C in the Equation for Reciprocating Pump Acceleration

An important consideration in the design and operation of a crankshaft driven reciprocating pump is acceleration pressure (Pacc) or acceleration head (ha = Pacc*144/( γ_w *SG)). Acceleration pressure is one of several factors that effectively reduce the ability of a reciprocating pump to properly fill the pump pressure chamber before discharging. On a slightly higher level, acceleration pressure is the product of fluid acceleration in the pump suction line, multiplied by the mass of the fluid in the pump suction line (i.e., now we have a force), divided by the average cross-sectional area of the suction line ID (i.e., now we have pressure), then multiplied by a constant to get the desired units of pressure.

Ideally, the acceleration of the fluid in the suction line is the sum of the fluid acceleration contribution of each piston/plunger in the pump when the related velocity of that section is negative (i.e., on suction). This acceleration is a function that oscillates about zero and has the appearance of a saw tooth, such as that seen in Figure 1. The acceleration used to estimate acceleration pressure is the amplitude of this function multiplied by the ratio (Dp/Ds)² to get acceleration of the fluid in the suction line.

Acceleration Pressure

If we take the basic equation for acceleration pressure and substitute the generalized equation for pipe fluid velocity of a double acting reciprocating pump, then we get the general equation for acceleration pressure in a double acting reciprocating pump [(1) and (2)]. These general equations also work for single acting pumps. A single acting pump is the special case of a double acting pump where the rod diameter equals the piston/plunger diameter (i.e., δ = 1).   
On page 23 is the general equation for acceleration pressure1 for any inline double acting reciprocating pump for English and SI units.

These equations work for any variation of a double acting pump where δ varies from 0 to 1, including the special case for single acting pumps in which δ = 1.

The Constant C