I didn't say nobody can do it. I said I doubt anybody remembers the formula. The square root is in the numerator, not the denominator.
The math was the easiest part - it took 2 steps (rearranging, integrating) then plugging in numbers. Most terms were constants with respect to our integration variables. The only tricky part, integrating (C-x)^(-1/2)dx, is about as simple an integral as you can do - sqrt is 1/2 power - same rules apply. I forgot and asked google, then a web site. Whole thing took less than 5 minutes.
http://integrals.wolfram.com/index.jsp?expr=(c-x)^(-1/2)&random=false
The numerical solution is correct. The symbolic calculus solution is not. You have the sign wrong on the exponent. It is easy to find a solution using a spread sheet or numerically. It just takes a little algebra. Below is my solution using a spread sheet. I used open office but saved the spreadsheet in excel format.
ftp://ftp.deltacompsys.com/public/N...tacompsys.com/public/NG/UnderMorePressure.zip
Notice what happens when the time period is 100 microseconds. The solution oscillates. I could make the time period smaller but I would need 10 times more rows and the spread sheet would be very small. There are better ways to compute the slope or rate of change.
Thanks for the hydraulics lesson - I haven't studied anything but the very basics.
Δp=-B*ΔV/V is the basic formula for how pressure changes. The key is the ΔV can come from flow or motion of the piston.