Question

The engine of an aircraft propeller delivers an amount of power 176 hp to the propeller at a rotational velocity of 2300 rev/min.

a) How much torque does the aircraft engine provide?
b) How much work does the engine do in one revolution of the propeller?

Answer 1

Answer:

a) τ = 544.8Nm
b) E = 5456 J

Explanation:

a) The torque provided by the aircraft engine can be calculated using the formula:

P = τω

where P is the power delivered to the propeller, τ is the torque provided by the engine, and ω is the rotational velocity of the propeller in radians per second.

We first need to convert the rotational velocity from revolutions per minute (rpm) to radians per second. There are 2π radians in one revolution, so:

ω = (2300 rev/min) * (2π rad/rev) * (1 min/60 sec)
= 240.7 rad/s

Now we can solve for τ:

τ = P/ω
= (176 hp) * (745.7 W/hp) / 240.7 rad/s
= 544.8 Nm

Therefore, the torque provided by the aircraft engine is 544.8 Nm.

b) The work done by the engine in one revolution of the propeller is equal to the energy delivered to the propeller. The energy delivered can be calculated using the formula:

E = P * (1 rev/ω)

where E is the energy delivered, P is the power delivered to the propeller, and ω is the rotational velocity of the propeller in radians per second.

Using the value of ω calculated above, we can solve for E:

E = P * (1 rev/ω)
= (176 hp) * (745.7 W/hp) * (1 rev/240.7 rad/s)
= 5456 J

Therefore, the work done by the engine in one revolution of the propeller is 5456 J.