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LoopInt
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Homework Statement
This is a experimental problem that I am trying to model:
I have an air source with constant pressure P connected with a small chamber (cylinder). The chamber has initial internal pressure P_0 and as time t goes, the pressure in the chamber raises to P.
So, find the step response of P_chamber(t).
Homework Equations
Thats a great question itself, hehe. These are the ones I tried:
P+ρU^2+ρgh = const
PV=mRT
dm/dt = ρU A
The Attempt at a Solution
P_chamber = (m(t)RT)/V
m varies over time, V is constant, R is constant and T is a problem. (don't know if I can keep it constant, but I did)
I assume the tank is very large compared with the chamber, so U for the tank is 0. I also neglected the hydrostatic term as ρ and h are very small.
So,
P=P_0+P_chamber+ρU^2
well, I'm stuck at this point. Can't reach a diff eq.
Experimentally the step response looks like P_chamber(t) = P(1-e^(-t/B)) ; where B is a time constant
So it should be a first order diff. eq.
Thanks in advance!