Reciprocating pump is a positive displacement pump, which causes a fluid to move by trapping a fixed amount of it then displacing that trapped volume into the discharge pipe. The fluid enters a pumping chamber via an inlet valve and is pushed out via a outlet valve by the action of the piston or diaphragm. They are either single acting; independent suction and discharge strokes or double acting; suction and discharge in both directions.

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Reciprocating pumps are self priming and are suitable for very high heads at low flows. They deliver reliable discharge flows and is often used for metering duties because of constancy of flow rate. The flow rate is changed only by adjusting the rpm of the driver. These pumps deliver a highly pulsed flow. If a smooth flow is required then the discharge flow system has to include additional features such as accumulators. An automatic relief valve set at a safe pressure is used on the discharge side of all positive displacement pumps.
There are two general types of reciprocating pumps.   The piston pump and the diaphragm pump.
These types of pump operate by using a reciprocating piston or diaphragm.   The liquid enters a pumping chamber via an inlet valve and is pushed out via a outlet valve by the action of the piston or diaphragm.
The reciprocating pump is not tolerant to solid particles and delivers a highly pulsed flow.   If a smooth flow is required then the discharge flow system has to include additional features such as accumulators to provide even flows.
Reciprocating pumps designed for delivering high pressures must include methods for releasing excessive fluid pressures.   The pumps should include for built in relief valves or relief valves should be included in the fluid circuit which cannot be isolated from the pump.   This feature is not required for safety for the air operated diaphragm valve.
Piston Pumps /Plunger pumps
A piston pump can be based on a single piston or, more likely, multiple parallel pistons.   The pistons are reciprocated using cams or crankshafts.   The stroke is generally adjustable.  This type of pump can deliver heads of up to 1000 bar.   The largest sizes of piston pumps can deliver flows of 40m3/hr. In practice these pumps are more likely to be used for metering low flow rate fluids at more modest pressures in laboratories and chemical process plants.   Piston pumps are not generally suitable for transferring toxic or explosive media.
Diaphragm Pumps
There are two types of diaphragm pumps. The hydraulically operated diaphragm metering pumps and the air actuated type.
Hydraulically operated diaphragm pump
The hydraulically operated diaphragm metering pump is used for similar duties as the piston pump.   It has some significant advantages compared to the piston pump in that the design does not require glands or piston seals. The diaphragm in the hydraulically operated diaphragm pump shown below is actuated using a plunger pump arrangement. This provides full support of the diaphragm allowing high pressure operation. The pump can include for duplex diaphragms with the interface being monitored for failure of the diaphragm in contact with the fluid.   This type of pump can be used for pumping toxic and explosive fluids.   The pump can deliver heads of up to 700 bar and transfer flows of up 20 m 3 /hr.  These pumps require continuous monitoring as the diaphragm is under high fatigue loading and the inlet and outlet valves are subject to erosion and blocking.   Under a high quality maintenance regime these pumps are very reliable.
Air Operated Pump
The air operated pump is generally a low cost work horse pump used for transferring any type of liquid including sludge.   The inlet and outlet valves are often low cost easily replaced flap or ball valves.   The pump is comprises two circular chambers each split by a large elastomeric diaphragm.   The two diaphragm centers are mechanically coupled together with a shaft. An interlocked valve admits air pressure to one side of one of the chambers and exhaust the air from the opposite side of the other chamber. This causes both diaphragms to move. One diaphragm pushing fluid out through a non return valve.  
The other diaphragm draws fluid in through a non return valve.    On completion of a full stroke the valve reverses the air supply and exhaust directions causing the diaphragms to move back. The diaphragm which was pushing fluid out of the pump now sucks fluid and the diaphragm admitting fluid now pushes fluid out.   The system is therefore double acting.
The pump capacity is limited by the air pressure available (generally 7 bar) and the design of the diaphragm.  An elastomeric diaphragm has a limited life and will only operate for a few million cycles.    A flow rate of about 40 m3 /hr is a reasonable maximum achievable flow with a larger pump.
For any air operated diaphragm pump the higher the flow the lower the discharge head possible.
Performance of Reciprocating Pump
The performance of a pump is characterized by its net head h, which is defined as the change in Bernoulli head between the suction side and the delivery side of the pump. h is expressed in equivalent column height of water.
The subscripts stand for suction or delivery sides.
where, P = Absolute water pressure, (N/m2)
V = Velocity of water inside the pipe, (m/s)
ρ = Density of the water, (kg/m3)
g = acceleration due to gravity, (m/s2)
Z = elevation, (m).
The velocity of water can be calculated using discharge and area of the pipes.
The discharge produced by the pump can be determined using the collecting tank and stopwatch setup.
where,
a = area of the collecting tank.(m2).
H = height difference of the water column in the piezometer, (m).
t = time taken to rise H meters, (sec).
The net head is proportional to the useful power actually delivered to the fluid in the pump. Traditionally it is called the water horsepower (whp), even if the power is not measured in horsepower. It is defined as,
The input electrical energy to the motor can be determined using the watt hour energy meter. The expression for power is,
where,
n = number of revolutions of the energy meter disk.
k = energy meter constant, rev=kW hr.
t = time taken for n revolutions, (sec)
In pump terminology the external energy supplied to the pump is called the brake horsepower (bhp) of the pump, which can be calculated by considering the efficiency of the motor.
The pump efficiency ηpump is defined as the ratio of useful power to supplied power,
The theoretical discharge of a reciprocating pump can be calculated by knowing the geometrical specifications and and rate of travel of the piston, since it is positive displacement type. The volume of the fluid displaced will be equal to the stoke volume of the piston inside the cylinder. For a double acting single cylinder reciprocating pump the displaced volume of water per second is given by,
where,
L = Stroke length of piston, (m).
N = Rotating speed of the pump crankshaft, (rpm).
A = Area of the piston, (m2).
Apr= Area of the piston rod, (m2).
The slip of a reciprocating pump is defined as,
Discharge of reciprocating pumps
The instantaneous velocity Vd in the delivery pipe may be obtained from equation by writing subscript d as
………….(a)
where D is the diameter of the piston or plunger.
From the equation a curve between Vd and θ can be plotted which will be a sine curve.
For a single acting pump since for one complete revolution of the crank there is only one delivery stroke during which the liquid is delivered, the mean velocity in the delivery pipe can be obtained by integrating equation (a) as follows
……(b)
However, the above expression for the mean velocity may also be obtained by dividing the theoretical discharge Qth of the pump given by equation, , by the area of the pipe
From eqn.
When θ = 90°, sin θ = 1; the velocity Vd has a maximum value given by
………………… (c)
By dividing equation (b) by equation (c) we obtain the ratio between the mean velocity and maximum velocity in the delivery pipe as
……………… (d)
The instantaneous rate of discharge Qd in the delivery pipe may be obtained by using equation (a) as
………(e)
From equation (e) a plot of Qd versus e “an be obtained, which will be a sine curve as shown in Fig. below For a single acting pump during the first half revolution of the crank i.e., for e = 0° to 180°, there is only suction and no delivery and during the second half revolution of the crank i.e., for e = 180° to 360° there is delivery of liquid. The same cycle is repeated afterwards. Thus the part of the sine curve below the axis will represent suction and that above it will represent delivery. However, in Fig. only that part of the curve is shown which represents the delivery of the liquid.
Fig. (1)
The mean discharge (Qd)mean for a single acting pump can be obtained by integrating equation (e): as follows:
……(f)
The above expression for the mean discharge may also be obtained by multiplying (VD)mean given by equation (b) by the area of the pipe
Again from equation (e) for Ó¨ = 90°, sin Ó¨ = 1, the discharge Qd has a maximum value given by
…………….. (j )
Again by dividing equation (f) by equation (f),we obtain
…………..(h)
For a double acting pump since there are two delivery strokes for one complete revolution of the crank, the mean velocity of flow of liquid in the delivery pipe may be obtained by integrating equation (b) as follows :
……….. (i)
Again the above expression for the mean velocity may also be obtained by dividing the theoretical discharge Qth given by equation
by area of the pipe
By dividing equation (i) by equation (c) we obtain for a double acting pump
The instantaneous rate of discharge Qd for a double acting pump is also given by equation (e). As such in this case also a plot of Qd versus θ will be a sine curve. But for a double acting pump during one complete revolution of the crank i.e., for θ = 0° to 360°, there being two delivery strokes, the Qd versus θ will be a resultant of two sine curves drawn at a phase difference of 1800, as shown in Fig.(1) , in which only the curves corresponding to the delivery of the liquid are shown. Thus the mean discharge (Qd)mean for a double acting pump can also be obtained by integrating equation (e) as follows
(k)
However the above expression for the mean discharge may also be obtained by multiplying (Vd)mean given by equation (i) by the area of pipe
Again by dividing equation (k) by equation (j) we obtain for a double acting pump
However, if the area of piston rod is taken into account then it can be shown that the instantaneous discharges Qdl and Qd2 for the two delivery pipes on either side of the piston or plunger will be