quixotron

Hi Guys,

Name's Quixotron. I am writing to you to ask about a electromagnetics problem(well its a flux problem, but its in an EM book). I have already computed the answer and just want to double check my work, because the book gives another answer and books tend to have typos from time to time.

Ok.

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.

Alright. My first assumption is that I cannot use the B*A cos (theta) dot product, because the flow rate B, is not uniform, it varies linearly.

1: Compute B
Since it varies linearly I can derive an equation that gives me the flow rate as a function of position.

Used y=mx +b

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
y=B=-(375*x)+300
m/s

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

3: Plug in and solve

pi* SS (-375*r+300) dr dr limits: 0-0.8; 0-0.8
((-375*(r^2))/2) + 300*r limits 0-0.8
ANS: 120

integrate 120 wrt r, 120* r limits 0-0.8
ANS: 120*0.8*pi=301 approx

The book says 201 m^3/ s. I know how hey can get it, they can integrate B twice but only solve using the limits once.

So I'm a bit stuck. Is my logic faulty? I must admit its been a while since I cracked open my vector calculus em books. If anyone can walk me through, I would most appreciate it.

A 1000 thank yous in advance,

Quixotron

juanbbv

Hi
I ´ve been looking your problem and it seems to be ok, altougth i dont understand very well your matemathic sintaxis. I solve the problem too and the final result is the same as yours!
Dont worry books sometimes have missmaches in the results, it has happened a lot to me!
Good luck!

Juan