Acceleration pressure is an important factor in estimating the necessary boost pressure to prevent cavitation in reciprocating pumps. The Hydraulic Institute provides an equation for estimating acceleration pressure for crankshaft-driven reciprocating (CDR) pumps with piston centerline coincident with crankshaft centerline. This equation contains a numerical variable “C,” which is dependent on the number of cylinders in the pump and whether the pump is single acting or double acting. By means of the Maple™ [1] symbolic algebra computer program, this paper presents the following: • Analytic solutions for “C” for double-acting pumps with any odd number of cylinders and another analytic solution for pumps with any even number of cylinders. • General solutions for “C” that make the acceleration pressure equation analytic for pumps with 1 to 9 cylinders. • Estimated solutions for “C” for pumps with any numbers of cylinders greater than or equal to 3. The analytic solutions demonstrate that “C” is dependent on the connecting rod length, the crank throw radius, the effective diameter of the push rod, and the diameter of the piston.

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