the mechanical principal involved in transfer of energy  Positive displacement pump  Rotodynamic pump

1. FLUID MECHANICS
AND MACHINERY
PUMPS

2. PUMP
❖ The normal duty of pump is to lift a quantity of
liquid from a low level to high level or to transfer
from one place to another place.
❖ The pump must provide energy
❖ To lift the liquid to required height against the
force of gravity
❖ To overcome the fluid resistance to flow of the
liquid through the pipe and the pump itself

3. PUMP
❖ Pump is defined as a device which transfers the
input mechanical energy of a motor into pressure
energy or kinetic energy.
❖ Pump is classified according to the mechanical
principal involved in transfer of energy
❖ Positive displacement pump
❖ Rotodynamic pump

4. CLASSIFICATION OF PUMP
PUMP
Non – Positive
Displacement Pump
Positive
Displacement Pump
Centrifugal Pump Reciprocating Pump Rotary Pump
Piston Diaphragm Gear
Pump
Vane
Pump
Lobe
Pump
Screw
Pump

5. APPLICATIONS OF PUMP
❖ To pump water from source to fields for agricultural and
irrigation purposes.
❖ In petroleum installations to pump oil
❖ In steam and diesel power plants to circulate feed water and
cooling water respectively
❖ Hydraulic control systems
❖ Pumping of water in buildings
❖ Fire fighting

6. COMPONENTS OF A CENTRIFUGAL PUMP
❖ A centrifugal pump has
the following main
components
✓ Impeller
✓ Casing
✓ Suction pipe with
strainer and foot
valve
✓ Delivery pipe

7. IMPELLER
❖ An impeller is a wheel or
rotor having series of
backward curved vanes
❖ An impeller is mounted on
a shaft which usually
coupled to a motor
❖ The motor provides the
required input energy to
rotate the impeller

8. CASING
❖ The impeller is enclosed in a
watertight casing with delivery
pipe on one side and with an
arrangement on suction side
called eye of impeller.
❖ The main functions of casing are
❖ It guides the water from entry
to exit of impeller
❖ It helps in partly converting the
kinetic energy of liquid into
pressure energy

9. SUCTION PIPE
❖ The pipe which connect
the sump to the eye of
impeller is called suction
pipe
❖ It caries the liquid to be
lifted by the pump
❖ The suction pipe at inlet
is provided with strainer
and foot valve.

10. STRAINER & FOOT VALVE
❖ The function of strainer is to
prevent the entry of debris
into the pump.
❖ The foot valve is a non
return valve which allows
the flow of water only in
upward direction
❖ The valve does not allow
the liquid to drain out from
the suction pipe

11. WORKING OF CENTRIFUGAL PUMP

12. WORKING OF CENTRIFUGAL PUMP
❖ It works on the principle that when a certain mass
of fluid is made to rotate along the impeller from
the central axis of rotation, it impresses a
centrifugal head
❖ It causes the water to move radially outwards at
high velocity and causes the water to rise to a
higher level
❖ The motion of water is restricted by casing of
pump, it results into pressure build up.

13. STEPS INVOLVED IN OPERATION OF CENTRIFUGAL PUMP
❖ The delivery valve is closed.
❖ The priming of the pump is carried out
✓ Priming involves the filling of liquid in suction
pipe and casing up to the level of delivery valve, so
that no air pockets are left in the systems
✓ If any air or gas pockets are left in this portion of
pump, it may result into no delivery of liquid by the
pump

14. STEPS INVOLVED IN OPERATION OF CENTRIFUGAL PUMP
❖ The pump shaft and impeller is now rotated with the help
of an external source of power like motor
✓ The rotation of impeller inside a casing produces a
forced vortex which is responsible in imparting the
centrifugal head to the liquid
✓ It also creates vacuum at the eye of impeller
and causes liquid to rise into suction pipe from the
sump

15. STEPS INVOLVED IN OPERATION OF CENTRIFUGAL PUMP
❖ The speed of impeller should be sufficient to produce the
centrifugal head such that it can initiate the discharge from
delivery pipe.
❖ The delivery valve is opened and the liquid is lifted and
discharged through the delivery pipe due to its high pressure
❖ The liquid is continuously sucked from the sump to impeller eye
and it is delivered from the casing of the pump through the
delivery pipe.
❖ Before stopping the pump, it is necessary to close the delivery
pipe otherwise the back flow of liquid will take place

16. CAVITATION
❖ It is defined as the phenomenon of formation of vapour bubbles of
a flowing liquid in a region
❖ The pressure of the liquid falls below its vapour pressure the
liquid will vapourise and flow will no longer will be continues.
❖ These vapour bubbles travel into the region of higher pressure,
they suddenly collapse on metallic surfaces and the surroundings
liquid rushes to fill the cavities of vapour bubble
❖ The severe rush of liquid causes the development of extremely
high pressure
❖ Prolonged cavitation causes erosion and pitting of metals
❖ Prolonged cavitation causes severe vibrations and noise

17. TYPES OF CASING
❖ The shape of casing is designed such a way to reduce the
loss of kinetic head to minimum. Based on the shape of
casing it is classified
❖ Volute Casing (Constant Velocity)
❖ Vortex Casing (Variable Velocity)
❖ Diffuser (Turbine)

18. VOLUTE CASING
❖ The cross section is designed to give a constant velocity in the
volute of spiral shape
❖ The centrifugal pump with volute
casing round the impeller of gradually
increasing area from point A and B
❖ The loss of energy is reduced
compared with circular casing
❖ The conversion of kinetic energy into
pressure energy is not possible, so
there is only slight improvement in
efficiency

19. VORTEX CASING
❖ The overall diameter of the pump is large compared volute casing.
❖ The increase in diameter will provide
an annular space between the
impeller and volute passage.
❖ The annular space called vortex
chamber, there is a free vortex in
which the velocity of liquid falls as it
passes into this chamber from
impeller outlet entry of volute passage
❖ Due to decreases in velocity the pressure increases radially from centre
outwards
❖ The pump is bulky and expensive (due to excessive dimension)

20. DIFFUSER CASING
❖ The diffuser casing is similar to volute and
vortex casing, but a diffuser ring with guide
vanes is fixed in annular space
❖ The function of guide vanes is to guide the
liquid leaving the impeller in streamlined
diverging passages into the volute chamber
from where it flows to the delivery pipe.
❖ The guide vanes passages have an increasing
in cross sectional which reduces the velocity
of flow, hence the partial kinetic energy(K.E)
is converted into pressure energy(P.E)
❖ The conversion of K.E to P.E takes place in
volute chamber of increasing cross sectional
area

21. TYPES OF IMPELLERS
❖ Depending on the
viscosity of liquid
the impellers are
selected
❖ Closed Impeller
❖ Semi Open Impeller
❖ Open Impeller

22. TYPES OF IMPELLERS
❖ In closed type impeller the vanes of impeller are cast between two
circular disc.
✓ This type of impeller are mostly used for clear water with low
viscosity free from dirt.
❖ In semi open type impeller the vanes are covered with plate on one side.
✓ This type of impeller are mostly used in sewage installations, sugar
and pulp industry with small amount of debris.
❖ In open type impeller the vanes are don not have any cover plate.
✓ This type of impeller is less efficient and used deal with liquids
which contain suspend solids like sand etc…

23. TYPES OF VANES
❖ There are three types vanes according to the shape of vane
✓ Curved forward vane ✓ Curved backward vane ✓ Radial vane

24. VARIOUS HEADS OF A CENTRIFUGAL PUMP
❖ Suction Head (hs):
It represents the vertical
distance between the top surface
level of sump and the centre of
impeller.
❖ Delivery Head (hd):
It represents the vertical
distance between the centre of
impeller and the discharge.

25. VARIOUS HEADS OF A CENTRIFUGAL PUMP
❖ Static Head (Hs):
It is the sum of suction
head and delivery head.
It represents the vertical
distance between the top
surface level of sump to the
discharge level in delivery
tank.
𝑯𝒔 = 𝒉𝒔 + 𝒉𝒅

26. VARIOUS HEADS OF A CENTRIFUGAL PUMP
The total head against which
the pump has to work is called as
gross head
𝑯𝒈 = 𝑯𝒔 + 𝒉𝒇𝒔 + 𝒉𝒇𝒅 +
𝐕𝐬
𝟐
𝟐𝒈
+
𝐕𝐝
𝟐
𝟐𝒈
❖ Gross Head (Hg):
The pump is required to work
against the static head and the
other losses like friction losses in
pipes and head corresponding to
kinetic energy due to suction and
delivery velocity of liquid.

27. VARIOUS HEADS OF A CENTRIFUGAL PUMP
𝑯𝒎 = 𝑯𝒔 + 𝒉𝒇𝒔 + 𝒉𝒇𝒅 +
𝐕𝐝
𝟐
𝟐𝒈
❖ Manometric Head (Hm):
It is defined as the minimum
amount of head against which the
pump has to work to deliver the
required discharge.
Note:
The manometric head does not
include the friction loss head in
impeller and casing of the pump

28. LOSSES IN PUMPS
❖ Various losses which occurs during the operation of centrifugal
pump are
✓ Hydraulic Losses:
➢ Losses in Pump:
 Loss of head due to friction in impeller
 Loss of head due to shock and eddy from inlet to exit of impeller
 Loss of head due in guide vanes due to diffusion and in casing
➢ Other Hydraulic Losses:
 Friction loss in suction and delivery pipes
 Loss of heads in bends, fittings, valves etc.
Theses losses represents the loss of head in pump installation

29. LOSSES IN PUMPS
✓ Mechanical Loss:
Due to disc friction in impeller, friction in bearings and
other mechanical parts of the pump
✓ Leakage Loss:
A certain amount of energy is lost due to liquid which
leaks from high pressure side to low pressure side of
pump
The liquid is leaked through the glands, stuffing box etc.

30. WORK DONE BY IMPELLER
❖ The liquid enters the impeller at its centre and leaves at
its outer periphery
❖ Assumptions
✓ Liquid enters the impeller eye in radial direction, the whirl
component 𝑽𝒘𝟏(of absolute velocity 𝑽𝟏) is zero and flow
component 𝑽𝒇𝟏is equal to absolute velocity 𝑽𝟏 and 𝜶 = 𝟎
✓ No loss of energy in the impeller due to friction
✓ No loss due to shock at entry
✓ There is uniform velocity distribution in the narrow passages
formed between two adjacent

31. WORK DONE BY IMPELLER

32. WORK DONE BY IMPELLER
𝒖𝟏 & 𝒖𝟐 → 𝑷𝒆𝒓𝒊𝒑𝒉𝒆𝒓𝒂𝒍 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝒕𝒉𝒆 𝒊𝒎𝒑𝒆𝒍𝒍𝒆𝒓 𝒂𝒕 𝒊𝒏𝒍𝒆𝒕 & 𝒐𝒖𝒕𝒍𝒆𝒕
𝑽𝟏 & 𝑽𝟐 → 𝑨𝒃𝒔𝒐𝒍𝒖𝒕𝒆 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝒕𝒉𝒆 𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒊𝒏𝒍𝒆𝒕 & 𝒐𝒖𝒕𝒍𝒆𝒕
𝑽𝒓𝟏& 𝑽𝒓𝟐 → 𝑹𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝒕𝒉𝒆𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒊𝒏𝒍𝒆𝒕 & 𝒐𝒖𝒕𝒍𝒆𝒕
𝑽𝒘𝟏& 𝑽𝒘𝟐 → 𝑾𝒉𝒊𝒓𝒍 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝒕𝒉𝒆 𝒍𝒊𝒒𝒖𝒊𝒅 𝒂𝒕 𝒊𝒏𝒍𝒆𝒕 & 𝒐𝒖𝒕𝒍𝒆𝒕
𝜶 & 𝜷 → 𝑮𝒖𝒊𝒅𝒆 𝑩𝒍𝒂𝒅𝒆 𝒂𝒏𝒈𝒍𝒆 𝒂𝒕 𝒊𝒏𝒍𝒆𝒕 & 𝒐𝒖𝒕𝒍𝒆𝒕
𝜽 & 𝝓 → 𝑽𝒂𝒏𝒆 𝒂𝒏𝒈𝒍𝒆 𝒂𝒕 𝒊𝒏𝒍𝒆𝒕 & 𝒐𝒖𝒕𝒍𝒆𝒕
𝒅𝟏 & 𝒅𝟐 → 𝑫𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒊𝒎𝒑𝒆𝒍𝒍𝒆𝒓 𝒂𝒕 𝒊𝒏𝒍𝒆𝒕 & 𝒐𝒖𝒕𝒍𝒆𝒕
𝝎 → 𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚
𝝎 =
𝟐 × 𝝅 × 𝑵
𝟔𝟎

33. WORK DONE BY IMPELLER
❖ While passing through the impeller, the velocity of whirl
changes and there is a change of moment of momentum
𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎 𝒂𝒕 𝑰𝒏𝒍𝒆𝒕 = ሶ
𝒎 × 𝑽𝒘𝟏
= 𝝆 × 𝒂 × 𝑽𝟏 × 𝑽𝒘𝟏 𝑸 = 𝒂 × 𝑽
= 𝝆 × 𝑸 × 𝑽𝒘𝟏
𝒔𝒑𝒆𝒄𝒊𝒇𝒊𝒄 𝒘𝒆𝒊𝒈𝒉𝒕 𝒘 = 𝝆 × 𝒈
=
𝒘
𝒈
× 𝑸 × 𝑽𝒘𝟏
𝑾𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒍𝒊𝒒𝒖𝒊𝒅 𝑾 = 𝒘 × 𝑸
𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎 𝒂𝒕 𝑰𝒏𝒍𝒆𝒕 =
𝑾
𝒈
× 𝑽𝒘𝟏

34. WORK DONE BY IMPELLER
❖ Similarly
𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎 𝒂𝒕 𝒐𝒖𝒕𝒍𝒆𝒕 =
𝑾
𝒈
× 𝑽𝒘𝟐
𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎 𝒂𝒕 𝒊𝒏𝒍𝒆𝒕 =
𝑾
𝒈
× 𝑽𝒘𝟏 × 𝒓𝟏
𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎 𝒂𝒕 𝒐𝒖𝒕𝒍𝒆𝒕 =
𝑾
𝒈
× 𝑽𝒘𝟐 × 𝒓𝟐

35. WORK DONE BY IMPELLER
𝑻𝒐𝒓𝒒𝒖𝒆 𝑻 = 𝑹𝒂𝒕𝒆 𝒐𝒇 𝒄𝒉𝒂𝒏𝒈𝒆 𝒐𝒇 𝒎𝒐𝒎𝒆𝒏𝒕𝒖𝒎
𝑻 =
𝑾
𝒈
× 𝑽𝒘𝟏 × 𝒓𝟏 −𝑽𝒘𝟐 × 𝒓𝟐
𝑾𝒐𝒓𝒌 𝑫𝒐𝒏𝒆 = 𝑻𝒐𝒓𝒒𝒖𝒆 × 𝑨𝒏𝒈𝒖𝒍𝒂𝒓 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚
𝑾. 𝑫 =
𝑾
𝒈
× 𝑽𝒘𝟏 × 𝒓𝟏 −𝑽𝒘𝟐 × 𝒓𝟐 × 𝝎
𝑾. 𝑫 =
𝑾
𝒈
× 𝑽𝒘𝟏 × 𝒓𝟏× 𝝎 − 𝑽𝒘𝟐 × 𝒓𝟐× 𝝎

36. WORK DONE BY IMPELLER
𝑾. 𝑫 =
𝑾
𝒈
× 𝑽𝒘𝟏 × 𝒓𝟏× 𝝎 − 𝑽𝒘𝟐 × 𝒓𝟐× 𝝎 𝒖 = 𝒓 × 𝝎
𝑾. 𝑫 =
𝑾
𝒈
× 𝑽𝒘𝟏 × 𝒖𝟏 −𝑽𝒘𝟐 × 𝒖𝟐
❖ Since the centrifugal pump is the reverse of turbine
𝑾. 𝑫 = −
𝑾
𝒈
× 𝑽𝒘𝟏 × 𝒖𝟏 −𝑽𝒘𝟐 × 𝒖𝟐
𝑾. 𝑫 =
𝑾
𝒈
× 𝑽𝒘𝟐 × 𝒖𝟐 −𝑽𝒘𝟏 × 𝒖𝟏

37. WORK DONE BY IMPELLER
❖ If 𝜶 = 𝟗𝟎° 𝒕𝒉𝒆𝒏 𝑽𝒘𝟏 = 𝟎
𝑾. 𝑫 𝒑𝒆𝒓 𝒔𝒆𝒄 =
𝑾
𝒈
× 𝑽𝒘𝟐 × 𝒖𝟐
𝑾. 𝑫 𝒑𝒆𝒓 𝒔𝒆𝒄
𝑼𝒏𝒊𝒕 𝑾𝒆𝒊𝒈𝒕𝒉 𝒐𝒇 𝒘𝒂𝒕𝒆𝒓 𝒑𝒆𝒓 𝒔𝒆𝒄
=
𝑾
𝒈
× 𝑽𝒘𝟐 × 𝒖𝟐
𝑾
𝑾. 𝑫 𝒑𝒆𝒓 𝒔𝒆𝒄
𝑼𝒏𝒊𝒕 𝑾𝒆𝒊𝒈𝒕𝒉 𝒐𝒇 𝒘𝒂𝒕𝒆𝒓𝒑𝒆𝒓 𝒔𝒆𝒄
=
𝟏
𝒈
× 𝑽𝒘𝟐 × 𝒖𝟐

38. WORK DONE BY IMPELLER
❖ If 𝑽𝒘𝟏 ≠ 𝟎
𝑾. 𝑫 𝒑𝒆𝒓 𝒔𝒆𝒄 =
𝑾
𝒈
× 𝑽𝒘𝟐 × 𝒖𝟐 −𝑽𝒘𝟏 × 𝒖𝟏
𝑾. 𝑫 𝒑𝒆𝒓 𝒔𝒆𝒄
𝑼𝒏𝒊𝒕 𝑾𝒆𝒊𝒈𝒕𝒉 𝒐𝒇 𝒘𝒂𝒕𝒆𝒓𝒑𝒆𝒓 𝒔𝒆𝒄
=
𝑾
𝒈
× 𝑽𝒘𝟐 × 𝒖𝟐 −𝑽𝒘𝟏 × 𝒖𝟏
𝑾
=
𝟏
𝒈
× 𝑽𝒘𝟐 × 𝒖𝟐 −𝑽𝒘𝟏 × 𝒖𝟏
❖ The above equation is Euler Momentum Equation for centrifugal
pump

39. EFFICIENCY OF THE CENTRIFUGAL PUMP
❖ Manometric efficiency
❖ Volumetric efficiency
❖ Mechanical efficiency
❖ Overall efficiency

40. MANOMETRIC EFFICIENCY
The ratio of the manometric head developed by the
pump to the head imparted by the impeller to the liquid is
known as manometric efficiency
𝜼𝒎𝒂𝒏𝒐 =
𝑴𝒂𝒏𝒐𝒎𝒆𝒕𝒓𝒊𝒄 𝑯𝒆𝒂𝒅
𝑯𝒆𝒂𝒅 𝑰𝒎𝒑𝒂𝒓𝒕𝒆𝒅 𝒃𝒚 𝒊𝒎𝒑𝒆𝒍𝒍𝒆𝒓 𝒕𝒐 𝑳𝒊𝒒𝒖𝒊𝒅
𝜼𝒎𝒂𝒏𝒐 =
𝑯𝒎
𝑽𝒘𝟐 × 𝒖𝟐
𝒈
𝜼𝒎𝒂𝒏𝒐 =
𝒈 × 𝑯𝒎
𝑽𝒘𝟐 × 𝒖𝟐

41. VOLUMETRIC EFFICIENCY
The ratio of the actual liquid discharged per second
from the pump to the total liquid discharge per second
passing through the impeller.
𝜼𝑽𝒐𝒍 =
actual liquid discharged at the pump outlet per second
𝑯𝒆𝒂𝒅 𝑰𝒎𝒑𝒂𝒓𝒕𝒆𝒅 𝒃𝒚 𝒊𝒎𝒑𝒆𝒍𝒍𝒆𝒓 𝒕𝒐 𝑳𝒊𝒒𝒖𝒊𝒅
𝜼𝑽𝒐𝒍 =
𝑸
𝑸 + 𝒒

42. MECHANICAL EFFICIENCY
The ratio of the power delivered by the impeller to the
liquid to the power input to the pump shaft is known as
mechanical efficiency
𝜼𝒎𝒆𝒄𝒉 =
Power delivered by the impeller to the liquid
Power input to the pump shaft
𝜼𝒎𝒆𝒄𝒉 =
𝑾𝒐𝒓𝒌𝒅𝒐𝒏𝒆 𝒃𝒚 𝒊𝒎𝒑𝒆𝒍𝒍𝒆𝒓 𝒑𝒆𝒓 𝒔𝒆𝒄
𝑺𝒉𝒂𝒇𝒕 𝒑𝒐𝒘𝒆𝒓
𝜼𝒎𝒆𝒄𝒉 =
𝑾
𝒈
× 𝑽𝒘𝟐 × 𝒖𝟐
𝑷
𝑾𝒉𝒆𝒓𝒆, 𝑾 = 𝒘 × 𝑸 = 𝝆 × 𝒈 × 𝑸

43. OVERALL EFFICIENCY
The ratio of the power output of pump to the power input
to the pump is known as overall efficiency
𝜼𝐨 =
Power output of pump
Power input to the pump shaft
𝜼𝒐 =
𝝆 × 𝒈 × 𝑸 × 𝑯𝒎
𝑷
𝜼𝒐 = 𝜼𝒎𝒂𝒏𝒐 × 𝜼𝒎𝒆𝒄𝒉 × 𝜼𝑽𝒐𝒍

44. TYPES OF PERFORMANCE CHARACTERISTIC CURVES
❖ Main characteristics curves
❖ Operating characteristics curves
❖ Iso – efficiency (or) Muschel curves
❖ Constant head and Constant discharge curves
The performance characteristics curves are broadly divided to
four categories

45. MAIN CHARACTERISTICS CURVES
❖ Main characteristics curves are obtained by test run at constant speed
and the discharge is varied by means of delivery valve.
❖ At each discharge, the manometric head 𝑯𝒎 and input power 𝑷 are
measured and the overall efficiency 𝜼𝒐 is calculated
❖ Test curves are plotted between 𝑯𝒎 𝑽𝒔 𝑸, 𝑷 𝑽𝒔 𝑸 𝒂𝒏𝒅 𝜼𝒐 𝑽𝒔 𝑸 is shown
figure for that constant speed. The test are repeated for different speed.

46. OPERATING CHARACTERISTICS CURVES
❖ The pumps are designed for
maximum efficiency at the given
speed called design speed
❖ The pumps are test run at design
speed as provided by the
manufacturer of the pump
❖ The discharge is varied as discussed
in main characteristic curve and the
head and power input is measured
❖ The overall efficiency of the pump is
calculated
❖ The performance curve thus
obtained at design speed are called
operating characteristics curves

47. ISO – EFFICIENCY (OR) MUSCHEL CURVES
❖ Constant efficiency curves are useful in
predicting the performance on entire
operations and its best performance
❖ The curves are plotted between
𝑯𝒎 𝑽𝒔 𝑸 𝒂𝒏𝒅 𝜼𝒐 𝑽𝒔 𝑸
❖ Draw a line on 𝜼𝒐 𝑽𝒔 𝑸 representing
constant efficiency line.
❖ The points at which the constant efficiency
line cuts the constant speed lines the
discharges are noted

48. ISO – EFFICIENCY (OR) MUSCHEL CURVES
❖ At the given discharge and speed the
𝑯𝒎 is noted from 𝑯𝒎 𝑽𝒔 𝑸 graph.
❖ The values of 𝑯𝒎 & 𝑸 at constant
efficiency is projected in graph
❖ The points corresponding to same overall
efficiency are then joined with a smooth
curve as shown in figure
❖ These curves represents iso – efficiency
curves. The curves help to locate the
region where the pump would operate at
maximum efficiency

49. CONSTANT HEAD AND CONSTANT DISCHARGE CURVES
❖ Often centrifugal pump is draw
required to operate variable speed
than the design speed.
❖ It is necessary to the performance
curves of a pump at variable speed
so that these curves can be used to
predict the performance.
❖ The delivery valves opening is fixed
and kept constant during the test on
pump.
❖ Then operated at variable speed. For
each speed 𝑯𝒎, 𝑸 𝒂𝒏𝒅 𝑷𝒊 are measured
❖ The graph 𝑯 𝑽𝒔 𝑵, 𝑷𝒊 𝑽𝒔 𝑵 𝒂𝒏𝒅 𝑸 𝑽𝒔 𝑵 𝒂𝒓𝒆 𝒅𝒓𝒂𝒘𝒏.

50. SPECIFIC SPEED OF THE PUMP
❖ The specific speed of a centrifugal pump is defined as the
speed of a geometrically similar pump which would deliver
discharge of one cubic meter per second under a head of one
metre.
❖ Discharge
𝑸 = 𝑨𝒓𝒆𝒂 × 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒐𝒇 𝑭𝒍𝒐𝒘
𝑸 = 𝝅 × 𝒅 × 𝒃 × 𝑽𝒇
❖ The Width “b” is proportional to the diameter of the impeller
𝑸 ∝ 𝒅𝟐
× 𝑽𝒇 𝑬𝒒 … … … . . ①

51. SPECIFIC SPEED OF THE PUMP
❖ Peripheral velocity
𝒖 =
𝝅 × 𝒅 × 𝑵
𝟔𝟎
❖ The velocity “u” is proportional to the diameter and speed of
the impeller
𝒖 ∝ 𝒅𝑵
𝒅 ∝
𝒖
𝑵 𝑬𝒒 … … … . . ②

52. SPECIFIC SPEED OF THE PUMP
❖ The tangential velocity “𝒖” of the impeller and flow velocity
𝑽𝒇𝟏 are proportional to manometric head 𝑯𝒎
𝒖 ∝ 𝑯𝒎 𝑬𝒒 … … … . . ③
𝑽𝒇 ∝ 𝑯𝒎 𝑬𝒒 … … … . . ④
❖ From 𝑬𝒒 … … … . . ②
𝒅 ∝
𝒖
𝑵
𝒔𝒖𝒃 𝑬𝒒 ③ 𝒊𝒏 ②
𝒅 ∝
𝑯𝒎
𝑵
𝑬𝒒 … … … . . ⑤

53. SPECIFIC SPEED OF THE PUMP
❖ From 𝑬𝒒 … … … . . ① ④ ⑤
𝑸 ∝ 𝒅𝟐
× 𝑽𝒇 𝑽𝒇 ∝ 𝑯𝒎
𝒅 ∝
𝑯𝒎
𝑵
𝒔𝒖𝒃 𝑬𝒒 ④ & ⑤ 𝒊𝒏 ①
𝑸 ∝
𝑯𝒎
𝑵
𝟐
× 𝑯𝒎
𝑸 ∝
𝑯𝒎
ൗ
𝟑
𝟐
𝑵𝟐
𝑸 = 𝑲
𝑯𝒎
ൗ
𝟑
𝟐
𝑵𝟐
𝑬𝒒 … … … . . ⑥

54. SPECIFIC SPEED OF THE PUMP
❖ From the definition at 𝑵 = 𝑵𝒔 𝒘𝒉𝒆𝒏 𝑸 = 𝟏 Τ
𝒎𝟑
𝒔 𝒂𝒏𝒅 𝑯𝒎 = 𝟏 𝒎
𝑸 = 𝑲
𝑯𝒎
ൗ
𝟑
𝟐
𝑵𝟐
𝟏 = 𝑲
𝟏 ൗ
𝟑
𝟐
𝑵𝒔
𝟐
𝑲 = 𝑵𝒔
𝟐 𝑬𝒒 … … … . . ⑦
𝒔𝒖𝒃 𝑬𝒒 ⑦ 𝒊𝒏 ⑥
𝑸 = 𝑵𝒔
𝟐
𝑯𝒎
ൗ
𝟑
𝟐
𝑵𝟐
𝑵𝒔 =
𝑵 × 𝑸
𝑯 ൗ
𝟑
𝟒

55. THANK YOU