To determine the mass flow through the propeller, we can use the equation:
Mass flow rate = Thrust / Jet velocity
Given that the thrust is 10 Newtons and the jet velocity is 50 kilometres per hour (which needs to be converted to meters per second), we can calculate the mass flow rate:
Jet velocity = 50 km/h = 50,000 m/3600 s = 13.89 m/s
Mass flow rate = 10 N / 13.89 m/s = 0.72 kg/s
Now, we can use the equation:
Mass flow rate = Air density * Propeller area * Speed of flow through the propeller
Given that the air density is 1.225 kg/m^3, the mass flow rate is 0.72 kg/s, and the speed of flow through the propeller is equal to the jet velocity (13.89 m/s), we can solve for the propeller area:
0.72 kg/s = 1.225 kg/m^3 * Propeller area * 13.89 m/s
Propeller area = 0.72 kg/s / (1.225 kg/m^3 * 13.89 m/s) = 0.0525 m^2
Finally, we can find the propeller diameter by assuming it is a circular shape:
Propeller area = π * (Propeller diameter/2)^2
0.0525 m^2 = π * (Propeller diameter/2)^2
Solving for the propeller diameter:
(Propeller diameter/2)^2 = 0.0525 m^2 / π
Propeller diameter/2 = sqrt(0.0525 m^2 / π)
Propeller diameter = 2 * sqrt(0.0525 m^2 / π) ≈ 0.321 m
Therefore, the propeller diameter is approximately 0.321 meters.
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)Again consider the model propeller of the previous problem. If we assume the jet velocity to be equal to the velocity of the air through the propeller, then we can say that , where is the air density, is the propeller area and is the speed of the flow through the propeller.
Given that the test was performed with an air density of 1.225 kilograms per cubic metre, determine the propeller diameter (in metres).
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