Thrust from a stationary mounting

Question

If a propeller, on a stationary mounting, blows back 36kg of air per second at a speed of 45 knots, what thrust does it produce?

Answer 1

Thrust is simply how much force the propeller makes. Also force is the rate of change of momentum with respect to time.

 

Momentum is p=mv where,

 

m = mass

v velocity

 

Now taking the derivative of momentum with respect time you get

 

F=d(mv)/dt=mdv/dt + vdm/dt

 

The first term is the familiar force being equal to mass time acceleration and the second term can be used to calculate thrust in which is equal to velocity of air flow times the rate of change of mass with respect to time.

 

Before using the equation to calculate thrust, you need to convert the velocity 45 knots to m/s in order to make the units cosistent to what would be the thrust the propeller produces.

 

1 knot is simply equal to 1.852 km/hr 

 

Convert 45 knots to m/s

 

45 knot*1.852 km/hr*1000 m/km*1hr/3600s = 23.15 m/s

 

Thus, the thrust is:

 

T=23.15*36=833.4 N ≅ 830 N if using 2 significant figures

 

Therefore the thrust would be about 830 N.