# Pressure wave in pipe

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1. Feb 16, 2015

### Trevorman

1. Problem statement
• In a straight pipe there is at t = 0 an over-pressure for |x| ≤ a of the form p0(x) = A(1–
• |x| ), where A is small. The velocity is zero at t = 0. Determine the pressure in the
• pipe for x > 0 and t > 0. Determine also the pressure at the closed end located at x = L (L > a)
2. Relevant equations
D'Alembert Equation

$p(x,t) = \frac{p(\epsilon) + p(\eta)}{2} +\rho c \frac{u(\epsilon) - u(\eta)}{2}$
where p is the pressure, u is the velocity
$\epsilon = x-ct$
$\eta = x+ct$

3. The attempt at a solution

I made characteristics in a t-x diagram, but I do not know how to proceed.

2. Feb 21, 2015