I need to calculate the force on a fitting upstream of a pump (on the suction side) to determine whether restraint is needed across a flexible coupling at the pump.  The reservoir that the pump is taking water from is below the pump (suction lift condition).  How do I calculate the forces on the suction piping?  Is it based on the suction lift capability of the pump?

You need to consider weight of the pipe, as well as the weight of the fluid contained within it.  Assuming steady-state conditions, the flow of the fluid will not exert a force on the piping.

The instances in which you need to worry about these forces (i.e. those in line with the piping) would be due to thermal growth ( T > 200 F) or for seismic loads.  Additionally, some transients events would exert a lateral or axial load on the pipe, such as waterhammer or check-valve slam.

Keep in mind that this information is merely a snapshot of things to consider; I also recommend checking the applicable code you are working to for any additional considerations/requirements.

Flexible couplings are being used for this pump replacement project to provide some alignment flexibility because we are connecting some new piping at the pump to existing suction and discharge piping.  The suction piping is 8" (and the discharge piping is 6").  There is a 90 degree elbow a few feet from the coupling.

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You need a long straight pipe run into the pump suction: At least 6 to 10 pipe diameters worth.  8 x 8" dia = 64 inches straight minimum.  Preferably more.   If you don't you'll lose efficiency, start tearing up your impeller.  "A few feet" isn't enough for this size pipe with that 8" 90 deg elbow in your suction run.

I disagree with using a flex coupling on the inlet this way: your pump and piping need to be keep rigorously straight to maintain alignment on the pump shaft, and the shaft seal in particular.  You should be able to get that pipe to line up, rather than let the flex coupling permanently take an offset in left-right/up-down position.

Use at least 2 pipe supports between the flex coupling and the pump inlet to grab and maintain the inlet pipe run straight in line with the pump centerline, and additional pipe supports on the far side of the coupling  to hold the supply piping from the field.  

Don't let the pipe weight cross the flex coupling either!

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