# Reciprocating Pump: Definition, Parts, Working, Types, Discharge, Work Done, Power Calculation

In this article, we will learn all the basic details of the Reciprocating Pump along with definition, parts, function, working procedure, discharge flow rate, work done, power, slip, derivation for acceleration head, etc. This pump is a widely used positive displacement pump in many industries where high delivery pressure is required. In this kind of pump, the piston moves forward & backward and mechanical energy is converted into hydraulic energy. Let’s explore in detail!

## What is Reciprocating Pump? Definition

### Reciprocating Pump Basics

Do you want to learn all about the Reciprocating pump? We have already got the basic idea about the positive displacement pump. Reciprocating Pumps are one kind of Positive Displacement type pump. It works based on the ‘to and fro’ movement of the piston/plunger etc. in,

• forward direction which is called forward stroke and
• backward direction which is called backward or reverse stroke and increase the pressure of the liquid. As piston or plunger moves in ‘to and fro’, motion, i.e., reciprocating action, these pumps are called reciprocating pumps.

We will see different types of reciprocating pumps here later on, however, to simplify & easy understanding, a piston arrangement reciprocating pumping system has been opted. We will discuss the basics of reciprocating pumps with a lot of examples & diagrams. A single-acting reciprocating pump is the simplest reciprocating pump. Here, we will consider the same for an easy explanation as well as understanding.

Single-acting means only a single side of the piston is acting. It consists of One number (1) piston, One number (1) suction pipe, One number (1) suction valve, One number (1) delivery pipe and One number (1) suction valve

### Reciprocating Pump Definition

The reciprocating pump means a machine or especially a hydraulic machine that converts mechanical energy or electrical energy into hydraulic energy. So, what are these energies?

• Mechanical energy means the energy which is created by the motion of mechanical device or position of the device.
• Hydraulic energy means the energy which is created by the water.

Reciprocating pumps are used when a certain quantity of liquid needs to be transported from the lower level to a higher level. Higher-level means pressure should be high enough. In this case, a certain volume of liquid is collected within the pump enclosed area and increased the pressure in line with requirements. There are so many places, where high-pressure with low-volume pumps are required. So, what to do? It’s simple! Select Reciprocating pumps!

### Reciprocating Pump Example & Explanation

If you observe oil filling in the car in any petroleum station, you need to know that there are some big tanks or reservoirs in the underground. This big tank is filled with oil. But when we go to fill our car fuel oil tank, that time we see that the fuel from the petroleum station is coming from the nozzle.

Here, fuel is coming from the underground tank to the nozzle. In-tank, the pressure of fuel is very less but when it is injected into the car, the pressure is very high. This is due to reciprocating pumps that are installed between.

### History of Reciprocating Pump

It was long ago; Egyptians have invented the shadoof in 2000 BC. Later, a Greek inventor as well as mathematician, Ctesibius invented a basic pump. It consists of one water source, an air pump, valves, a tank, and a row of pipes.

## Parts of Reciprocating Pump and Functions

Reciprocating pumps are used in many industries as well as our few home applications too. Now, whatever the application, a reciprocating pump or pumping system consists of several parts.

The various important parts of the Reciprocating Pump are as follows.

• A sump of liquid, or water sump or water reservoir
• Strainer
• Suction Pipe
• Suction Valve (non-return valve)
• Cylinder or liquid cylinder
• Piston or plunger and Piston rod
• Piston rings
• Diaphragm or membrane
• Plunger
• Packing
• Crank and Connecting rod
• Delivery valve (non-return valve)
• Delivery pipe
• Suction and delivery flanges
• Air Vessel or Pulsation Dampener
• Driver

The explanation for the parts of the Reciprocating Pump are as follows:

### Water Sump or Liquid Sump

What is Sump in Reciprocating Pump System? Sump means a reservoir or a simple language, a source of water or liquid. We need to transfer Water or liquid from one place to another by this pump. It means there should be some water or liquid or fluid, which needs to be transferred. This fluid is stored or kept in a sump.

We have considered water here as a circulating medium, however, just keep in mind that this pump can handle liquid as well as gases based on applications.

• Fluid is sucked by the pumps from the sump. Later on, water is undergoing a process by the piston within the pump cylinder.
• Finally, it is transported to the delivery pipes and ready for application.

What is the Main Importance of Sump in Reciprocating Pumping System? Let’s see the main importance,

• No water in the sump means no water in the pump intake; hence, the pump will not be in action.
• This is not part of the reciprocating pump but it is a part of the pumping system

### Strainer

What is Strainer in Reciprocating Pumping System? We all know that if the water is having dirt or dust particles or solid particles, or other pollutants, the same will be entered within the pump cylinder.

• These unwanted foreign particles can jam the cylinder, and reduce efficiency.
• In short, this problem will affect the working principle of reciprocating pumps.
• It can clog the suction pipe as well as choked the delivery.

To avert this problem, a wire mesh is provided at the end of the suction pipe to prevent the entrance of these foreign particles from the sump to the cylinder.

What is the Main Importance of Strainer in Reciprocating Pumping System? Let’s see the importance of strainer in the reciprocating pumping system,

• Without a strainer, dirt will come into the system, and impact on the workability of pumps.
• This is also not a part of this pump, but it’s a system requirement.

### Suction Pipe

What is Suction Pipe in Reciprocating Pumping System? We got a water sump, now this sump needs to be connected to the pump basically the main body (cylinder) of the pump. There is a pipe that is connected and helps to suck the liquid from the sump to the pump. This pipe is known as a suction pipe. Since it is on the suction side of the pump & helps to suck, this pipe is known as the suction pipe. There is a valve in the suction pipe.

Important of Suction Pipe Without a suction pipe, the pump will not be connected with the reservoir, hence, the pump will not work. It is also a part of the system.

### Suction Valve

What is Suction Valve in Reciprocating Pumping System? The suction valve is fitted in the suction pipe. Why is the suction valve important? What will be the problem if there is no suction valve? Let me explain, the purpose of this valve.

• This valve allows liquid from the water sump to pump only not the reverse flow to the reservoir.
• Hence, no return will be encountered in the reservoir.
• Due to this no return philosophy, it is called a non-return valve.

So, the flow will be always in one direction. If there is suction, then only this valve will be opened. This valve will be closed during the discharge of liquid to the outside.

Importance of Suction Valve: Importance are as follows,

• If this valve is not provided, during the discharge there will be a backflow of liquid to the sump which is not acceptable.
• It is a Part of the pumping system

### Cylinder or Casing

What is Cylinder in Reciprocating Pump? This is a hollow tube-shaped cylinder known as the body or the casing of pumps. This is commonly fitted with a metallic lining referred to as a ‘cylinder liner‘. The liner helps for the smooth operation and is replaceable when it becomes worn and inefficient.

• This cylinder is consisting of piston and piston arrangements and it is the main portion where water is undergoing a change of pressure.
• This cylinder may be made of cast iron, or steel, or any other suitable material based on the applications. In case of dosing system, this cylinder can be made of Stainless Steel like SS316L as well.

Main Importance of Cylinder or Casing: It is the main part where the piston or piston rod is accommodated and acted for pump action.

### Piston and Piston rod

What is Piston & Piston Rod? Piston and piston rod arrangement is the main workforce in the cylinder. A piston is a solid type cylindrical part and moves forward and background inside the cylinder, to perform suction and delivery of liquid.

In the case of the suction:

• the piston moves back inside the cylinder
• the piston moves in the forward direction for discharging liquid

Now, to move backward and forward of the piston, there is a rod that helps the piston to have continuous linear motion.

Importance of Piston & Piston Rod: Importances are as follows:

• If the piston is not there, the pressure of the liquid will not change, and if the piston rod is not there.
• The piston cannot move or acts.

### Piston Rings

The piston head is fitted with the piston rings for sealing. It helps to seal against the cylinder lining and minimize internal leakage. It is mandatory for the smooth operation of reciprocating pumps.

### Diaphragm or Membrane

The reciprocating pump doesn’t mean only piston arrangements, it can be with diaphragm or membrane as well. That pump is called diaphragm or membrane pump.

Diaphragm or Membrane means a flexible part normally made of rubber or Teflon and can have reciprocating action. To simplify this concept, in the cylinder or chamber where the diaphragm is installed, it will create the chamber into two parts.

• One side is having air or any other hydraulic fluid which will be compressed
• Another side is having the fluid which needs to be pumped
• Movement of the diaphragm can be mechanical or electrically driven.

When the diaphragm moves towards the air or hydraulic fluid, there will be low pressure and fluid to be pumped enters and after that diaphragm moves towards the pumping fluid & pressure increases so that fluid will be delivered into the destination.

### Plunger

The function of the plunger is the same as a piston. This plunger is reciprocating and makes the action of the pump. Instead of piston and piston arrangement, a single cylindrical part is sliding within the cylinder through the sealing. The plunger can be two or multiple in the reciprocating pump based on the applications. This plunger can create very high pressure.

### Packing

The piston is moving backward and forward continuously in the cylinder. Hence, a packing is required to seal the joint between the piston and the cylinder tightly to prevent leakage of liquid from the cylinder. Improper packing may create many problems in reciprocating pumps:

• Problem in lubrication
• Excessive friction.
• Misalignment of piston or piston rod
• May cause wear
• Reduce the efficiency of the pump etc.

### Crank and Connecting Rod

The crank is the metallic part of the pump.  It looks like a solid circular disc and it is connected to the power source.

• The power source can be the engine or the motor, etc.
• The name connecting rod simplifies that it is connecting something. Here, it is connecting the crank and piston.
• Normally for large pump, it is used. Else, piston rod connects the piston & crank.
• When the engine or motor rotates, the crank also rotates.

Due to this rotation, the connecting rod converts this rotary motion into linear motion into the piston.

Important: Connecting rod makes the connection between the Crank and piston. It changes the crank rotational motion into the linear motion of the piston. Don’t be confused between piston rod and connecting rod. The differences between piston rod and connecting rod are as follows:

### Delivery Pipe

When the liquid comes out from the pump the delivery pipe comes into the picture. The delivery of water from the outlet of the pump to the desired place is the main purpose of the delivery pipe. Importance:

• If the delivery pipe is not there, the pump cannot deliver the required liquid at the desired locations.
• Part of system

### Suction & Delivery Flanges

Discharge pipe, as well as suction pipe, needs to be connected to the pump. Now, how are these pipes connected? Here comes, suction and discharge flanges. These flanges are attached to the pumps as an integral part of the reciprocating pump and pipes are connected with the help of bolts. There are flexible connections between flanges and pipes so that the pump vibration will not be transmitted to the piping system.

### Delivery valve

The delivery valve, like the suction valve, acts as a non-return valve and it is placed in the delivery of pumps. Like the suction valve, a delivery valve is also a Non-return valve.

• During the suction of the pump, the delivery valve is closed and
• During Discharge, there will be a pressure of a liquid and the suction valve is closed
• In the same way, due to pressure, the delivery valve is opened to transfer the liquid.

Important:

• The delivery valve is essential. If it is not there, the pump will not work properly & in case of a pump stop, backflow will happen which is very dangerous for pump health.
• Part of system

### Air Vessel or Pulsation Dampener in Reciprocating pump

What is Air Vessel or Pulsation Dampener? An air vessel is basically a chamber or container which contains two halves, the upper part consists of compressed air and the lower part consists of water. The bottom has one hole which is connected to a suction or discharge pipe. Both the parts are separated by one diaphragm and it can be flexible based on the pressure difference.

How Does Air Vessel or Pulsation Dampener Work? There are frictional heads in both suction and discharge pipes, and these all need to be removed from the system to have a uniform discharge rate by reducing the acceleration head. Air vessels are related to each suction and discharge pipe and offer a uniform discharge rate.

Let’s see how does air vessel or pulsation dampener works? Acceleration head means the head which is developed by the fluid acceleration. We know that the flow from the reciprocating pump is pulsating type.  Hence, a separate air vessel consisting of water, as well as compressed air, is considered.

Compressed air is at the top side of the vessel and water is at the lower side. Compressed air is used as it can easily expand or contract to absorb the pressure fluctuation. The air vessel is basically working as a reservoir and is mainly used to stabilize the pulsating flow. As this vessel is used to stabilize the pulsating flow, it is called a pulsation dampener.

• Pressure increase: In case the water pressure is increased, water is forced to enter into the air vessel and compressed air will be compressed.
• Pressure decrease: In case the water pressure in decreased, water is required in the pipe to maintain the required pressure in the pipe. Here, compressed air force the water to enter into the pipe to maintain the pressure.

As we need a stable flow, the pump is always designed in such a way that fluid reaches to the delivery side through the air vessel.

What are the Functions of Air Vessel in Reciprocating Pumps? The main functions of air vessels are as follows:

• To get the discharge flow at continuous rate.
• Air vessel in supply or discharge pipe helps to reduce the flow separation.
• Reduce the probability of cavitation.
• It changes the pulsating flow into continuous flow.
• It reduces the frictional head
• It reduces the acceleration head.
• It makes the pump energy efficient by reducing power consumption.
• It will not have any problem to increase the length of suction pipe below air vessel.

### Driver

Let’s try to understand what is the driving mechanism? How does this piston or plunger, etc. move? There is one drive system. Normally, an electrical motor is used, however, in case of a big reciprocating pump, the engine is used as a driving mechanism. Hence, we have got an idea about the basic parts of a reciprocating pump. Let’s try to understand the working philosophy of the reciprocating pump!

## How Does Reciprocating Pump Work? Diagram

### Working Principle of a Reciprocating Pump with Animation

The reciprocating pump consists of a piston in an enclosed cylinder, crank, piston, connecting rod. Connection details are as follows:

• The connecting rod is one of the main parts of the pump and it connects the crank and the piston.
• Crank connects the driving motor or the driving machine and connecting rod.

Due to the rotation of the crank, the piston also moves forward and backward inside the cylinder by means of a connecting rod.

• Pumps or the cylinder are connected to the suction pipe with a non-return suction valve and discharge pipe with a non-return discharge valve.
• Non-return valve means it will not allow the liquid to flow in the opposite direction.
• The suction valve allows liquid from the suction pipe to the cylinder only.
• In the same way, the delivery valve allows liquid from the cylinder to the delivery pipe.
• When the crank starts its rotation, the piston will start moving in the cylinder.

A nice Animation of Reciprocating Pump has been created just to understand the working process.

### Reciprocating Pump Working Procedure with Diagram

Let’s analyze, working procedure of the reciprocating pump in a few steps:

Step #1: The crank is at point A; it will make an angle θ=0º with respect to the horizontal line. Look at the image, the piston is at point P, extreme left side, inside the cylinder.

Step #2: When power will be supplied to the reciprocating pump, the crank will start to rotate by the electric motor. When A moves towards point C, the angle increases, and the piston will move towards the right in the cylinder. When A reaches at point C, the angle becomes angle θ=180º and the piston reaches to point Q.

When the piston moves towards the right side, a partial vacuum will be created left side of the cylinder. Vacuum means the pressure, which is less than the atmospheric pressure. As the vacuum pressure is the main driving factor for entering the fluid into the pump, it is correlated with force and this pump is also called a Force Pump as well.

Now, on the suction side of the pump, the surface of the water is having normal atmospheric pressure. Since the cylinder creates a vacuum or less pressure than the atmospheric pressure, the liquid will be forced into the suction pipe of the pump. This liquid then opens the suction valve and enters the cylinder.

Step #3: When the crank rotates from C (θ=180º) to A (θ=360º), then the piston will move from the extreme right position towards the left side in the cylinder. When the piston starts to move the left side, it will increase the pressure of the liquid inside that region and that will be more than atmospheric pressure.

Due to that pressure, it reaches to the delivery pipe via a delivery valve. Now, since the valve is a non-return type, water will not be back. Hence, the crank changes its rotational motion into linear motion and makes the movement of the piston inside the cylinder.

Step #4: Due to this higher pressure, the Suction valve will be closed, and the delivery valve will be opened. Hence, the liquid is forced into the delivery pipe through the pump outlet and raised to the required height.

## What are the Types of Reciprocating Pump?

Reciprocating pumps are classified into a few categories based on,

• Mechanism,
• Air vessel,
• Numbers of cylinders.

Let’s try to understand the brief description of each type of reciprocating pump.

### Based on Mechanism Reciprocating Pump Types

Single-Acting Reciprocating Pump: As the name suggests, a single-acting reciprocating pump means, only one side of the piston is acting to produce work.

• ‘Single’ implies one delivery pipe, delivery valve along with one suction pipe, suction valve.
• Only one side of the piston acts on the liquid.
• The liquid is sucked in one direction that is suction stroke and it delivers that is called deliver stroke.

Double Acting Reciprocating Pump: As the name suggests, a double-acting reciprocating pump means, both sides of the piston are acting to produce work. In each double acting reciprocating pump, there will be two suctions pipes, two suction valves, two delivery pipes and two delivers valves.

• When the piston is in between the cylinder, one side will have one suction and one delivery pipe
• Another side also will have the same things.
• It means both sides of the piston works on the liquid.

### Based on Air Vessel Reciprocating Pump Types

#### Pump with Air Vessel

• In this case, the continuous flow of water at a uniform rate.
• It reduces the acceleration head.
• This pump accumulates water in the vessel by compressing air.

#### Pump without air vessel

• When the In this case, some amount of air present in the water.
• In domestic applications, these types of pumps used.

### Based on Number of Cylinders Reciprocating Pump Types

Single cylinder: Here, a single-cylinder or one cylinder is connected to a shaft.

Double cylinder: In this pump, double cylinders or two cylinders are attached to a single shaft. Here, each cylinder is having separate suction and delivery system.

Triple cylinder: In this pump, three-cylinders are connected. Apart from all the above, reciprocating pump, there are three different pumps are widely used:

Piston Pump: The piston pump is a single or double-acting pump. In a single-acting piston pump, pump sucked liquid in suction stroke and the pump delivers liquid in discharge. For example:

• Well-pumps,
• Football pumps
• Cycle pumps,

In double-acting piston pumps, both sides of the piston compress the liquid. Fluid comes in contact with both sides of the piston. These pumps can be:

• Simplex (one cylinder),
• Duplex (two cylinders),
• Triplex (three cylinders) and so on.

Plunger Pump: The plunger pump is a single-acting pump. These pumps are able to build very high pressure.

• These pumps can be vertical or, horizontal
• These pumps can be simplex or multiplex.
• These pumps are widely used for building up the highest pressure in many industries.

Diaphragm Pump: Diaphragm pumps are widely used in chemical injections and other industries.

• The operation is possible both hydraulically or mechanically.
• These can be simplex or multiplex design
• It can have variable stroke arrangements.

Diaphragm pumps are the best suitable pump when the system required zero leakage.

Two Throw Reciprocating Pump: Two throw pump means,

• It has two cylinders
• Two pistons
• There is one suction for two cylinders.
• There is one discharge for two cylinders.
• Flow rate, Q = 2 LAN/60 m3/s

Three Throw Reciprocating Pump: Three throw pump means,

• It has three cylinders
• Three pistons
• There is one suction for three cylinders.
• There is one discharge for three cylinders.
• Flow rate, Q = 3 LAN/60 m3/s

## Reciprocating Pump Discharge, Work Done, Power Requirement & Slip Explanations

### Discharge of Reciprocating Pump

Let’s calculate the discharge from the reciprocating pump. Discharge means the fluid flow rate from the pump per second. Now, we already know that due to the revolution of the crank, the piston moves forward and backward which helps to discharge the fluid from the pump. So, the pump will deliver some fluid in one revolution.

Now, this is not the discharge! Discharge means fluid flow rate per second. So, we have to know that how many revolutions happen in one second and the same can be multiplied with the flow rate per revolution to get discharge per second. Let’s consider,

• A = cross-section area of the cylinder
• r = radius of crank
• L = Stroke length, which means travel of piston in each forward or backward stroke, it equals to 2r, i.e L = 2r [as half cycle rotation or 180 deg rotation gives one stroke]
• V = volume of discharge in one revolution = area x length = A x L, m3
• N = RPM, that means rotation per minute or
• N/60 = rotation per second
• Qh = Fluid flow rate per second, m3/s

Qh = discharge in single revolution x nos. of revolution per second

• Qh = V x N/60
• Qh = A x L x N/60
• Qh = ALN/60

Qh = ALN / 60

This is for single-acting reciprocating pumps, if we derive the equation for double-acting reciprocating pumps, it will be as follows for both sides:

• Qh’ = Qh1 + Qh2

Where,

• Qh’ = Total discharge of considering both side of piston.
• Qh1= Discharge for Bottom side of piston
• Qh2= Discharge for piston rod area

Now, from single-acting reciprocating pump, we get the value,

Qh1 = Qh = ALN / 60

However, the area of the piston rod side area will be slightly less considering the area of the piston rod. Let’s consider, Ap is the area of the piston rod. Hence, the actual area of the cylinder, A’ = A-Ap. So,

• Qh2 = A’LN/60
• Qh2 = (A-Ap)LN/60
• Qh2 = ALN/60 [As Ap is negligible]

Total discharge of considering both sides of the piston.

• Qh’ = Qh1 + Qh2
• Qh’ = ALN/60 + ALN/60
• Qh’ = 2ALN/60

### Reciprocating Pump Work Done

Work done means here, the work to be done to lift the fluid per second by the pump. Simply, we can say, work done means the force required to displace the fluid. Work done,

• W.D = Force x Displacement.
• W.D = W x h

Where,

• W.D = Work Done
• W = force = force required to lift or displace the fluid = weight per second
• h = displacement or the height of lifting fluid = hs + hd
• hs = suction head, m
• hd = discharge head, m
• ρ = density of liquid, kg/m3
• g = acceleration of gravity, N-m/s2
• Q = discharge of liquid, m3/s

So, to derive the work done for the reciprocating pump, first, we have to derive weight per second. So, Weight,

• W = mg/second
• W = V ρ g/second [Mass = volume x density, or m =V ρ,]

Work Done,

• W.D = W x h
• W.D = V ρ g/second x h
• W.D = (V/second) ρ g h
• W.D = Q ρ g h
• W.D = ρgQh
• W.D = ρg ALN/60 (hs+hd) Joule/Second or watt

This is the work done per second in (S.I unit)

### Reciprocating Pump Power Requirement

We have already derived the work done per second, however, we know that power means work done per second. Hence, in this derivation, the power requirement is the same as work done as it states work done per second. Then, the power requirement will be,

• P = Power Requirement,
• P = Work done/Second
• P = ρgQh
• P = ρgQ (hs+hd)
• P = ρgQ (hs+hd)
• P = ρg ALN/60 (hs+hd) watt
• P = ρg ALN/60 (hs+hd)/1000 kW [As 1 kW = 1000 watt]

### Slip of Reciprocating Pump

Slip means the loss of capacity due to friction, it can be calculated as

Slip = Theoretical discharge – Actual discharge

• Slip = Qth – Qact
• % of slip = (Qth – Qact)/Qth x 100%

Where,

• Qth = theoritical discharge
• Qact = actual discharge

### What is Negative Slip? What is the reason for negative slip?

We know that slip is always positive. But it may be negative as well. Let’s try to understand. If a pump has a suction pipe that is very long, and the delivery head requirement is small. In case, the pump operates at a very high speed, what will happen? There may be a chance of increasing fluid inertia pressure (due to long travel) which causes the delivery valve to open without even completing the suction stroke. This results in fluid at the outlet without completing delivery stroke.

In this case, the actual discharge becomes higher than the theoretical discharge and the Cd value becomes more than 1. Hence, the slip becomes negative. Let us try to see one example, for calculating pump work done, power requirement & slip percentage.

Have you thought about the water inside the cylinder? What happens exactly during the suction and discharge strokes? There will be acceleration due to these movements and that can be calculated.

## Derivation for Acceleration Head in Reciprocating Pump

### Arrangement

Piston continuously makes forward stroke and backward stroke and these strokes happen between two extreme positions of the cylinder,

• Bottom dead center or BDC, which is on the crank side
• Top dead center or TDC, which is opposite to crank side

The piston moves from BDC to TDC and from TDC to BDC continuously. Now, let’s try to visualize & understand properly. The piston starts at BDC and increases its speed and reaches to the maximum speed in the middle. Then it has to stop at TDC, so it starts to reduce its speed from the middle of the cylinder and stops at the TDC. So, the piston speed shall be as follows:

### Diagram for Velocity

During suction stroke,

• Speed 0 at TDC ———-> Speed increases up to the middle towards BDC  ———–> Maximum speed at the middle ———> Speed decreases towards the BDC ———->  Speed 0 at BDC

During the discharge stroke, it will be as follows:

• Speed 0 at BDC ———-> Speed increases up to the middle towards TDC ———–> Maximum speed at the middle ———-> Speed decreases towards the TDC ———->  Speed 0 at TDC

### Acceleration

We know that increase in velocity per unit time means acceleration. So, piston velocity increase means acceleration is coming into the picture. Now, as water is moved by the piston, the velocity, as well as acceleration of water inside the cylinder, will also be changed with the piston. This will also change the velocity and acceleration at the suction and discharge pipe. During suction stroke,

• Acceleration 0 at TDC ———> Acceleration increases up to the middle towards BDC  ———–> Maximum acceleration at the middle ———> acceleration decreases towards the BDC ———->  Acceleration 0 at BDC

During the discharge stroke, it will be as follows:

• Acceleration 0 at BDC ———-> Acceleration increases up to the middle towards TDC  ———–> Maximum acceleration at the middle ———-> acceleration decreases towards the TDC ———–>  Acceleration 0 at TDC

Let’s try to calculate the acceleration. First, we will draw a simple diagram.

Let’s consider,

• ω = Angular speed of crank in Rad/sec
• r = Radius of the crank
• A = Cross sectional area of the pump cylinder
• a = Suction pipe or deliver pipe cross sectional area
• V = Velocity of water in the cylinder
• v = Velocity of water in the pipe
• l = Length of pipe
• x = Displacement of the piston in time t second

At the start of the suction stroke,

• Crank is at Point A
• Piston is at TDC

Now, the crank will rotate and the piston will move due to their arrangements. Consider, the crank will make an angle θ after t seconds. In this case,

• Crank creates angle θ with respect to horizontal line
• Time spent = t second
• Angular velocity ω means simply the rate of change of an angle, i.e., ω = θ/t or θ = ω.t

What is the velocity of the piston? Velocity = distance/time

V = dx/dt

Here, we have to find out the value of displacement of piston, x

• x = AO – PO
• x = r – r cosθ  [cosθ =PO/QO, or PO = OQ cosθ = r cosθ]
• x = r – r cos (ωt) [θ = ω.t]

Velocity, V

• V = dx/dt
• V = d [r – r cos (ωt)]/dt
• V = rω  d[1 –  cos (ωt)]/dt
• V = rω [- (-sinωt)]
• V = rω sinωt

The fluid flow rate in the cylinder, Q1,

• Q1 = Velocity of water x cross sectional area of cylinder
• Q1 = V x A
• Q1= rω sinωt x A
• Q1= Arω sinωt

The fluid flow rate in the pipe, Q2,

• Q2 = Velocity of water x cross sectional area of pipe
• Q2 = v x a

As per the continuity equation, the fluid flow rate in the cylinder will be the same as the fluid flow rate within the pipe. So,

• Q1 = Q2
• Arω sinωt = v x a
• v x a = Arω sinωt
• v = A/a . rω sinωt

Acceleration of water in the pipe, fp

• fp = dv/dt
• fp = d(A/a . rω sinωt}/dt
• fp = A/a . rω  ω cosωt
• fp = A/a . rω2 cosωt

Now, we need to calculate the acceleration head, ha.

ha = P/W

Where,

• P = Pressure intensity
• W =Weight density

Pressure intensity,

• P = Force / Area
• P = Mass of water x Acceleration / Area [Force = Mass of water x Acceleration]
• P = Volume x Density x Acceleration / Area [Mass of water = Volume x Density]
• P = Area x Length x Density x Acceleration / Area [Volume = Area x Length]
• P = a x l x ρ x fp /a [as, area =a]
• P = l x ρ x A/a rω2 cosωt
• P = l x ρ x (A/a) rω2 cosωt

Weight density, W = ρg

• ha = P/W
• ha = l x ρ x (A/a) rω2 cosωt / ρg
• ha = l /g x (A/a) rω2 cosωt
• ha = (l /g) x (A/a) rω2 cosθ [θ = ωt]

Now, this acceleration head can be easily calculated, as follows:

The acceleration head at the suction pipe, has

• has = (ls /g) x (A/as) rω2 cosθ

• hmax = (l /g) x (A/a) rω2 [cosθ =1, where θ=90 deg]

## Reciprocating Pump Calculation Examples

### Reciprocating Pump Sample Problem

A single-acting reciprocating pump with 200mm piston diameter, stroke length 400 mm, rotational speed 60 RPM. Now, the water is to be pumped at 20 m height. Find out, theoretical discharge. If the actual discharge is 20.2 liters/sec, then what will be volumetric efficiency, slip & power requirement. Mechanical efficiency 80%.

### Solution:

Theoretical Discharge

Input data,

• d = piston diameter = 200mm = 0.2m
• N = rotational speed = 60 RPM
• L = Stroke length = 400mm = 0.4m

A = cross sectional area = 3.14 x d2/4 = 3.14 x 0.2 x 0.2 / 4 = 0.0314 m2

Discharge of liquid, Qth

•  Qth = ALN/60
•  Qth = 0.0314 x 0.4 x 60/60 m3/s
•  Qth = 0.013 m3/s
•  Qth = 13 litre/s

Hence, theoretical discharge is 13lit/s

Volumetric efficiency

• N = volumetric efficiency
• Qact = 11.96 litre/sec

Here,

• N = actual discharge / theoretical discharge
• N = 11.96 / 13 x 100%
• N = 92%

Hence, volumetric efficiency is 92%

Slip

• Slip = (Qth – Qact)/Qth x 100%
• Slip  = (13 – 11.96) / 13 x 100%
• Slip  = 80%

Power Input

We know,

• ρ = density of water =1000 kg/m3
• g = gravitational acceleration = 9.81 N-s/m2
• Q = 0.013 m3/sec
• H = total head = 20 m

Power required ideal, P

• P = ρgQ (hs+hd)
• P = ρqQH
• P = 1000 x 9.81 x 0.013 x 20
• P = 2550.6 watt
• P = 2.55 kW

Mechanical efficiency, n   = 80%

Power input required at actual, P’,

• P’ = Power required ideal / efficiency = P/n
• P’ = 2.55/0.8
• P’ = 3.19kW

Therefore, in this way, the water is sucked and discharged from the sump to the desired location and we can calculate discharge, slip, power inputs, etc. This is a simple calculation to understand the subject matter, you can check reciprocating pump detail calculation as well.

## What is the Difference between Reciprocating Pump and Centrifugal Pump?

Let’s see the differences of reciprocating pump vs centrifugal pump, in the below table,

## What are the Main Factors to Determine Reciprocating Pump Efficiency?

There are a few key parameters that determine the efficiency of a reciprocating pump.  Let’s see all those factors:

• Flow rate or the capacity of the pump.
• Power consumption to meet the flow rate and head requirements.
• Mechanical efficiency
• Capacity loss percentage with respect to suction capacity, i.e. slip
• Displacement with no slip loss.
• Suction pressure and discharge pressure

## What is Indicator Diagram of Reciprocating Pump?

### Definition of Indicator Diagram

As the name suggests, the indicator diagram means a graph that mainly indicates pressure head and piston displacement from the inner dead center in one revolution of the crank. The work done by a reciprocating pump can be easily calculated with the help of an indicator diagram.

### Plotting in the Graph

Let’s see how an indicator diagram looks like,

• Pressure – Vertical Line
• Stroke – Horizontal Line

Notes:

• Acceleration lose is very small and it is neglected.
• Friction lose is very small and it is neglected.

### Example of an Indicator Diagram

Let’s see an example of an indicator diagram below.

• AB: Atmospheric Pressure
• PQ: Pressure at suction stroke
• RS: Pressure at delivery stroke
• L: Length of stroke

Single Acting Reciprocating Pump: Area of Indicator diagram,

• A’ = PQRS
• A’ = L x (hs+hd)

Work Done per one revolution of the crank

• W.D = Weight per second x displacement
• W.D = ρg ALN/60 x h
• W.D = ρg AN/60 x L h
• W.D = ρg AN/60 x L (hs+hd)
• W.D = ρg AN/60 x A’
• W.D = ρg AN/60 x Area of Indicator Diagram

Double Acting Reciprocating Pump: The work done for the double-acting reciprocating pump will be as follows:

W.D = 2ρg AN/60 x Area of Indicator Diagram

## Reciprocating Pump Applications

The main application of the Reciprocating pump is discussed here. Reciprocating pumps are widely used for a long and in various industries. Proper selection in the proper industry is a vital role, improper selection results in repeatable works. The following industries are widely used reciprocating pumps:

• Oil drilling operations.
• Oil production, oil disposal, oil injections.
• Offshore oil applications.
• Light oil pumping.
• Gas industries
• Petrochemical industries
• Pneumatic pressure applications.
• Oil refineries
• Feeding Boiler/condensate returns/heat exchanger/evaporator tube cleaning/pipe cleaning
• Vehicle cleaning workshops.
• Tank cleaning/vessel cleaning
• Wet sandblasting
• Hydro testing of tanks, vessels, pipes, valves & fittings, hoses & systems
• Boiler feeding
• High-pressure pumps for the RO system (Reverse osmosis)
• Cleaning services, like vehicle cleaning or glass cleaning, etc.
• Firefighting system this kind of pumps are used
• Sewer cleaning
• Wastewater treatment process
• Paper manufacturing, pulp manufacturing industries
• Mining industries
• HVAC system
• Refrigeration industries
• Chemical processing, food processing, etc.,

There are few major advantages of the Reciprocating Pump and the same is explained:

• High pressure can be obtained at the outlet of the pump.
• The high-pressure liquid can be supplied to the desired height.
• No priming process is required in this pump except few conditions and this a one of the main advantages over centrifugal pumps.
• Reciprocating Pump provides a high suction lift since it can create high negative pressure in the cylinder.
• Air can be used as the working fluid in reciprocating pump.
• The liquid flow rate of a centrifugal pump may fluctuate but the reciprocating pump provides a steady flow rate.

These pumps operate at very higher efficiencies than other pumps, generally reaching levels of 90% or more efficiency.

The major disadvantages of Reciprocating Pumps are:

• Maintenance is very high due to the wear and tear of the components.
• The flow rate is low means discharge is limited.
• The initial cost is very high.
• These are bulky and heavy.
• It is very difficult to handle viscous liquids.
• There may be a problem in the alignment of the piston or piston rod.

Based on the above discussion on the advantage and disadvantages of reciprocating pumps, sometimes it is very difficult to select the pumps. There are some pros and cons for both the pumps and the following points needs to be considered:

• Location of the pump to be installed.
• Which kind of fluids to be handled.
• Type of Operation requirements.
• Type of maintenance requirements and facilities.

## Reciprocating Pumps Package

In addition, when we talk about a reciprocating pump package, many components are associated with it, these are, as follows:

• Reciprocating pump that means casing, piston, bearing housing or bracket, etc.,
• Base frame,
• Driver, it may be a motor or diesel engine or turbine-driven or gas engine driven,
• All valves, suction & delivery pipes
• Strainers
• Pressure gauges or pressure transmitter to measure the pressure in suction and discharge side
• Shut off valves
• Safety valves
• Auxiliaries like sealing system, cooling system, etc.,

## Reciprocating Pumps Key Notes

• In reciprocating pumps, a piston can create very high pressure and it should not be operated in a closed discharge system. A safety relief system is mandatory to prevent damage to the pump or driver against high pressure.
• The flow in the reciprocating pump is always uneven or pulsating. This can be smoothed out by using few tools like dampeners or stabilizers at the inlet and outlet piping which also protects the entire pumping mechanism.

## Manufacturers of Reciprocating Pump

There are a lof of manufacturers available, few of them are listed,

• Milton Roy
• Liwa
• Flowserve
• DMW
• Ruhrpumpen GMBH etc.

## FAQs on Reciprocating Pump

What is a reciprocating pump used for?

Reciprocating pumps are used where a high head is required. Generally, this pump is suitable for high head and low flow applications. In addition, this pump is used to deliver a very precise flow as well.

Oil production, oil disposal, oil injections, offshore oil applications, dosing, light oil pumping, gas industries, etc.

What is indicator diagram of reciprocating pump?

As the name suggests, the indicator diagram means a graph that mainly indicates pressure head and piston displacement from the inner dead center in one revolution of the crank.

The area of the plot in the indicator diagram is proportional to the work done.

How does a reciprocating pump work?

The working principle of the reciprocating pump is very simple and the steps are as follows:
(1) Crank is connected to the main power source. When power is on, crank starts to rotate (2) Crank is connected to the connecting rod, if crank rotates, connecting rod also moves (3) Due to this crank & connecting rod arrangement, the rotation of the crank converts into reciprocating motion (4) Connecting rod is connected to piston rod as well as piston (5) As connecting rod moves, associated piston also moves (6) This reciprocating motion of the piston, makes forward stroke & backward strokes (7) Fluid enters and becoming pressurized & left with the help of these strokes.

In case of plunger or diaphragm type reciprocating pumps, instead of piston, plunger or diaphragm is used but the working process is the same.

What is principle of reciprocating pump?

The main principle of the reciprocating pump is the piston movement in forward & backward stroke and mechanical energy is converted into hydraulic energy.

The working principle of plunger or diaphragm type reciprocating pumps is are the same although instead of a piston, plunger or diaphragm is used.

Which is an example of reciprocating pump?

There are so many examples of reciprocating pumps and we can give one here.
Oil filling in the petrol station. Oil is supplied from an underground tank and is connected to a nozzle. The injection of the oil is due to the reciprocating pump.

## Conclusion

So, we have learned the basics of Reciprocating Pump! Any doubt, please don’t hesitate to write to us! Remember, Centrifugal pumps are different in terms of construction, working principles, and application.

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