Allow for "overlap" of one displacement to the next. This is dependent on the volumetric efficiency, due to compressibility of your system liquid.
This may radically effect the level of flow fluctuation and pressure pulsation.
1. Input Data
VE – actual displacement divided by 100% volumetric displacement
L – Connection rod length
R – Crankshaft radius
VI – Volumetric inefficiency
X – stroke before valve opening
Parameter for calculation purposes
If in this example, the pump was a triplex then the flow would come to a complete halt between strokes. This is because a rotary driven reciprocating pump sucks & discharges for 180° of rotation and the next displacement begins after 120°. The overlap on triplex at 100% efficiency is therefore 60°. At 77.512% the calculation shows that the 60° has been lost, hence with no overlap the flow will come to a halt between displacements. It will be as "pulsatious" as a duplex.
By the same calculation as the example, if the efficiency was 85% then the lost angle would become 48°. With a "Quin" a new displacement should begin every 72 degrees (360/5), and as discussed above a triplex should displace every 120°. 120° minus 72°=48°. But at 85% efficiency, 48 has been lost, so a Quin can cause as much flow fluctuation as a perfect Triplex if the quin has low volumetric efficiency.
Therefore, A three headed diaphragm metering pump may produce flow fluctuations as bad as, or worse than, a duplex pump or double acting simplex pump.
A quintuplex, or 5 plunger pump, may produce flow fluctuations as good as, or worse than, a good triplex pump, it all depends on volumetric efficiency.
Consequently, where N2 is a divisor, you would have to treat a triplex N2 as 2x2=4, not 3x3=9.