How much kerosene was consumed by the engines of an aircraft that flew a distance of 500 km

| May 21, 2021 | education

How much kerosene was consumed by the engines of an aircraft that flew a distance of 500 km at an average speed of 250 km / h, if the average net power of its engines was 2300 kW? The efficiency of the motors is 25%.

S = 500 km = 5 * 10 ^ 5 m.

V = 250 km / h = 69.4 m / s.

Np = 2300 kW = 23 * 10 ^ 5 W.

r = 4.6 * 10 ^ 7 J / kg.

Efficiency = 25%.

m -?

Let us write down the formula for the efficiency of the aircraft engine: efficiency = Np * 100% / Nz.

We will write the consumed engine power Nz according to the formula: Nz = Az / t, where Az is the amount of thermal energy that is released during the combustion of kerosene in the engine, t is the engine operation time, that is, the flight time.

Az = r * m.

t = S / V.

Nz = r * m * V / S.

Efficiency = Np * 100% * S / r * m * V.

m = Nп * 100% * S / r * efficiency * V.

m = 23 * 10 ^ 5 W * 100% * 5 * 10 ^ 5 m / 4.6 * 10 ^ 7 J / kg * 25% * 69.4 m / s = 1440 kg.

Answer: during the flight, the aircraft engine consumed m = 1440 kg of kerosene.



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