The problem is to calculate the flux emanating from the exhaust of a jet engine.
The air gas velocity from a jet engine varies linearly from a maximum of 300 m/s at the center of the circular exhaust opening to zero at the edges. If the exhaust diameter is 1.6 m, find the exhaust flow.
The answer is 201 meters cubed over second
The Attempt at a Solution
b=300 m/s at center
x =radius in meters = r
m=slope=0-300/(0.8-0)=-375 cycles/s, 0.8 is radius of circular opening
2: Compute Flux, Psi
flux(non-uniform flux denisity) = Double integral B dot dS
dS = surface area of circle=pi*r^2 in this case.
limits are 0-0.8 of both integrands
variable of interest is r. similar to integrating acceleration twice to get position
I know I need to ulimately set up a double integral