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- Homework Statement
- I am trying to find the power generated by a helicopter blade spinning, sweeping out a circular area A each time, and causing the air below to flow uniformly at speed v. The density of air is ##\rho##

- Relevant Equations
- Power = Fv

Power = Energy/time

Solution 1:

Force on air = Force on helicopter.

##F = \frac {dp} {dt} = v \frac {dm} {dt} = v^2 \rho A##

##P = Fv = \rho A v^3##

Solution 2:

Power from helicopter converted to rate of kinetic energy increase of air

##P = \frac {dE} {dt} = \frac {1} {2} v^2 \frac {dm} {dt} = \frac 1 2 \rho A v^3##

I am almost certain solution 1 is the correct solution. This appears similar to the sand falling on conveyor belt problem. The energy loss in the 'sand' problem comes from the fact that sand particles have to be sped up to reach speed v. In this case, is there energy loss due to air friction between air particles? And so energy is lost by speeding air particles up to speed v. This is quite hard to imagine, given how little friction between air particles there should be.

Thanks for all the help.

Force on air = Force on helicopter.

##F = \frac {dp} {dt} = v \frac {dm} {dt} = v^2 \rho A##

##P = Fv = \rho A v^3##

Solution 2:

Power from helicopter converted to rate of kinetic energy increase of air

##P = \frac {dE} {dt} = \frac {1} {2} v^2 \frac {dm} {dt} = \frac 1 2 \rho A v^3##

I am almost certain solution 1 is the correct solution. This appears similar to the sand falling on conveyor belt problem. The energy loss in the 'sand' problem comes from the fact that sand particles have to be sped up to reach speed v. In this case, is there energy loss due to air friction between air particles? And so energy is lost by speeding air particles up to speed v. This is quite hard to imagine, given how little friction between air particles there should be.

Thanks for all the help.