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Wed 7 Nov, 2012 07:36 am
the efficiency of turbofan engines of commercial airplanes depend on air pressure and usually is maximum near about 10973 m, above mean sea level. Find the air pressure y(x) at this height given the rate of change y'(x) is proportional to the pressure, and at 5486 m the pressure has decrease to half its value Y0 at mean sea level.
@zetshield21,
You have two relations for pressure with gasses.
The idel gas law (PV=nRT) and pressure P=rho*g*h
Rap
@zetshield21,
The rate of change of air pressure with height is proportional to height.
dy/dh = kh where a and k are constant so
y = ae ^ kh
y(0) = a = 1 atm
y(5486) = ae ^ 5486k = 1/2 a
e^ 5486k = 1/2
5486k = ln .5 = -.6931
k = -1.263e-4
y(10973) = (1 atm) e^(10973*-1.263e-4) = 0.25 atm
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