The helicopter shown in the figure below has a mass of 12 tons and it needs...

The helicopter shown in the figure below has a mass of 12 tons and it needs to rotate its 14 meter blades (diameter of the blades = 14 meters) at 670 rpm just to hover (stand still in mid air) without any additional load. The air flow caused by the rotation of the helicopter blades may be modeled as a moving cylindrical body of air having a 14 meter diameter. The average velocity of the airflow of that cylindrical air-body is proportional to the rotational speed of the helicopter blades (RPM).
Determine the airflow rate when the helicopter hovers and the power that its engines produce.
If the helicopter is now loaded with an 8 tons load as shown in the figure. Determine again the airflow rate when the helicopter hovers and the power that its engines produce.

Expert Solution

Assumptions

1 The flow of air is steady and incompressible.

2 Air leaves the blades at a uniform velocity at atmospheric pressure.

3 Air approaches the blades from the top through a large area at atmospheric pressure with negligible velocity.

4 The frictional effects are negligible, and thus the entire mechanical power input is converted to kinetic energy of air (no conversion to thermal energy through frictional effects).

5 The change in air pressure with elevation is negligible because of the low density of air.

6 There is no acceleration of the helicopter, and thus the lift generated is equal to the total weight.

The density of air is taken as 1.18 kg/m3 .

samet mamat answered 1 year ago

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