A fully loaded plane weighs 200,000 lbf as it lands at a speed of 125 mph. The m

Question

A fully loaded plane weighs 200,000 lbf as it lands at a speed of 125 mph. The mass of the brakes on the plane is 200 lbm and the brake assembly has an equivalent specific heat of 0.20 Btu/lbm ·°R. Approximately 20% of the energy of the plane is dissapated by means of the brakes while the remainder is dissapated by means of reversing the thrust of the engines and viscous drag to the surrounding air. Estimate the maximum temperature rise that the brake assembly will reach when bringing the plane to rest.

Explanation / Answer

Given:

mass of plane , m = 200000 lbm

Velocity of plane, v = 125 mph = 183.33 ft/s

equivalent specific heat capacity of the brakes = 0.2 Btu/lbm.0R

20% of the energy is dissipated by brakes

Mass of the brakes , m0 = 200 lbm

Solution:

Kinetic energy of the plane = (1/2) m v2 = 0.5 x 200000 x 183.33 = 3.361 x 109 Btu

20% of this energy is 0.672 x 109 Btu

This energy is transfered to the brakes.

0.672 x 109 = m0cT

=> T = 0.672 x 109/(200 x 0.2) = 16.8 x 1060R

T = 16.8 x 1060R

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