This document provides an overview of centrifugal pumps and reciprocating pumps. It defines key components of centrifugal pumps like impellers and casings, and describes how they work by imparting centrifugal force to increase fluid pressure. It also defines important pump parameters like head, efficiency, specific speed, and NPSH. Cavitation in pumps and methods to prevent it are explained. Performance curves for pumps are introduced. Finally, the working principle and equations for reciprocating pumps are outlined.

1. Fluid Mechanics
and
Fluid Machines
(A3MET305)

2. UNIT V- Syllabus and Concepts
Hydraulic Pumps: Rotodynamic pump, various heads and efficiencies,
centrifugal pumps, working principle, velocity components at entry and
exit of the rotor, work done by the impeller, specific speed of pump,
NPSH, cavitation in pumps, performance curves, reciprocating pump
working principle.
• Rotodynamic pumps
• Various heads and efficiencies of centrifugal pump
• Concept of velocity triangles of centrifugal pumps
• Different vane configurations of impellers
• Specific speed of pump
• Similarity laws of pump
• NPSH
• Cavitation in pumps
• Performance curves
• Reciprocating pump

3. Hydraulic Pumps
• The hydraulic machines which convert the mechanical energy into
hydraulic energy are called pumps
• It increases pressure energy or kinetic energy or both by using
mechanical energy. The energy level of the fluid can be increased by
either roto dynamic action or by positive displacement of the fluid.
• If the mechanical energy is converted into pressure energy by means
of centrifugal force acting on the fluid, the hydraulic machine is
called Centrifugal pump

4. Classification of Hydraulic Pumps

5. Components and Working of a Centrifugal Pump
Main parts of a centrifugal pump (refer
Fig) are:
1. Impeller
2. Casing
3. Suction pipe
4. Delivery pipe

6. Working of a Centrifugal Pump
• The electric motor is started to rotate the impeller and the delivery valve is still
kept closed to reduce the starting torque.
• The rotation of the impeller in the casing full of liquid produces a forced vortex
which provides a centrifugal head to the liquid and thus, it results in increase of
pressure throughout the liquid. The rise in pressure head at any point of the
rotating liquid is proportional to the square of the tangential velocity of the liquid
at that point and the distance of the point from the axis of rotation. Thus, if the
speed of the impeller of the pump is high enough, then the pressure of the liquid
surrounding the impeller increases considerably. When the delivery valve is
opened, the liquid flows in an outward radial direction and leaves the vanes of the
impeller at the outer radius with high velocity and pressure.
• The rotation of the impeller due to centrifugal action causes a partial vacuum at
its eye which causes the suction of the liquid from the sump through the suction
pipe. The sucked liquid replaces the liquid which is being discharged from the
whole circumference of the impeller.
• The high pressure of the liquid leaving the impeller is utilized in lifting the liquid
to the required height.

7. .Casing: It is an airtight chamber which surrounds the impeller. It is similar to the
casing of a reaction turbine. It is designed in such a way that the kinetic energy
of the water discharged at the outlet of the impeller is converted into pressure
energy before the water leaves the casing and enters the delivery pipe. The three
types of casing, namely volute casing, vortex casing and casing with guide
blades are commonly used and the pump is named after the casing it uses.
(i) Volute casing: The volute casing is of spiral shape in which the area of flow
increases gradually from the impeller outlet to the delivery pipe. The increase in
area of flow decreases the velocity of flow with corresponding increase in the
pressure of water flowing through the casing. Single stage pumps are mostly
having volute casing. The volute casing has higher eddy losses which results in
lower overall efficiency. The pumps having volute casing are known as volute
pump.

8. Different heads in a centrifugal pumping system
(Refer and draw the diagram available in slide 5 of this ppt)
1. Suction head: It is the vertical height of the centre line of the pump
shaft above the water surface in the sump from which water is being lifted.
It is also known as static suction lift and it is denoted by hs.
2. Delivery head: It is the vertical height of the water surface in the tank
to which the water is delivered above the centre line of the pump shaft. It
is also known as static delivery lift and it is denoted by hd.
3. Static head: It is the vertical distance between the water surface in the
sump and the tank to which the water is being delivered by the pump.
Thus, static head is the sum of suction head and delivery head. It is
denoted by Hs and it is givenby the below expression.
Hs = hs + hd
4. Manometric head: Manometric head (Hm) is the head against which a
centrifugal pump has to work. It is measured across the pump inlet and
outlet flanges. If there are no energy losses in the pump (i.e., in the
impeller and casing), then manometric head will be equal to the energy
given to water by the impeller

9. Efficiencies of Centrifugal Pumps
1. Manometric efficiency: It is defined as the ratio of manometric head
developed by the pump to the head imparted by the impeller to the water.
Manometric efficiency takes into account the hydraulic losses in the pump.
It is denoted by ɳman and the expression is given below.
2.Volumetric efficiency: Volumetric efficiency is defined as the ratio of
actual discharge (Q) from the pump to the total discharge per second
through the impeller. It is denoted by ɳv and its expression is given below.

10. 3.Mechanical efficiency: An electric motor is used to give the power
input to the pump shaft which is more than the power delivered by the
impeller to the water. Mechanical efficiency is defined as the ratio of the
power available at the impeller (Pim) to the power at the shaft (P) of the
centrifugal pump. It is denoted by m and its expression is given below.
4. Overall efficiency: It is defined as the ratio of power output of the
pump (Po) to the power input to the pump (P). It is denoted by ɳo and its
expression is given below.

11. Velocity triangles and work done by centrifugal pump
1.U1 = π D1N / 60
2.U2 = π D2N / 60
3. Discharge Q = π D2B2Vf2
(Where , B – Width of runner)
4. Hydraulic (or) ɳman = gH / Vw2 U2
5. W.D by impeller on water per sec, or
Impeller Power = WVw2 U2 / g
6. Mech efficiency, Impeller Power / S.P
7. Overall efficiency,
8. pressure rise in the impeller,
(p0 – pi / ρg) = (Vf1
2 + u2 – Vf2
2 cosec2 φ) / 2g
Vf1 = Vf2

12. Specific speed of centrifugal pumps
•The specific speed (Ns) of a centrifugal pump is defined as the speed of a
geometrically similar pump which would deliver 1m3 of liquid per second
against a head of 1 m.

13. Specific speed of centrifugal pumps

14. Model Testing of centrifugal pumps
⮚ Model and prototype must follow the below coefficient rules:
• Power coefficient:
• Head coefficient:
• Capacity or Flow Coefficient:

15. Cavitation in centrifugal pumps
• When the pressure at the suction side of the pump impeller falls below
the Vapour pressure of the liquid, some of the liquid vaporizes and
bubbles of the Vapour is carried along with the liquid.
• These Vapour bubbles condense and collapse rapidly on reaching to high
pressure zone (near the impeller exit).
• This process continues and creates high pressure which may damage the
impeller. This phenomenon is called cavitation which is highly
undesirable.
• At the inlet of the impeller, the pressure remains lowest on the underside
of vanes from where cavitation commences and the vanes tips at impeller
exit are the most common site for cavitation attack. The cavitation can be
noticed by a sudden drop in efficiency and head.

16. • To indicate whether cavitation will occur, the Thoma’s cavitation factor
(σ ) is used and the expression is given below.
• Here, Ha = pa / (ρg) and Hv = pv /(ρg) are the atmospheric and vapour
pressure heads in terms of meters of liquid, respectively , hs be the
suction height (or lift), hfs is the loss of head in the suction pipe, Hm is
effective or manometric head.
• When the value of σ is less than the critical value (σc ), then cavitation
occurs in the pumps.
• The value of σc depends on the specific speed (Ns) of a pump.
• The value of σc can be determined by the following relation.
• Net positive suction head (NPSH): Net positive suction head (NPSH) is
defined as the available suction head at the pump inlet above the

17.  The cavitation in pumps can be avoided by the following factors
1. By reducing the suction lift that increases the value of which ensures
sufficient availability of NPSH.
2. By reducing the velocity in the suction pipe.
3. By avoiding the bends.
4. By reducing hfs in suction pipe.
5. By selecting the pump of lower specific speed.
 Cavitation is undesirable due to the following harmful effects
1. A large number of Vapour bubbles formed suddenly collapse in a high
pressure region which causes the rush of surrounding liquid and results in
shock, noise and vibration. This phenomenon is called water hammer.
2. The continuous water hammering action of collapsing bubbles causes
pitting and erosion of the surface.
3. The water hammer causes fatigue of the metal parts and reduces their
lifetime.
4. Cavitation causes sudden drop in head and efficiency

18. Performance characteristic curves of centrifugal pumps
• Pump provides maximum efficiency when it operates at designed
values of speed, discharge and head. In actual practice, a pump has to
operate at different conditions than the designed ones under which the
behavior of the pump may be different. In order to predict the behavior
and performance of a pump under varying conditions, various tests are
performed and the results of the tests are plotted in the form of curves.
These curves are known as the characteristic curves of the pump.
• The important characteristic curves of a pump are (i) main
characteristic curves, (ii) operating characteristic curves, (iii) constant
efficiency or Muschel curves, and (iv) constant head and constant
discharge characteristic curves
i) Main Characteristic Curves:

19. ii) Operating characteristic curves iii) Constant efficiency or Muschel curves
iv) Constant head and constant discharge characteristic curves

20. Reciprocating Pumps
• The reciprocating pumps are positive displacement pumps in which a certain
volume of liquid is taken in an enclosed volume and then it is forced out against
pressure to the required application.
• The mechanical energy is converted into pressure energy by sucking the liquid
into a cylinder in which a piston is reciprocating which exerts the thrust on the
liquid and increases its pressure energy.
• The reciprocating pumps may be classified into (i) Single acting pump: If the
water (liquid) is in contact with one side of piston.
• (ii) Double acting pump: If the water is in contact with both sides of the piston.

21. • For single acting reciprocating pump, Theoretical discharge of the pump
per second is given by,
• For Double acting reciprocating pump, Theoretical discharge of the
pump per second is given by, (If piston rod area is neglected)
• For Double acting reciprocating pump, Theoretical discharge of the
pump per second is given by, (If piston rod area is considered)
• Ap is the area of piston rod = Π d2 /4, where d is the diameter of piston
rod
A is area of cylinder = Π D2 /4 where
D is the diameter of the cylinder
L is the length of cylinder
N is speed in rpm

22. • Slip of the Reciprocating Pump: The difference between the theoretical
discharge (Qth) and actual discharge (Qact) is known as slip (S).
• Generally, the slip is expressed as percentage slip and its expression is
given below. (cd – coefficient of discharge)
• Theoretical power required for driving the pump is given by,
• H is the total head, sum of suction head (hs) and delivery head (hd) i.e.

23. Important long answer questions (Refer your notes for solutions)
1. Explain the working principle of a centrifugal pump with the help of
a line sketch, naming all the parts.
2. With the help of a neat sketch, explain in brief the functioning of
volute casing of a centrifugal pump
3.What are the different efficiencies of a centrifugal pump? Explain
4.Briefly explain different heads in a centrifugal pumping system
5.A centrifugal pump has an impeller of 80 cm diameter and it delivers
1.144 m3/s against a head of 70 m. The impeller runs at 1000 rpm and
its width at outlet is 8 cm. If hydraulic efficiency is 82%, calculate the
blade angle at outlet .
6. A centrifugal pump delivers water against a net head of 10.0 m at a
design speed of 1000 rpm. The vanes are curved backwards and make
an angle of 30o with the tangent at the outer periphery. The impeller
diameter is 30 cm and has a width of 5 cm at the outlet. Determine the
discharge of the pump if the manometric efficiency is 95%.
7.The external and internal diameters of the impeller of a centrifugal
pump are 0.4 m and 0.2 m, respectively. The centrifugal pump runs at
1200 rpm and its vanes at the exit are set back at an angle of 25°. If a
constant radial flow through the impeller is maintained at 2.5 m/s, then
determine (i) the inlet vane angle, (ii) angle made by absolute velocity
at the outlet and (iii) work done by the impeller per unit weight of

24. 8. The internal and external diameters of a centrifugal pump are 10 cm and
20 cm, respectively. It runs at 2800 rpm and delivers 0.105 m3/s of water.
The widths of impeller at the inlet and outlet are 2 cm and 1 cm,
respectively. The water enters the impeller radially at the inlet and impeller
blade angle at the exit is 45°. Determine the pressure rise in the impeller
by assuming that flow velocity as constant and neglecting losses through
it.
9. Determine the specific speed of a centrifugal pump which delivers water
at the rate of 2 m3/s under a head of 20 m while running at 3500 rpm and
operating at a maximum efficiency of 85%. Also determine the discharge,
head and power input to the pump at the speed of 2500 rpm assuming that
the efficiency remains constant at all the speeds.
10. Define specific speed of a centrifugal pump. Derive an expression for
the same
11.Two geometrically similar pumps run at the same speed of 1200 rpm.
One pump with impeller diameter of 0.4 m delivers water at the rate of
0.03 m3/s against the head of 20 m. Determine the diameter and head
delivered by the other pump if it has to deliver 50% discharge of the first
pump

25. 12. Two homologous pumps A and B are to run at the same speed of 600
rpm. Pump A has an impeller of 50 cm diameter and discharges 0.4 m3/s of
water under a net head of 50 m. Determine the diameter of impeller of
pump B and its net head if it is to discharge 0.3 m3/s
13. Determine the height from water surface a centrifugal pump should be
installed to avoid cavitation when atmospheric pressure (abs) is 101.325
kPa, vapour pressure is 2.5 kPa (abs), the inlet and other losses in suction
pipe are 1.5 m, effective head of the pump is 50 m and cavitation factor is
0.115.
14. The following particulars are given for a centrifugal pump, such as
discharge = 0.15 m3/s of water, manometric head = 35 m, speed of the
pump = 1150 rpm, atmospheric pressure (abs) = 1.01325 bar, vapour
pressure at the temperature of water pumped = 3.5 kPa (abs), inlet and
other losses in suction pipe = 0.25 m of water. Determine minimum NPSH
and maximum allowable height of the pump from the free surface of water
in the pump.
15. Define cavitation. What are the effects of cavitation? Give the necessary
precautions against cavitation

26. 16. Describe cavitation phenomenon in centrifugal pump
17. Write a note on the main performance curves of centrifugal pump
18. Explain the properties for a centrifugal pump, such as (i) main
characteristics curves, (ii) operating characteristics curves and (iii)
Muschel curves
19. A single acting reciprocating pump delivers 9 litres per second of water
against a suction head of 4 m and a delivery head of 16 m while running at
a speed of 60 rpm. The diameter and stroke of the piston are 200 mm and
300 mm, respectively. Determine (i) the theoretical discharge, (ii)
coefficient of discharge, (iii) slip, (iv) percentage slip and (v) power
required to drive the pump.
20. A double acting reciprocating pump operating at 55 rpm has a piston
diameter of 0.2 m and piston rod of diameter 40 mm which is on one side
only. The stroke of the piston is 0.3 m. The suction and delivery heads are
5 m and 20 m, respectively. Determine (i) the theoretical discharge and (ii)
power required to drive the pump.

27. 13. Sol:)

28. 14. Sol:)

29. 19. Sol:)

30. 20. Sol:)