A Course on Reciprocating Pump

III year Mech-Recip Pump

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A Course on Reciprocating Pump

Mech Diploma – III year

Introduction:

Turbo machines are mechanical devices that either extract energy from a fluid (turbine)

or add energy to a fluid (pump) as a result of dynamic interactions between the device and the

fluid. There are two main types of pumps namely ‘Dynamic pumps’ and ‘Positive displacement

pumps’.

Dynamic pumps consist of centrifugal, axial and mixed flow pumps. In these cases

pressure is developed by the dynamic action of the impeller on the fluid. Momentum is imparted

to the fluid by dynamic action.

Positive displacement pumps consist of reciprocating and rotary types. These types of

pumps are discussed in this course. In these types a certain volume of fluid is taken in an

enclosed volume and then it is forced out against pressure to the required application.

Classification of Positive Displacement Pumps:

Type and construction features of reciprocating pump:

1. Position: Vertical, Horizontal

2. Purpose: Metering Pump, Power Pump

3. Piston or Plunger acting : Single acting, Double acting

4. Number of Plunger in One Casing : Single, Duplex, Triplex, Multiplex

5. Liquid End Type : Direct exposed, Diaphragm

6. Plunger direction: Forward, Backward.

Generally, there are the following types of Positive Displacement Pumps:

Rotary Lobe Pump, Rotary Gear Pump, Screw Pump, Vane Pump, Regenerative Pump,

Peristaltic Pump, Diaphragm Pump, Progressive Cavity Pump, etc.

Reciprocating pumps can be single acting, double acting, etc.

a) Single acting Recip Pump consists of one suction and one delivery pipe simply connected to

one cylinder.

b) Double acting single cylinder Recip pump has two suction and two delivery pipes connected

to one cylinder.

c) Two-throw Recip pump has two cylinders each equipped with one suction and one delivery

pipe. The pistons reciprocating in the cylinders are moved with the help of connecting rods fitted

with a crank at 180o.

d) Three-throw Recip pump has three cylinders and three pistons working with three connecting

rods fitted with a crank at 120o


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We will study Single-acting Recip pump & Double acting Recip Pump in some detail.

Single-acting Recip Pump

Description of a Single-acting Recip Pump:

Main components:

The main components are:

1. Single Cylinder with suitable valves at inlet and delivery.

2. Plunger or piston with piston rings.

3. Connecting rod and crank mechanism.

4. Suction pipe with one-way valve.

5. Delivery pipe with one-way valve.

6. Supporting frame.

A diagrammatic sketch is shown in Fig. 20.1

Working description:

A reciprocating pump has a piston which gets its motion by means of a Crank shaft –

Connecting Rod arrangement. Therefore it is called ‘Reciprocating’ Pump. Liquid is sucked into

the cylinder and then ejected out by the motion of the piston and hence it is called ‘Positive

Displacement’ Pump. If delivery occurs only during the delivery stroke of the piston, then such a

reciprocation pump is called ‘Single-acting’ Pump.

Mechanical rotary motion is obtained from a motor to which a crank-rod is attached.

Rotary motion is translated into reciprocatory motion using a connecting-rod and piston

arrangement as shown. The piston is placed inside a sealed cylinder that has an inlet and outlet.

A suction pipe is connected to the inlet of the pump and delivery pipe is connected to outlet of


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the pump. The inlet and outlet of the pump are covered by a one-way non-return valve which

allows flow of liquid along only one direction.

The pump functions in two distinct stages:

1. Suction phase: : When , the piston is at the inner dead center [IDC].

As the piston moves away from the IDC, pressure inside the cylinder drops and the one-

way suction valve opens. This happens because the liquid is incompressible. Liquid

rushes in through the suction pipe into the cylinder.When , the piston is at the

outer dead center [ODC]. The cylinder is completely filled with the liquid.

2. Delivery phase: : When the piston starts moving away from

ODC towards the IDC. Pressure builds up inside the cylinder. Immediately, the one-way

delivery valve opens and the suction valve closes. Liquid is pushed out of the cylinder. At

the entire liquid inside the cylinder has been emptied and the cycle gets

repeated.

Naturally, the delivery occurs only during one half of the crank-shaft’s rotation and in the

other half there will be no delivery. Thus, a single-acting Recip pump gives a fluctuating

delivery of liquid.

Pump characteristics:

1. Delivery: [Qact]

Suppose the length of the cylinder is assumed to be equal to the sweep of the piston,

which is again equal to the diameter of the circle made by the crank-shaft rotation. Let

the length of the crank-shaft be ‘L’ meters. Let the cross-sectional diameter of the

cylinder be ‘D’ meters.

We know that the delivery of liquid in one revolution is volume of liquid in the cylinder.

Again, the delivery of liquid in m3/s is:

( ) ( ).

Let the pump make ‘N’ revolutions per minute.

Then, ( )( )(

)

m3/s

2. Slip:There can be leakage along the valves, piston rings, gland and packing which will

reducethe discharge to some extent. This reduction in the actual discharge is accounted

for by using the term ‘Slip’.

3. Coefficient of Discharge: Cd is an important Pump characteristic. It is defined as the

ratio of actual discharge of a pump to its theoretical discharge.

4. Percentage Slip: is another common Pump characteristic that is used to define a Recip

pump. It is calculated as follows:

[

]


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(

)

( )

It is generally seen that Slip is a positive quantity in most cases. In other words,

the actual discharge is lesser than theoretical discharge in most cases. However, it has

been found in some cases that , due to operating conditions. In this casethe

slip is called Negative Slip.

Reason for negative slip: When the delivery pipe is short or the delivery head is

smalland the accelerating head in the suction side is high, the delivery valve is found to

open before the end of suction stroke and the liquid passes directly into the delivery pipe.

Such a situationleads to negative slip.

5. Power required to run the pump:

We know that:

If the pump raises the liquid from a height hs and delivers it to a height hd, then

( )watts.

Indicator Diagram

The pressure variation in the cylinder during a cycle consisting of one revolution of the

crank, when represented in a diagram is termed as indicator diagram. The same is shown in

figure below:

It must always be noted that indicator diagram is only ‘indicative’ of the actual piston positions

and pressures inside the cylinder and not a true graphical representation.

Let us suppose that:

Point 1 represents position of the piston at its IDC or . This is the start of the suction

cycle.


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Point 2 represents position of the piston at its ODC or . This is the end of the suction

cycle.

Point 3 represents position of the piston again at its ODC or . This is the start of the

delivery cycle.

Point 4 represents position of the piston again at its IDC or . This is the end of the

suction cycle.

The quadrilateral 1234 thus represents the total work done by the pump in one cycle of

the crank-shaft. The suction pressure-head, delivery pressure-head and atmospheric pressure-

head are also represented in the figure.

This is the Indicator Diagram for an ideal cycle. In an ideal cycle, we consider that only

suction pressure-head and delivery pressure-head are present in the two cycles and no other

pressure-heads are present inside the cylinder.

In reality, however, many other components of pressure-heads come into play inside the

cylinder in a cycle. Some of them are acceleration pressure-head and friction pressure-head. We

shall consider the effect of acceleration pressure-head on the working of a single-acting Recip

pump and on its Indicator Diagram.

Effect of acceleration pressure-head:

When to , the piston creates a suction pressure inside the cylinder. So the

liquid rushes into the cylinder from the suction pipe. The piston however is moving and hence

has acceleration from The piston has deceleration from The

fast moving liquid also has acceleration and deceleration corresponding to that of the piston. This

acceleration of the liquid generates a pressure component. This is denoted as during the

suction phase and as during the delivery phase.

When we include this component of pressure-head due to acceleration of liquid, the

Indicator Diagram gets modified as shown above.


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At , the pressure-head due to acceleration of liquid gets added on to the suction pressure-

head and hence Point 1 gets shifted to Point 1`.

At , since the acceleration is 0, the only pressure-head present inside the cylinder is the

suction pressure-head.

At , the pressure-head due to deceleration reduces the suction pressure-head. Hence,

Point 2 gets shifted to Point 2` as shown.

Similarly, at , at the beginning of the delivery stroke, the pressure-head due to

acceleration of liquid gets added to the delivery pressure-head. Hence Point 3 gets shifted to

Point 3`.

And at , at the end of the delivery stroke, the pressure-head due to deceleration of

liquid reduces the delivery pressure-head inside the cylinder. Hence the Point 4 gets shifted to

Point 4` as shown in figure.

To derive an expression for variation of pressure inside a cylinder:

Consider the following figure:

We assume that the ratio of Connecting Rod to Crank-shaft is very large. Then we can

assume that the piston has simple harmonic motion. Let us therefore assume that as the Crank

moves through a radial distance of in time ‘t’ seconds, the piston moves a linear distance of

‘x’ meters. Let us further assume the following:

.


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The distance x travelled by the piston is given by:

Now, by differentiating this equation on time, we get the velocity of the piston.

So,

⁄ ( ) .

From Continuity equation, we know that the volume of liquid flowing into the cylinder per

second is equal to volume of water flowing through the suction pipe per second.

Or,

⁄

Or,

⁄ ( )

From this, we can get an expression for acceleration of liquid in suction pipe by differentiating

above relation against time:

⁄ (

⁄ ( ))

⁄ .

What we need to derive here is the pressure-head due to acceleration of the liquid in the suction

pipe or in the cylinder.

( ) ( )

Now,

And

( )

( )⁄

Again, from Newton’s Laws, we know that:

( )( )

( )( ⁄ )

(

) (

)( )

(

) (

)( )

From this expression, we can specify for various points in the cycle as follows:

Suction phase:

Beginning of suction phase:

(

) (

)( ); since


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Middle of suction phase:

; since End of suction phase:

(

) (

)( ); since

We can similarly derive expressions for the delivery phase too. However, we will have to

consider again instead of , for in the latter case, the

expressions we derive will not match with reality! Delivery phase:

Beginning of delivery phase:

(

) (

)( ); since

Middle of delivery phase:

; since End of delivery phase:

(

) (

)( ); since

Separation:

When the pressure reduces inside the cylinder or in some part of the suction pipe or

delivery pipe, in some cases, it may so happen that the absolute pressure-head1 may drop below

the ‘Vapor Pressure-head2’ of the liquid. Under that condition, the liquid inside the hydraulic

system undergoes a phase change and becomes a gas. The phenomenon is exactly like boiling.

The phase change occurs by formation of gas bubbles. When this happens, output drops and

further cavitation3 may occur. This has to be avoided in a Recip pump. This phenomenon is

called ‘Separation’. Therefore with reference to a Recip pump, the vapor pressure-head of the

liquid used is also called as ‘Separation pressure-head’ [ ].

As we saw above, the Delivery [Qact] of a Recip pump is a function of its speed. So, in

order to increase output, we have to increase its speed. However, the absolute pressure-head

inside the cylinder and pipes is a function of Qact. In our attempt to increase output of a Recip

pump, if we increase its speed to such a level that separation occurs, then our purpose is not

served. So is a limiting condition for increasing the speed of a Recip pump.

1Absolute Pressure-head: ; Take care to incorporate the appropriate sign for the

pressure-head in each case. Thus we have:

Suction stroke: Beginning: ( )

End: ( )

Delivery stroke: Beginging: ( )

End: ( )

2Vapor Pressure: A liquid will change phase and become a gas under two conditions. If its temperature goes higher

than its boiling temperature; or if it’s absolute pressure-head dips below its vapor pressure-head.

3Cavitation: When a liquid enters a region of pressure equal to or below its vapor pressure, the liquid changes its

phase. When this happens in a hydraulic system, it is called ‘Separation’. Generally gas bubbles are formed, which

later on collapse on the inner wall of the hydraulic system. When a bubble collapses, localized high pressure center

is created. This high pressure removes material from the wall. The process of loss of material is called ‘Pitting’. The

entire process of low pressure, separation, gas bubbles and pitting is called ‘Cavitation’.


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Use of Air-vessels:

We have now seen two problems we face when we use a Recip pump. The first one is

that there is constant pressure variation inside the pump during a cycle. The second one is that

we cannot increase its speed beyond a certain limit.

These two problems can be solved to some extent by use of Air-vessels at appropriate

places in the hydraulic system.

Air vessel is a closed chamber containing compressed air in the top portion and liquid at

the bottom portion, as shown in the figure. Air vessels are fitted on the suction and delivery

pipes, as close to the pump as possible.

We have already seen from the modified Indicator Diagram how pressure-head varies

inside the cylinder during the suction stroke. This pressure-head variation naturally affects the

behavior of liquid inside the suction pipe since the liquid is a continuum; similarly on the

delivery stroke. This pressure-head variation affects the discharge, making it uneven. Using Air

vessels on the suction & delivery pipes can reduce this fluctuation to a certain extent.

During the different points in the delivery stroke, the pressure-head components inside

the pump system are tabulated as shown below:

Piston position Pressure-head components

Suction stroke: Beginning ( )

Suction stroke: Middle

Suction stroke: End ( )

Delivery stroke: Beginning ( )

Delivery stroke: Middle

Delivery stroke: End ( )


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For easy understanding, we shall consider the delivery phase:

We find that the component is creating the pressure fluctuation in the delivery

stroke. If this component can be eliminated, then we will have a uniform pressure-head of

throughout the stroke. So, we can add an Air Vessel near the place where the

delivery pipe joins the Recip pump.

When a suitable Air Vessel is added, at the beginning of the delivery stroke, when the

discharge increases due to the effect of component, this extra discharge enters into the Air

Vessel. Only that discharge that is due to enters into the delivery pipe. At the end of

the stroke, ( ) component reduces the discharge, and then the extra liquid from the Air

Vessel is supplied into the delivery pipe. As a result, the output from the pump remains a

constant equal to the pressure-head of . Placing of the Air Vessel has to be as near to

the junction of the pump and delivery pipe so that the effect of is localized to as small a

region as possible. Similarly, the Air Vessel stabilizes the input into the pump during the suction

stroke. Therefore using an appropriate Air Vessel maintains a mean discharge from the pump.

Double-acting Recip pump:

Description

Main components:

The main components are:

1. Single Cylinder with suitable valves at inlet and delivery on both sides of piston.

2. Plunger or piston with piston rings.

3. Connecting rod and crank mechanism.

4. Suction pipes with one-way valves.

5. Delivery pipes with one-way valves.

6. Supporting frame.

A diagrammatic sketch is shown in Fig. 20.2


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Working description:

A double-acting reciprocating pump has a piston which gets its motion by means of a

Crank shaft – Connecting Rod arrangement. Therefore it is called ‘Reciprocating’ Pump. Liquid

is sucked into the cylinder and then ejected out by the motion of the piston and hence it is called

‘Positive Displacement’ Pump. Since delivery occurs during both the strokes of the piston, such

a reciprocating pump is called ‘Double-acting’ Pump.

The pump functions in the following way:

1. : When , the piston is at the inner dead center [IDC]. As the piston

moves away from the IDC, pressure inside the cylinder drops and the one-way suction

valve on the left-side of the piston opens. This happens because the liquid is

incompressible. Liquid rushes in through the suction pipe into the cylinder. But at the

same time, pressure builds up on the right-side of the piston and liquid is discharged out

of the cylinder. When , the piston is at the outer dead center [ODC]. The

discharge on the right-side is completed while the left-side is filled with liquid.

2. : The same process as described above gets repeated in a mirror way

and the cycle gets repeated.

Naturally, the delivery occurs during both halves of the crank-shaft’s rotation. Thus, a

double-acting Recip pump gives a steady delivery of liquid.

Pump characteristics:

1. Delivery: [Qact]

Suppose the length of the cylinder is assumed to be equal to the sweep of the piston,

which is again equal to the diameter of the circle made by the crank-shaft rotation. Let

the length of the crank-shaft be ‘L’ meters. Let the cross-sectional diameter of the

cylinder be ‘D’ meters.

We know that the delivery of liquid in one revolution is twice the volume of liquid in the

cylinder. Again, the delivery of liquid in m3/s is:

( ) ( ).

Let the pump make ‘N’ revolutions per minute.

Then, ( )( )( )(

)

m3/s

Thus, for a double-acting Recip pump is twice the for a single-acting Recip

pump. Once this is calculated, the rest of the pump characteristics can be calculated as before.

Note: Only one pump characteristic i.e. is twice of that for a single-acting pump. If you

have to determine any other pump characteristic for a double-acting pump, you cannot calculate

for a single-acting pump and double it! You will have to obtain the and then calculate using

it.

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A Course on Reciprocating Pump