seal pressure

I think you will find the answer to your first question in the stuffing box pressure thread just below.

As for seal flush flow, a good rule of thumb is a gallon a minute per inch of shaft size, for a Plan 11 recirculation from discharge. You can regulate that with an orifice or use one of the many flow and pressure control devices that seal mfgs offer.

The pump is a small flow, 80 gpm water pump, close coupled, water service. It has a mechanical seal with no provision for flow control to the seal. My concern is when discharge is restricted, that there is sufficient flow in seal area on the back side of the impeller to provide adequate cooling of the seal. Is there a way to approximate this or does the 1 gpm per inch of shaft size apply?

Like I said the gallon of flush per inch is a rule of thumb. Most people recirculate a portion of the discharge into the seal chamber. Most pump OEMs provide flats for machining or already machined NPTs on the volute or just below the discharge flange. Using the NPT closest to the discharge flange tube a flush line into the lantern ring connection unless there is a flush connection on the seal gland plate. If there isn't a good place on the pump to machine an connection, piping upstream of the check and block valves can be modified to provide the flush. If needed an orifice can be used to achieve the proper flow.

The heat generated at the seal faces and minimum flow can be calculated. You might want to contact the seal vendor as they will have information about the seal face friction that is important for this. This way you can find the requirements of your worst case scenerio.

How restricted?

I think they ran deadhead for some time. They lost seals a few times. Likely while they were making steam when the pump was churning.

If it runs deadheaded it won't matter. As you vaporize the water the seal chamber liquid level drops and you end up running the seal without face lubrication. (boiler feed water pump anyone?)

Perhaps a minimum flow loop or a motor power monitor would help. (Power monitors are cheap, and can be set up to get the operator to check out the pump before re-starting it. That way the operator can learn why the pump stopped in the first place.)

There are a few tricks that can be done to help the seal survive this but they really boost the price of the seal. Unless the deadheaded operation is impossible to get around I'd try to fix that first. In the long run the damage to the pump isn't worth it.

take a thumb rule for single stage back suction cetrifugal pump as the suction pressure + 25 % of the differential between the suction and discharge pressures