I recently saw this lecture from NPTEL on water hammering. I suppose example used for explaining the wave motion is widely used. (flow from a reservoir and valve closure).
(https://www.youtube.com/watch?v=mN9d6h3Qlx4)
I have following doubts
1) On gradual closing, pressure wave is not created?
2)In the example, the flow is from the reservoir, but sudden closure of continous flow will trigger breakage. For instance when there is a flow in a pipe (hose) if I squeeze it or manually prevent the flow, the pipe breaks due to high pressure. Is this considered as water hammer?
3)In the example pressure wave occurs only between o < t
No it is not the only case, that causes a positive surge upstream, but closing causes a negative surge downstream as well.
In opening the gates or [fast] starting of pumps you can cause a positive surge downstream and a negative surge upstream.
I think need some more clarifications on my doubt rather +ve or -ve surge.
1)
It depends how gradual, you can find the limit in books for "surge design" if the wave goes forward and backward once and gate is still closing it is not considered a shock (water hammer)
2) In the hose as it is very elastic, it kills big portion of the surge and damp it, also you cannot squeeze it too fast to seal a hose, so I do not know if it is okay to call it a water hammer per say
3) Write the equations of water hammer for "rigid" pipe (zero strain steel). System of two equations, mass and momentum balance in the pipe direction (or mass and two momentum balances in pipe and radial direction). you can find them in this book:
https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/TR029i002p00227
Those equations are a system of hyperbolic equations, water hammer is shock, follow the characteristics with your initial condition (/a)
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