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bob_confused2

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I am trying to better understand transient fluid dynamics in pipes. First, I am attempting what I believe should be relatively simple problem. I have a constant area horizontal pipe partially filled with a stationary incompressible inviscid fluid. The part of the pipe that is filled is upstream of a burst disc which separates the rest of the pipe. Upstream of the burst disc is at pressure P1 and downstream is P2. At t=0sec, the disc bursts. What is the velocity v2 of the fluid as it flows as a function of time? Here, I am assuming that I am looking only at the velocity at the location of the burst disc and that the flow is uniform. Once I understand this problem, I hope to add in friction and varying location.

I've started with F=ma=m(dv/dt)

--> rho(A)dx(dv/dt)=-AdP

rho(dv/dt) = -dP/dx

And I want to see how long it takes for the velocity to reach the velocity that would be calculated from Bernoulli's equation: P1-P2=rho(v2)^2/2

Any assistance/guidance would be greatly appreciated.

Thank you