Re: M Waheed.

To answer the question about imbalanced forces. Remember, when someone says "relief loads," they can mean:
1. The relief valve (or rupture disc or rupture pin, etc) activation force, where the surface that is normally sealed becomes unsealed. (t=0)
2. The resulting pressure wave as the discharge piping goes from P(operating) to P(relieving). (t=0 to some small number)
3. Steady state conditions. (t=∞)

At step 3, most forces have balanced themselves out. The exception would be for any tail pipe. Even at the relief valve. There is, as Mario indicates, a hydraulic imbalance as a result of having P1, A1, v1, and mdot on one side of the device and a P2, A2, v2, and (same) mdot on the other side of the device. I will note that this same force exists at every reducer and every elbow and especially reducing elbow, but we have a habit of ignoring those, because we assume they're minimal or otherwise cancel themselves out with other bends (though technically, this places piping into tension).

Direction of force of fluid onto pipe is always opposite the direction of flow.

Re: Mariog

Liquid relief loads and liquid hammer loads are directly analogous. Both result in a nearly instantaneous exchange of energy between pipe and liquid.

Imagine a pump, long pipe, and open valve at the end. Close the valve. Water hammer, right?

Imagine a pump, long pipe, and two valves at the end, 90° from the pipe, 180° from each other. One's closed, one's open. Open one simultaneously as the other one closes simultaneously. There is no hammer load, despite the fact that you closed a valve.

Imagine a pump, long pipe, and one closed valve at the end. Assume the pump's on recirculation or is capable of withstanding 0 flow but still supply the pressure. Open the valve at the end, and potential energy is released, and you have the same hammer loads, except in the opposite direction of opening said valve.

Replacing liquid with gas, notionally nothing changes. The loads are still there, but the energy is swept up into the gas's ability to compress, and the pressure waves are vastly mitigated.

re: Borzki

I agree that it could be theoretically done... Finding the longitudinal wall natural frequency assuming an infinitely long run of pipe, and compare with the frequency of a water hammer frequency, similar to pipe configuration's natural frequency. But I would think acoustical fatigue due to relief / hammer loads is a subset problem within a subset problem, for which to truly design, we'd have to consider a host of real world conditions that would be extremely arduous to fully consider. Imagine having to guarantee your pipe not only in new conditions, but corroded conditions... and everywhere in between. Now do the same thing for Tmax and Tmin... and everywhere in between. We typically don't do that last part now with CAESAR. We analyze at discrete temperatures. Who's to say there isn't an intermediate temperature that can't result in higher stresses due to interactions with non-linear supports?

It's a good thought experiment, though. One day we might get there.