# Total energy of air, does it include pressure?

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I'll ask this in the form of an example. A bus is traveling at some speed and there is no wind. The bus experiences a drag force related to the pressure differential at the front and rear of the bus. Most of the divergence in pressure from ambient occurs behind the bus, where the air is accelerated forward to fill in what would otherwise be a void.

The power consumption related to drag should be this drag force times speed (this is a no wind condition, so ground speed = air speed).

The "exit velocity" for each tiny amount of mass of air affected by the bus it that bit of air's velocity at the moment and place where it's pressure returns to ambient. Will the work done on the air by the bus be equal to the integral sum of 1/2 mass (exit_velocity)2?

The velocities in the immediate vicinity of the bus will be different than the exit velocities. The higher pressure areas will have velocities lower than exit velocity and vice versa. Is the work done on the air instead related to these velocities as opposed to the exit velocities?

Now to reask the original question, is the work done only related to the kinetic energy change of the air, or is the pressure energy of the air also a factor?

another example

Take a second bus with a streamlined tail section to reduce the drag. Bus2 travels faster so that it consumes the same amount of aerodynamic power as bus1 :

drag2 speed2 = drag1 speed1

Will the integral sum of the 1/2 mass (immediate_velocites)2 or 1/2 mass (exit_velocities)2 (or maybe both?) be the same for bus1 and bus2?

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