Why does water power depend on density and velocity cubed?

[MrPotatoHead]

Hi,

Just out of curiosity, why is the density and volume used to find the power of a flow of water for example. I know the equation for this is P=0.5ρAv^3 where ρ=density and v=speed of the water cubed.

Any suggestions?

Thank you

 

[sankalpmittal]

Hi,

Just out of curiosity, why is the density and volume used to find the power of a flow of water for example. I know the equation for this is P=0.5ρAv^3 where ρ=density and v=speed of the water cubed.

Any suggestions?

Thank you

You've put Volume as area times velocity. Instead of volume , you've put volumetric flow of fluid per second. Your equation is dimensionally correct.

Work done by fluid in motion = Kinetic energy = mv²/2
Putting m = ρV
we have
Work done by fluid in motion = ρVv²/2
Now putting V= Ah where h is height
Work done = ρAhv²/2/2
Dividing by time , we have
Power of flow of fluid = ρAv³/2

Through this derivation I think its clear why density and velocity of fluid are related with power.

Also Power is force times velocity. So power depends on velocity of fluid. Work done here is the kinetic energy possessed by the fluid which of course depends on mass and hence depends on density of fluid. So Since power depends on work , so here in this case , power has to depend on density as well.