Reciprocating Plunger Pump

There may not be a hard-and-fast number for this, but 4 seems to be common.

You need to first measure the depth of the stuffing box. Then also measure the free space between stuffing box and shaft. This "space size" will give you the dimensions of the stuffing you'll use. Now subtract the distance that the collar will start into the stuffing box. now you will be able to calculate number of rings you'll require. Remember to tighten the collar finally when the pump is running until you have an occasional drip. The drip is of course to lubricate and cool the shaft. ( If you dont have the axact size of the "space" you may use slightly larger stuffing and flatten it with a hammer, but now you'll have rectangular stuffing and you have to recalculate the number of rings)

The number of packing rings:

This depends on the size (length ) of the stuffing box and the size (thickness) of the packing being used.

Also, from design point of vue (if this is your objective), it will depend on the max. pressure expected to be developped by the pump in operation. Therefore, the higher the pressure design, the longer the stuffing box might be. ( Increasing the pressure on the packing is limited by the requirement to allow a small leak to lubricate the shaft, as already pointed out).