservation of energy, so long as you can account for the energy changes due to density change

You can still use Bernoulli, but as Woody says you need a more complicated version, for instance, ignoring gravity,


$\displaystyle \frac{\gamma }{{\gamma - 1}}pV + \frac{{{v^2}}}{{2g}} = {\rm{a}}\;{\rm{constant}}$
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Last edited by studiot; May 5th 2018 at 09:03 AM.
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Old May 7th 2018, 02:36 AM   #4
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What is the system (in the thermodynamic sense) to be considered?

I guess it is the closed system (fixed number of particles)?
But then the internal energy is not p*V but rather the Integral p(V)dV.
Should this be calculated isothermal or adiabatic under normal conditions and say 30m/s.

What is gamma in your equation?
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