*The Thirteenth in a Series*

If a centrifugal pump is started with the discharge valve open too far and with a low discharge pressure, the liquid in the suction line may accelerate at a rate that causes the suction pressure to drop below vapor pressure. In other words, you can cause cavitation by allowing the pumpage to accelerate too rapidly in the suction line.

If the pump's capacity is controlled by a quick opening valve on the discharge side (such as seen in steel mill descaling systems), the pump may be provided with insufficient NPSH when the pumpage is accelerating to the rated capacity.

The equation for calculating the head drop due to the acceleration (assuming uniform acceleration) may be reduced to the following:

*Where*:

h_{a} = Head required to accelerate the liquid in the suction line, feet or meters

L = Total length of the suction line, feet or meters

V_{2} = The final velocity of pumpage, feet/sec or meters/sec

V_{1} = The initial velocity of pumpage, feet/sec or meters/sec

g = Acceleration of gravity (32.2 ft/s^{2} or 9.8 m/s^{2})

t = Time increment that pumpage accelerates from V_{1} to V_{2}, seconds

## Acceleration Head for Reciprocating Pumps

*Pulsing Flow Requires More NPSH*

The flow in the suction and discharge piping of a reciprocating pump is not constant. The pumpage must accelerate and decelerate a number of times for each revolution of the crankshaft. Because the liquid has mass, and therefore inertia, energy is required to produce the acceleration. This energy is returned to the system upon deceleration, so there is no loss. However, sufficient NPSH must be provided on the suction side of the pump to accelerate the liquid to prevent cavitation in the suction pipe and/or pumping chambers.

Figure 1 plots the *ideal* relative fluid velocity in the suction pipe for a typical triplex power pump as a function of the rotative angle of the crankshaft. (To achieve this ideal velocity profile, the pumpage must be incompressible, and the pump valves must open and close at the beginning and end of the plunger stroke, which is often not the case.) Acceleration may be more clearly visualized if we change the scales on this curve. If we change the abscissa from *degrees of rotation *to* time *(which is done by dividing by 360 and revolutions per second), and change the ordinate to *pipe velocity* rather than *relative velocity* (by multiplying by average pipe velocity), we have a plot of velocity versus time in the suction pipe.

Since acceleration is the rate of change of velocity with respect to time (dv/dt), we can determine acceleration simply by measuring the slope of the velocity curves. We see that a triplex pump produces maximum acceleration at 0 deg, 120 deg and 240 deg of crankshaft rotation.

*The Acceleration Head Equation*

We can calculate the mass of liquid in the suction line, and its acceleration. Then using Newton's second law (F = ma) we can calculate the force required to accelerate that mass. We can then convert this to pressure by dividing by the cross-sectional area of the pipe. Fortunately this has already been done, and appears in a number of documents. The first known appearance of the equation shown below was in a section of *Marks' Handbook *(5) by Elliott Wright. The author accepted and promoted it, and it subsequently appeared in Hydraulic Institute standards (2). Those documents provide the following equation:

*Where*:

h_{a} = Acceleration head, feet

L = Actual length of suction line, feet (not equivalent length)

V = Average liquid velocity in suction line, feet/second

N = Speed of pump crankshaft, revolutions/minute

C = Constant depending on pump type

= 0.400 for single‑acting simplex

= 0.200 for single‑acting duplex

= 0.115 for double‑acting duplex

= 0.066 for triplex

= 0.040 for quintuplex

= 0.028 for septuplex

= 0.022 for nonuplex

g = Gravitational constant = 32.2 feet/sec^{2}

k = Constant depending on fluid compressibility

= 1.4 for non‑compressible liquids such as deaerated water

= 1.5 for most liquids

= 2.5 for compressible liquids such as ethane

*Two or More Pumps Running in Parallel*

If two or more pumps operate in parallel, with a common suction line, acceleration head is calculated for the common line by assuming that all pumps are synchronized, acting as one large pump. (The capacities of all pumps are added to determine line velocity.)