# Pressure, energy density, and power of a fluid flow

I've read that you can view static pressure of a fluid as energy density, which makes sense to me. I've also seen that the power of a fluid flow can be calculated by multiplying the pressure by the volumetric flow rate. However, doesn't a flow also have kinetic energy? How can you calculate the power delivered by a fluid flow without incorporating the kinetic energy per unit volume? Why isn't Power= (P+ density*v^2/2)*Q

http://hyperphysics.phy-astr.gsu.edu/hbase/press.html

Thanks!

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Jano L.
Gold Member
The hyperphysics article is wrong on two important things. First, it says

When you deal with the pressure of a liquid at rest, the medium is treated as a continuous distribution of matter. But when you deal with a gas pressure, it must be approached as an average pressure from molecular collisions with the walls.
This is not true, in normal conditions gases (air) are fluids and can be described by the same kind of continuous distribution of matter. Only when the gas gets very rare this breaks down and the ballistic description is necessary.

Pressure in a fluid can be seen to be a measure of energy per unit volume by means of the definition of work. This energy is related to other forms of fluid energy by the Bernoulli equation.
This is true only for ideal gas; the pressure P is proportional to kinetic energy of molecules per unit volume. In liquids, this is no longer true. The pressure is not proportional to total energy of liquid per unit volume.

This can be easily seen if we ask how much work need to be done to produce great pressure, says 10 bar, in water. Since the water is almost incompressible, the required work is very small. Hence the energy of pressurized water is almost the same as the energy under low pressure; the increase of pressure does not mean the energy increases as well. They are separate quantities.

256bits
Gold Member
I've read that you can view static pressure of a fluid as energy density, which makes sense to me. I've also seen that the power of a fluid flow can be calculated by multiplying the pressure by the volumetric flow rate. However, doesn't a flow also have kinetic energy? How can you calculate the power delivered by a fluid flow without incorporating the kinetic energy per unit volume? Why isn't Power= (P+ density*v^2/2)*Q

http://hyperphysics.phy-astr.gsu.edu/hbase/press.html

Thanks!
Pressure x volumetric flow rate , P x Q = Power
doesn't the volumetric flow rate already incorporate the velocity of the fluid? ( you have to say yes )

Force x velocity = power

just divide pressure and Q by the area ( you should get Force x velocity )

just remember, Bernoulli is an energy balance from one point to another point of the fluid flow.

If the energy density is described as that per unit weight

then you have pressure energy + kinetic energy + gravitational potential energy = constant.