A propeller engine for a model airplane is measured to have a jet velocity of 50 kilometres per hour. When strapped to a fixed support it is measured to produce 10 Newtons of thrust. Determine the mass flow through this propeller (in kilograms per second):
We can use the equation for thrust generated by a propeller:
Thrust = Mass flow rate x (Jet velocity + Air velocity) + Propeller efficiency x Power
Since the propeller is strapped to a fixed support and not moving through the air, we can assume that the air velocity is zero. Therefore:
Thrust = Mass flow rate x Jet velocity
Solving for mass flow rate:
Mass flow rate = Thrust / Jet velocity
Substituting the given values:
Mass flow rate = 10 N / (50 km/h) = 10 N / (13.89 m/s) = 0.720 kg/s
Therefore, the mass flow through this propeller is 0.720 kilograms per second.
To determine the mass flow through the propeller, we can use the equation:
Thrust = Mass flow x Jet velocity
Given:
Thrust (T) = 10 Newtons
Jet velocity (V) = 50 kilometers per hour = 50,000 meters per hour
First, let's convert the jet velocity from meters per hour to meters per second:
50,000 meters per hour = 50,000/3,600 meters per second ≈ 13.89 meters per second
Now, we can rearrange the equation to solve for mass flow:
Mass flow = Thrust / Jet velocity
Substituting the given values:
Mass flow = 10 Newtons / 13.89 meters per second
Finally, let's calculate the mass flow:
Mass flow ≈ 0.719 kilograms per second (rounded to three decimal places)
Therefore, the mass flow through the propeller is approximately 0.719 kilograms per second.