waross,
Yes it is correct that the transient is positive on the upstream side and negative on the downstream side of a closed valve. The downstream wave loses amplitude with friction and compression of product ahead of it. When it is reflected, it continues to lose energy on the way back and the amplitude of that one wave is always less when it returns. If the pressure goes below atmospheric pressure, or external water pressure on an offshore pipeline, a pipe of relatively thin wall thickness to diameter ratio might collapse. At least all of that is true for a flat pipeline and a valve that does not have a feedback and control function. If I said or implied something differently, sorry for the confusion.
Now, once you start adding pumps, control valves, relief valves and realistic elevations to the Joukowski equation, it loses its conservativeness. You must consider the action time of the controls in conjunction with the transient pressures wave leaving, arriving or passing by and how much energy you have stored in the pressure expanded pipeline, in the compressed product itself and the potential energy of all product at higher elevations downstream (and sometimes upstream too). If you are pumping to a high elevation, which is what a lot of pumps do, there is a lot of stored energy up there that is more than ready to go back to where it came from. When the pump stops, it can be free to do so. Mr. Murphy says it tends to do it at inconvenient times.
I'm not following what you mean by "connection". Are you saying a discharge shut-in valve, or a check valve closes to "disconnect" the pipeline from the pump?
An example of a case I was referring to would be something like, only one pump running and discharging into a downstream pipeline that has pressured the product and pipeline to its operating point pressure. The pump's motor abruptly stops running and the pump stops turning in a 1/2 second or so. The pipeline is still pressured to operating pressure and that hi pressure product will begin to flow back through the pump's discharge into the suction of the pump, tending to reverse spin the pump, effectively turning it into a turbine. If two additional pumps were running and discharging into the same manifold, they would only make things worse, since the manifold and pipeline would then have a continuing source of product and pressure, instead of a decreasing amount of product and pressure as was the case with only one pump running and tripping.
I've had cases where a slight overpressure is relieved through a relief valve, which stops product flowing into the pipeline downstream as pump discharge flow is diverted to the relief valve. The pressure near the relief valve begins to decrease and the relief valve closes. Product already downstream of the pipeline then comes to a stop and velocity head is converted to pressure head, increasing the pressure and reopening the relief valve again, just as the pump's discharge control valve is opening back up again. It created a continuous cycle between the pump discharge pressure control valve, the relief valve and the pipeline downstream that was difficult to stop without shutting down the pump and completely restarting the system again from 0.
"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics
