THE PUZZLER

Pump ED 101

Positive Displacement Pumps

Part I – Reciprocating Pumps

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There are many pump designs that fall into the positive displacement
category but, for the most part, they can be nicely divided into two basic
groups. The reciprocating group operates via pistons, plungers, or
diaphragms while rotary pumps use gears, lobes, screws, vanes, and
peristaltic action. Their common design thread is that energy is added to
the pumped fluid only periodically where, in dynamic pumps, it is added
continuously.

PISTON & PLUNGER PUMPS

The piston pump is one of the most common reciprocating pumps and, prior
to the development of high speed drivers which enhanced the popularity of
centrifugals, it was the pump of choice for a broad range of applications.
Today , they are most often seen in lower flow, moderate (to 2000 PSI)
pressure applications. Its close cousin, the plunger pump, is designed for
higher pressures up to 30,000 PSI. The major difference between the two
is the method of sealing the cylinders. In a piston pump the sealing system
(rings, packing etc) is attached to the piston and moves with it during its
stroke. The sealing system for the plunger pump is stationary and the
plunger moves through it during its stroke.

Reciprocating pumps operate on the
principle that a solid will displace a
volume of liquid equal to its own
volume. The figure to the right is
that of a generic double acting
piston pump. If we were to remove
the two valves at the left hand side
of the figure and replace them with
an extension of the cylinder, we would have a single acting pump. The single

acting pump discharges water only on its forward stroke while the double
acting pump discharges on its return stroke as well. During the suction
stroke (right to left) the single acting pump’s discharge valve closes and
allows fluid to enter the cylinder via the suction valve. When the piston
changes direction (reciprocates) the suction valve closes and water is
discharged through the discharge valve. In the double acting pump, the
same sequence occurs during both strokes and almost twice as much fluid is
discharged per unit time.

Pressure

The head created by a centrifugal pump depends upon the velocity it imparts
to the fluid via its impeller. Therefore, for any given impeller diameter and
rotational speed, head will be some maximum, unvarying amount. Not so for
reciprocating pumps. Although they will have a maximum operating pressure
rating, the maximum pressure (P) attained depends upon the application.
Against a closed discharge valve, pressure is limited only by the capability of
the driver and the strength of the materials employed. Only the “breaking
point” of some component will limit discharge pressure. Therefore some
form of pressure relief must be supplied if an application is capable of
exceeding the pressure rating of the pump.

Capacity

The capacity (Q) of a single acting piston or plunger pump is proportional to
its displacement (D) per unit time. The displacement is the calculated
capacity of the pump, assuming 100% hydraulic efficiency, and is
proportional to the cross sectional area of the piston (A), the length of its
stroke (s), the number of cylinders (n), and the pump’s speed in rpm. In
gallons per minute it is:

D = (A x s x n x rpm) / 231

In the case of double acting pumps the cross sectional area of the piston or
plunger is doubled and the cross sectional area of the piston rod (a) is
subtracted. Again, in gallons per minute D is:

D = ((2A - a) x s x n x rpm) / 231

In real life the theoretical capacity of a piston or plunger pump is tempered
by several factors. One is known as slip (S). The major component of slip is
the leakage of fluid back through the discharge or suction valve as it is
closing (or seated). It can reduce calculated displacement from 2 to 10%
depending upon valve design and condition. Increased viscosity will also
adversely affect slip.

Another important factor that affects
a reciprocating pump’s capacity is
something called volumetric efficiency
(VE). VE is expressed as a percentage
and is proportional to the ratio of the
total discharge volume to the piston or
plunger displacement. The figure to the
right illustrates how we arrive at this
ratio.

The ratio (r) is shown to be (c+d)/d where d is the volume displaced by the
piston or plunger and c is the additional volume between the discharge and
suction valves. The smaller this ratio, the better the volumetric efficiency.
Expressed mathematically, it looks like this:

VE = 1 - (P x b x r) - S

where P is pressure, b is the liquid’s compressibility factor, r is the volume
ratio, and S is slip. The compressibility factor for water is quite small (3 X
10

-6

inches per pound of pressure at ambient temperature) but at pressures

greater than 10,000 PSI it does become a factor.

The figure above also clearly illustrates the volumetric displacement
operating principle of these pumps. Although there is no cylinder wall around
the plunger at the bottom of its stroke, it still displaces fluid equal to its
own volume. Now, we can finally state the actual capacity of a reciprocating
pump. It is quite simply:

Q = D x VE

Power

The power required to drive a reciprocating pump is quite straight forward.
It is simply proportional to pressure and capacity. In brake horsepower it is:

bhp = (Q X P) / (1714 X ME)

where 1714 is the bhp conversion factor and ME is mechanical efficiency.
Mechanical efficiency is the percentage of the driver power that is not lost
in the pump’s power frame and other reciprocating parts. The mechanical
efficiency of a piston or plunger pump ranges between 80 and 95%
depending upon speed, size, and construction.

DIAPHRAGM PUMPS

Diaphragm pumps are reciprocating positive
displacement pumps that employ a flexible
membrane instead of a piston or plunger to
displace the pumped fluid. They are truly self
priming (can prime dry) and can run dry without
damage. They operate via the same volumetric
displacement principle described earlier. The
figure on the right shows the operational cycle
of a basic, hand operated single diaphragm pump.

Were its operation any simpler, it would
compete with gravity. The upper portion of the
figure shows the suction stroke. The handle
lifts the diaphragm creating a partial vacuum
which closes the discharge valve while allowing
liquid to enter the pump chamber via the suction
valve. During the discharge stroke the diaphragm is pushed downward and
the process is reversed. Hand operated pumps are designed to deliver up to
30 gpm at up to 15 feet but actual capacity is extremely dependent upon the
physical condition of the driver. Air, engine, and motor drive units are also
available and offer capacities to 130 gpm. Both suction and discharge head
vary from 15 to 25 feet.

You will note that, unlike pistons and plungers, diaphragms do not require a
sealing system and therefore operate leak free. This feature does,
however, preclude the possibility of a double acting design. If nearly
continuous flow is required, a double-diaphragm or duplex pump is usually
employed. The figure below is a cross section of an air operated, double
diaphragm pump.

The double diaphragm pump utilizes
a common suction and discharge
manifold teamed with two
diaphragms rigidly connected by a
shaft. The pumped liquid resides in
the outside chamber of each while
compressed air is routed to and
from their inner chambers. In the
figure, the right hand chamber has
just completed its suction stroke
and, simultaneously, the left
chamber completed its discharge
stroke. As would be expected, the
suction check is open so that liquid
can flow into the right chamber and the discharge check of the left
chamber is open so that liquid can flow out. Except for the double chamber
configuration, its operation is just like the double acting piston pump seen
earlier. The difference, of course, resides within the inner chambers and
the method in which the reciprocating motion is maintained. This is
accomplished by an air distribution valve that introduces compressed air to
one diaphragm chamber while exhausting it from the other. Upon completion
of the stroke the valve rotates 90 degrees and reciprocation occurs.

I introduced this section with the statement that diaphragm pumps are
positive displacement in nature. Generally this is an accurate statement but
they can also be referred to as “semi” positive displacement. The reason for
this is the elasticity of the diaphragm and a corresponding reduction in
volumetric efficiency as discharge pressure increases. Also, check valve
leakage is often significantly greater than that experienced by piston and
plunger pumps.

AFFINITY

Although we tend to associate affinity laws with centrifugal pumps, other
mechanical devices also exhibit these “natural” relationships. In the case of
positive displacement pumps the affinity laws are very straight forward.

Flow

- Flow varies directly with a change in speed. If the rotational speed is

doubled, flow is also doubled.

Pressure

- Pressure is independent of a change in speed. If we ignore

efficiency losses, the pressure generated at any given rotational speed will
be that required to support flow.

Horsepower

- Horsepower varies directly with a change in speed. If we

double the rotational speed, twice as much power will be required.

NPSHr

- Net Positive Suction Head required varies as the square of a

change in speed. If we double the rotational speed NPSHR increases by four.