1. Turbo Machinery Energy transfer from a fluid to a rotor
Prepared by : Jigar J. Vaghela

2. Introduction
A turbo machine is a prime mover, which converts hydro power (energy of water) into mechanical energy and further into hydro-electric power.
Turbines convert hydraulic energy or hydro-potential into mechanical energy.
Mechanical energy developed by turbines is used to run electric generators coupled to the shaft of turbines
Examples: water, gas or steam turbines, pumps, compressors and blowers etc.
A turbo machine is a rotating machine which adds energy to or extracts energy from a fluid by virtue of a rotating system of blades within the machine
Importance of hydraulic turbine w.r.t. non renewable resources

3. Giant Hydro Power Plants of India3

4. Tehri Dam (Bhagirathi river, Uttarakhand) 2400 MW
260.5 m high and 575 m length
10th tallest dam in world

5. Koyna Dam (Koyna River, Maharashtra) 1960 MW
Power generation in 4 stages
Generators located in underground

6. Srisailam Hydroelectric Project (Krishna River, Telagana) 1670 MW
6 reversible francis type of 150 MW
7 francis type of 110 MW

7. Nathpa Jhakri Hydroelectric power project (Satluj, Himachal Pradesh) 1530 MW
6 francis type of 250 MW

8. Sardar Sarovar (Narmada River , Gujarat) 1450 MW
6 francis type of 200 MW
5 Kaplan type in canal

9. Hydro electric Power plant
Hydro electricity is electricity generated by hydropower, i.e., the production of electrical power through the use of the gravitational force of falling or flowing water.
Elements of hydro electric power plant:
Dam
Penstock
Surge tank
Turbine
Electric generator
Tail race

10. Layout

11. HEAD

12. Heads

13. Efficiencies Hydraulic efficiency: Mechanical efficiency:
 ℎ = 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑 𝑡𝑜 𝑟𝑢𝑛𝑛𝑒𝑟 𝑝𝑜𝑤𝑒𝑟 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑎𝑡 𝑖𝑛𝑙𝑒𝑡 𝑜𝑓 𝑡𝑢𝑟𝑏𝑖𝑛𝑒 = 𝑅.𝑃. 𝑊.𝑃.
Mechanical efficiency:
 𝑚 = 𝑝𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑠ℎ𝑎𝑓𝑡 𝑜𝑓 𝑡𝑢𝑟𝑏𝑖𝑛𝑒 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑 𝑡𝑜 𝑟𝑢𝑛𝑛𝑒𝑟 = 𝑆.𝑃. 𝑅.𝑃.
Volumetric efficiency:
 𝑣 = 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑎𝑐𝑡𝑢𝑎𝑙𝑙𝑦 𝑠𝑡𝑟𝑖𝑘𝑖𝑛𝑔 𝑡ℎ𝑒 𝑟𝑢𝑛𝑛𝑒𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑡𝑜 𝑡ℎ𝑒 𝑡𝑢𝑟𝑏𝑖𝑛𝑒
Overall efficiency:
 𝑜 = 𝑆.𝑃. 𝑊.𝑃.
= 𝑆.𝑃. 𝑅.𝑃. × 𝑅.𝑃. 𝑊.𝑃.
∴  𝑜 =  ℎ ×  𝑚

14. Classification of hydraulic turbines
According to type of energy at inlet(hydraulic action)
Impulse
at inlet only K.E.
Pelton turbine
Reaction
at inlet both K.E. + Pressure Energy
Francis & Kaplan turbine
According to direction of flow of water in the runner
Tangential flow
Axial flow
Radial flow
Mixed-radial & axial

15. Classification of hydraulic turbines
According to water head and quantity of water availability
High head & small quantity of water flow
Above 250 m
Medium head & medium flow rate
60 m to 250 m
Low head & large flow rate
Less than equal to 60 m
According to specific speed of turbine
Low specific speed of turbine
< 60
Medium specific speed of turbine
High specific speed of turbine
>400
The specific speed of a turbine is the speed of a geometrically similar turbine that would develop 1KW power when working under a head of 1m.

16. Comparison Aspect Impulse Reaction Fluid energy conversion
K.E. in the nozzle
K.E. in the fixed blade
Flow path
Nozzle-runner
Fixed blade – runner
Energy inlet to moving blades
Only K.E.
K.E. + P.E.
Changes in pressure & velocity
Pressure =Constant
P & V both changes
Entering of water
Water may be admitted over apart or whole circumference of runner wheel
Must admitted over whole circumference of runner wheel
Water fills the turbine
Not required wheel run full
Run full and kept full of water
Flow regulation
Possible
Not
Casing
Prevent splashing & guide water to tail race
Water tight casing is required & has to sealed from atm.
Governing
Needle valve
Guide blade

17. (Pelton wheel/turbine)
Impulse turbine
(Pelton wheel/turbine)

18. Pelton wheel or turbine
Pelton wheel / turbine is…
Tangential flow turbine
Impulse turbine V
Tangent to runner

19. Pelton wheel or turbine
Main parts:
Runner and buckets
Nozzle and flow regulating arrangement
Breaking jet
Casing

20. Pelton wheel or turbine

21. Nozzle and Flow Regulating Arrangement
Bucket of Pelton Wheel

22. Pelton Wheel (Pelton turbine)…
4 November 2010

23. Pelton Wheel (Pelton turbine)…

24. Pelton Wheel (Pelton turbine)…

25. Pelton Wheel (Pelton turbine)…
The bucket or vane is so shaped that when the water strikes, it gets split into two and gives it an impulse force in the centre of the bucket. This bucket is also known as splitter.

26. Pelton Wheel (Pelton turbine)…

27. Heads, Losses and Efficiencies of Hydraulic Turbines
Various types of losses that occur in a power plant are given below:
(a) Head loss in the penstock:
This is the friction loss in the pipe of a penstock.
(b) Head loss in the nozzle:
In case of impulse turbines, there is head loss due to nozzle friction.
(c) Hydraulic losses:
In case of impulse turbines, these losses occur due to blade friction.
(d) Leakage losses:
In case of impulse turbines, whole of the water may not be striking the buckets and therefore some of the water power may go waste. These losses are called leakage losses. 27

28. Heads, Losses and Efficiencies of Hydraulic Turbines
(e) Mechanical losses:
The power produced by the runner is not available as useful work of the shaft because some power may be lost in bearing friction as mechanical losses.
(f) Generator losses:
Due to generator loss, power produced by the generator is still lesser than the power obtained at the shaft output. 28

29. Specific Speed 𝑵 𝒔
It is defined as the speed of a turbine which is identical in shape, geometrical dimensions, blade angles, gate openings, etc. with the actual turbine but of such a size that it will develop unit power when working under a unit head.
In MKS system,
Unit power → 1 Horse power
Unit head → 1 meter
In SI system,
Unit power → 1 KW

30. Specific Speed for Hydraulic Turbine

33. Significance of Specific Speed
Sr. No.
Specific Speed, 𝑵 𝒔
Type of Turbine
In MKS unit
In SI unit 1
10 to 60
10 to 50
Pelton Wheel 2
60 to 300
51 to 225
Francis Turbine 3
300 to 1000
255 to 860
Kaplan turbine

34. Design Aspects of Pelton Wheel

35. Design of Pelton Wheel means……….
To determine,
Diameter of jet (d)
Diameter of wheel (D)
Size of the bucket (Width and Depth)
No. of buckets on the wheel (Z)

36. Example
A turbine develops 7225KW power under a head of 25meters at 135 r.p.m. Calculate the specific speed of the turbine and state the type of the turbine.
A turbine is to operate under a unit head of 30m at 200 r.p.m. The discharge is 10 cumec. If the efficiency is 85%. Determine (1) Specific speed (2) Power Generated and Type of Turbine.
A pelton Wheel develops 2500KW under a head of 250m. The overall Efficiency of the turbine is 85%. If speed ratio(ᵩ) = 0.46, Cv= 0.98 and Specific speed is 18.5, then find : (a) Diameter of turbine (b) Diameter of jet.
A pelton Wheel is to be designed for the folloing Specifications:
Shaft Power = 11772KW, Head = 380m, Speed = 750r.p.m., Overall Efficiency = 86%, Jet Dia is not to exceed one sixth of the wheel diameter, Determine:
(i) The wheel dia & the jet dia.
(ii) width of buckets & depth of buckets on the wheels.
(iii) Number of buckets on a runner
Take Kv = and Ku = 0.45
5. A pelton Wheel is having a mean bucket dia. Of 1m and is running at 1000r.p.m. The net head on the pelton wheel is 700m. The discharge nozzle is 0.1m3/s. Find (i) Power available at the nozzle.

37. Unit Quantities and Model Relationship
A turbine operates most efficiently at its design point
In order to predict the behavior of turbine operating at varying conditions of head, discharge, speed and power output, the results expressed in terms of quantities which may be obtained when the head on the turbine is reduced to unity (1m).
Turbine can be compared with the help of the following common characteristics:
Unit Speed 𝑁 𝑢
Unit Discharge 𝑄 𝑢
Unit Power 𝑃 𝑢

38. Unit Speed 𝑵 𝒖
It is defined as the speed of a turbine working under a unit head (1 m). 𝑢∝𝑉 𝑎𝑛𝑑 𝑉∝ 𝐻 ∴𝑢∝ 𝐻 But, 𝑢= 𝜋𝐷𝑁 60 ∴𝑢∝𝐷𝑁 For a given turbine, the diameter 𝐷 is constant. ∴𝑁∝𝑢 ∴𝑁∝ 𝐻 ∴𝑁= 𝐾 1 𝐻 From definition of unit speed, if 𝐻=1𝑚, 𝑁= 𝑁 𝑢 ∴ 𝑁 𝑢 = 𝐾 1 Hence, 𝑵 𝒖 = 𝑵 𝑯

39. Unit Discharge 𝑸 𝒖
It is defined as a discharge passing through a turbine, which is working under a unit head (1m). Total discharge, Q = Area of flow x Velocity of flow But for a given turbine, area of flow is constant and, 𝑄∝ 𝑉 𝑓 ∝ 𝐻 ∴𝑄= 𝐾 2 𝐻 From definition of unit discharge, if 𝐻=1𝑚, 𝑄= 𝑄 𝑢 ∴ 𝑄 𝑢 = 𝐾 2 Hence, 𝑸 𝒖 = 𝑸 𝑯

40. Unit Power 𝑷 𝒖
It is defined as the power developed by a turbine, which is working under a unit head (1m). The overall efficiency, 𝜂 𝑜 = 𝑆ℎ𝑎𝑓𝑡 𝑃𝑜𝑤𝑒𝑟 𝑊𝑎𝑡𝑒𝑟 𝑃𝑜𝑤𝑒𝑟 = 𝑃 𝜌𝑔𝑄𝐻 1000 ∴𝑃= 𝜂 𝑜 × 𝜌𝑔𝑄𝐻 1000 ∴𝑃∝𝑄𝐻 𝑎𝑠 𝜌 𝑎𝑛𝑑 𝜂 𝑜 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 But, 𝑄∝ 𝑉 𝑓 ∝ 𝐻 ∴𝑃∝ 𝐻 ×𝐻 ∴𝑃∝ 𝐻 3 2 ∴𝑃= 𝐾 3 𝐻 3 2 From definition of unit power, if 𝐻=1𝑚, 𝑄= 𝑄 𝑢 ∴ 𝑃 𝑢 = 𝐾 3 Hence, 𝑷 𝒖 = 𝑷 𝑯 𝟑 𝟐

41. Use of Unit Quantities 𝑵 𝒖 , 𝑸 𝒖 , 𝑷 𝒖
If a turbine is working under different heads, the behavior of the turbine can be easily known from the values of the unit quantities.
From the definition of unit quantities, we get
𝑁 𝑢 = 𝑁 𝐻 1 = 𝑁 𝐻 2
𝑄 𝑢 = 𝑄 𝐻 1 = 𝑄 𝐻 2
𝑃 𝑢 = 𝑃 1 𝐻 = 𝑃 2 𝐻
Hence, if the speed, discharge and power developed by a turbine under a head are known, then by using above relations the speed, discharge and power developed by the same turbine under a different head can be obtained easily.

42. Example
A turbine develops 9000KW when running at 10 r.p.m. The head on the turbine is 30m. If the head on the turbine is reduced to 18m. Determine the speed and power developed by the turbine.
A turbine develops 500KW power under a head of 100m at 200 r.p.m. What would be its normal speed and output under a head of 81 meters?
A Pelton wheel turbine is revolving at a speed of 190r.p.m. and develops kW when working under a head of 220m with an overall efficiency of 80%. Determine unit speed, unit discharge and unit power. The speed ratio for the turbine is given as Find the speed, discharge and power when this turbine is working under a head of 140m.
A turbine is to operate under a head of 25m at 200r.p.m. The Discharge is 9cumsec. If the efficiency is 90%, determine the performance of the turbine under a head of 20meters.

43. Example (CX)
A Pelton wheel turbine is revolving at a speed of 190r.p.m. and develops kW when working under a head of 220m with an overall efficiency of 80%. Determine unit speed, unit discharge and unit power. The speed ratio for the turbine is given as Find the speed, discharge and power when this turbine is working under a head of 140m.
A turbine is to operate under a head of 25m at 200r.p.m. The Discharge is 9cumsec. If the efficiency is 90%, determine the performance of the turbine under a head of 20meters.
A Pelton wheel is to be designed for a head of 60m when running at 200 r.p.m. The Pelton wheel develops KW shaft power. The velocity of the buckets = 0.45 times the velocity of the jet, overall efficiency = and co-efficient of the velocity is equal to Design of Pelton wheel turbine. [ (1.) Diameter of jet(d) (2.) Diameter of wheel (D) (3.) Width and depth of buckets and number of buckets on the wheel.]
A Pelton Wheel is having a mean bucket dia. Of 1m and is running at 1000r.p.m. The net head on the Pelton wheel is 700m. The discharge nozzle is 0.1m3/s. Find (i) Power available at the nozzle.
Two jet strike the buckets of a Pelton wheel, which is having shaft Power as 15450KW. The diameter of each jet is given as 200mm. If the net head on the turbine is 400m, Find the overall efficiency of the turbine . Take Cv = 1.0

44. (Francis and Kaplan turbine)
Reaction turbine
(Francis and Kaplan turbine)

45. Reaction Turbine Kinetic energy + Pressure energy
Driving Force on the Runner:
Impulse Force: Deviation in the direction of flow
Reactive Force: Change in kinetic and pressure energy
The water through runner is under pressure and the runner is completely enclosed in an air-tight casing.
Casing and the runner is always full of water.

46. Francis turbine A Francis turbine is: Mixed Flow Turbine:
Water enters radially and leaves axially to the direction of rotation of shaft.
Reaction Turbine:
At the inlet of the turbine both kinetic as well as pressure energy is available. It is generally operated under medium head and medium flow rate.
It is designed by an American engineer J. B. Francis in 1849.

47. Components of Francis Turbine
Different components of Francis turbine are:
Penstock
Spiral Casing
Guide Blades
Governing Mechanism
Runner
Draft Tube

48. Main Components of Radial Flow Reaction Turbine
Casing
Guide Mechanism
Runner and
Draft tube

49. Working proportion for Francis turbine
Sr. no
Parameter
Equation
Approximate value 1
Flow ratio (Kf)
0.15 to 0.30 2
Speed ratio (Ku)
0.6 to 0.9 3
Breadth ratio (n)
0.1 to 0.4

50. Total discharge

51. Axial Flow Reaction Turbine
Axial flow type turbine
Used under low head and high discharge conditions
The shaft of the turbine is vertical
The lower end of the shaft is made larger which is known as “Hub” or “Boss”.
Vanes are fixed on the hub

52. Types of Axial Flow Reaction Turbine
Propeller Turbine
When the vanes are fixed to the hub and they are not adjustable, the turbine is known as Propeller turbine.
Kaplan Turbine
If the vanes on the hub are adjustable the turbine is known as a Kaplan turbine.
Work done, efficiency and power developed by Kaplan & Propeller turbine are similar to that of Francis turbine.

53. Components of Kaplan turbine
Main parts of the Kaplan & Propeller turbine are:
Scroll casing
Guide vane mechanism
Hub with vanes or runner
Draft tube

54. Discharge through Runner of Turbine
The discharge through the runner is obtained by,
𝑄= 𝜋 4 𝐷 𝑜 2 − 𝐷 𝑏 2 × 𝑉 𝑓1
Where,
𝐷 𝑜 = Outer diameter of the runner
𝐷 𝑏 = Diameter of the hub
𝑉 𝑓1 = Velocity of flow at inlet

55. Working Proportions of Kaplan and Propeller Turbine
Sr. no
Parameter
Equation 1
Peripheral velocity
𝑢 1 = 𝑢 2 = 𝜋 𝐷 0 𝑁 60 2
Velocity of flow
𝑉 𝑓1 = 𝑉 𝑓2 = 𝐾 𝑓 2𝑔𝐻 3
Area of flow
𝐴 1 = 𝐴 2 = 𝜋 4 𝐷 𝑜 2 − 𝐷 𝑏 2

56. Draft Tube Theory Draft tube is an integral part of reaction turbine.
It is an air tight diverging conduit with cross-sectional area increasing along its length.
One end of this diverging tube is connected to runner exit and the other is located below the level of tail race.
As the pressure of reaction turbine decreases continuously as water passes through the guide vanes and the runner, it does below atmospheric pressure at the outlet of the runner.
Draft tube is used to discharge the water to the tail race by increasing pressure above atmospheric.

57. Draft Tube Theory
𝐻 𝑠 = Vertical height of draft tube above the tail race
𝑦= Distance of bottom of draft tube from tail race

58. Types of draft tubes

59. Function of the draft tube
Increase working head ,output & efficiency
Helps to make easy inspection and maintenance of turbine

60. Example
A Francis turbine of 1 metre runner diameter working under a head of 4.5 metres at a speed of 200 rpm develops 90 Kw when the rate of flow of water is 1.8 m3 /s. If the head on the turbine is increased to 13.5 metres determine the new speed, discharge and power.
A Francis Turbine is proposed to be installed at an available head of 60m and a discharge of 40 m3/s. Determine the number of turbines and power available if the specific speed is 210 and these are to run at 540 rpm with an overall efficiency of 85 %.
A Kaplan Turbine develops KW power at an avg. head of 39m. Assuming a speed ratio of 2, Flow ratio of 0.6, dia. Of the boss equals to 0.35 times the dia. Of the runner and an overall effi. Of 90%. Calculate the dia. , Speed and the specific speed of the turbine.

61. Performance (Characteristic) Curves of Hydraulic Turbines
“Characteristic curves of a hydraulic turbine are the curves, with the help of which the exact behavior and performance of the turbine under different working conditions can be known.”
The important parameters which are varied during a test on a turbine are:
(1) Speed (N), (2) Head (H),
(3) Discharge (Q), (4) Power (P),
(5) overall efficiency (ηo) and (6) Gate opening (i.e. the percentage of the inlet passages provided for water to enter the turbine)
The following are the important characteristic curves for a hydraulic turbine:
Main Characteristic Curves or Constant Head Curves(H & G.O = constant)
Operating Characteristic Curves or Constant Speed Curves (H & N = constant)
Muschel Curves or Constant Efficiency Curves (H & G.O = constant and curve with same efficiencies are joined – ISO EFFICIENCY CURVES )

62. CENTRIFUGAL PUMPS
“The hydraulic machines which convert the mechanical energy into hydraulic energy are called pumps.”
“If the mechanical energy is converted into pressure energy or kinetic energy by means of centrifugal force acting on the fluid, the hydraulic machine is called Centrifugal pump.”
In a pump flow takes place from low pressure side to high pressure side.

63. Classification of Pumps on the basis of mechanical energy transfer

64. Application of centrifugal Pump
Agriculture and irrigation work
Municipal water works and drainage system
Condensate, boiler feed, sump drain and such other services in a steam power plant
Hydraulic control system
Oil pumping

65. Components and Working of a Centrifugal Pump
Main parts of a centrifugal pump (refer Fig. 4.19) are:
Impeller
Casing
Suction pipe
Delivery pipe

66. 1. Impeller A series of backward curved vanes or blades.
mounted on shaft
coupled to external source of energy (electric motor)
it gets mechanical energy and converts kinetic energy & pressure energy.
& then high energized liquid enters into pump casing.

67. 2. Volute casing
It is of spiral type in which area of flow increases gradually. [A(↑)→V(↓)→P(↑)]
It is observed that in case of volute casing, large amount of kinetic energy is lost due to eddy formation and hence lower overall efficiency.
These pumps hence give comparatively low head.

68. 3. Suction Pipe & 4. Delivery Pipe
It carries liquid from the sump to the pump.
Its lower end is dipped into the sump and upper end is connected with the eye of the pump (i.e. inlet of the pump).
A strainer and foot-valve are connected with the lower end.
Strainer keeps the debris away from entering into suction pipe and hence only clear water enters the impeller.
Foot-valve is a kind of non-return valve which does not allow the liquid to go back into sump.
4. Delivery Pipe
A pipe whose one end is connected to the outlet of the pump and other end delivers the water at a required height is known as delivery pipe.

69. Heads of a Centrifugal Pump

70. Heads of a Centrifugal Pump
1. Suction Head or Suction Lift 𝒉 𝒔
It is the vertical height of the center line of the pump shaft above the liquid surface in the sump from which the liquid is being lifted.
2. Delivery Head 𝒉 𝒅
The vertical distance between the center line of the pump shaft and the liquid surface in the tank to which liquid is delivered.
3. Static Head or Static Lift 𝑯 𝒔
The static head is the vertical distance between the liquid surface in the sump and the tank to which the liquid is delivered by the pump.
Thus the static head may be expressed as,
𝐻 𝑠 = ℎ 𝑠 + ℎ 𝑑
Thus static head is the net total vertical height through which the liquid is lifted by the pump.

71. Manometric head
It is defined as the head against which a centrifugal pump has to work.
It is the total head that must be produced by the pump to satisfy the external requirements.
1. Whole of the manometric head is not used to lift the liquid against the static lift; a part of it is used to overcome the losses in the pipes and fittings and to provide the kinetic energy at delivery outlet.
∴ Manometric head = static head + head losses in suction and delivery pipes + velocity head in delivery pipe
∴ 𝐻 𝑚 = ℎ 𝑠 + ℎ 𝑑 + ℎ 𝑓𝑠 + ℎ 𝑓𝑑 + 𝑉 𝑑 2 2𝑔

72. Priming of Centrifugal Pump
Before starting a centrifugal pump, the suction pipe, casing and portion of the delivery pipe up to delivery valve is completely filled with water by external source of water to remove the air from the suction pipe and casing. This is known as priming of a pump.
If the pump is primed with water, the head generated is same meter of water. But as the density of air is very low, the generated head of air is negligible compared to meter of water head. Hence the water may not be sucked from the pump. To avoid this difficulty, priming is necessary.

73. Multi-stage Centrifugal Pump
If a centrifugal pump consists of two or more impellers, the pump is called a multi-stage centrifugal pump.
The impellers may be mounted on the same shaft or different shaft.
A multi-stage pump is having the two important functions:
To produce a high head (Series)
To discharge a large quantity of water(Parallel)

74. Pump in series
When the pumps are connected in series discharge of the first pump enters the second pump where the pressure is further increased. If two pumps are connected final head would be
𝐻 = 𝐻 𝐻 2

75. Pump in parallel
Two or more pumps are used which are so arranged that each of these pumps working separately lifts the liquid from a common collecting pipe through which it is carried to the required height. Since in this Case each of the pump delivers the liquid against the same head, the arrangement is known as pumps in parallel.
𝑄= 𝑄 𝑄 2

76. Efficiencies of a Centrifugal Pump
1. Manometric Efficiency 𝜼 𝒎𝒂𝒏
It is defined as the ratio of the manometric head developed by the pump to the head imparted by the impeller to the liquid.
∴ 𝜂 𝑚𝑎𝑛 = 𝑀𝑎𝑛𝑜𝑚𝑒𝑡𝑟𝑖𝑐 ℎ𝑒𝑎𝑑 𝐻𝑒𝑎𝑑 𝑖𝑚𝑝𝑎𝑟𝑡𝑒𝑑 𝑏𝑦 𝑖𝑚𝑝𝑒𝑙𝑙𝑒𝑟 𝑡𝑜 𝑙𝑖𝑞𝑢𝑖𝑑 = 𝐻 𝑚 𝑉 𝑤2 𝑢 2 𝑔 = 𝑔 𝐻 𝑚 𝑉 𝑤2 𝑢 2
𝑷𝒐𝒘𝒆𝒓 𝒈𝒊𝒗𝒆𝒏 𝒕𝒐 𝒘𝒂𝒕𝒆𝒓 𝒂𝒕 𝒐𝒖𝒕𝒍𝒆𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒑𝒖𝒎𝒑= 𝑾 𝑯 𝒎 𝟏𝟎𝟎𝟎 = 𝝆𝒈𝑸 𝑯 𝒎 𝟏𝟎𝟎𝟎 𝒌𝑾   
𝑷𝒐𝒘𝒆𝒓 𝒂𝒕 𝒕𝒉𝒆 𝒊𝒎𝒑𝒆𝒍𝒍𝒆𝒓= 𝑾𝑫 𝒃𝒚 𝒕𝒉𝒆 𝒊𝒎𝒑𝒆𝒍𝒍𝒆𝒓 𝒑𝒆𝒓 𝒔𝒆𝒄 𝟏𝟎𝟎𝟎
= 𝝆𝑸 𝑽 𝒘𝟐 𝒖 𝟐 𝟏𝟎𝟎𝟎 𝒌𝑾

77. Efficiencies of a Centrifugal Pump
2. Mechanical Efficiency 𝜼 𝒎 It is defined as the ratio of the power actually delivered by the impeller to the power at the shaft of the centrifugal pump. ∴ 𝜂 𝑚 = 𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑖𝑚𝑝𝑒𝑙𝑙𝑒𝑟 𝑃𝑜𝑤𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑠ℎ𝑎𝑓𝑡 = 𝑚 𝑉 𝑤2 𝑢 𝑆.𝑃.𝑖𝑛 𝑘𝑊 3. Overall Efficiency 𝜼 𝒐 It is defined as the ratio of power output of the pump to the power input to the pump. 𝑃𝑜𝑤𝑒𝑟 𝑜𝑢𝑡𝑝𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑢𝑚𝑝= 𝑊𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑙𝑖𝑓𝑡𝑒𝑑 × 𝐻 𝑚 1000 = 𝑊 𝐻 𝑚 1000 𝑘𝑊 𝑃𝑜𝑤𝑒𝑟 𝑖𝑛𝑝𝑢𝑡 𝑡𝑜 𝑡ℎ𝑒 𝑝𝑢𝑚𝑝=𝑃𝑜𝑤𝑒𝑟 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑚𝑜𝑡𝑜𝑟 =𝑆ℎ𝑎𝑓𝑡 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑢𝑚𝑝 ∴ 𝜂 𝑜 = 𝑊 𝐻 𝑚 1000 𝑆.𝑃. ∴ 𝜂 𝑜 = 𝜂 𝑚𝑎𝑛 × 𝜂 𝑚

78. Specific Speed
“The specific speed of a centrifugal pump is defined as the speed of a geometrically similar pump which delivers unit quantity against a unit head.”
It is used to compare the performance of different pumps.
For a centrifugal pump,
𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒, 𝑄=𝐴𝑟𝑒𝑎×𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑓𝑙𝑜𝑤
∴𝑄=𝜋𝐷𝐵× 𝑉 𝑓
∴𝑄∝𝐷𝐵 𝑉 𝑓
We know that,
𝐵∝𝐷
∴𝑄∝ 𝐷 2 𝑉 𝑓
Tangential velocity is given by,
𝑢= 𝜋𝐷𝑁 60 ∝𝐷𝑁

79. Specific Speed
Now tangential velocity 𝑢 and velocity of flow 𝑉 𝑓 are related to the manometric head 𝐻 𝑚 as,
𝑢∝ 𝑉 𝑓 ∝ 𝐻 𝑚
Substituting value of 𝑢 in equation ,we get,
𝐻 𝑚 ∝𝐷𝑁
∴𝐷∝ 𝐻 𝑚 𝑁
Substituting value of D in equation , we get,
𝑄∝ 𝐻 𝑚 𝑁 2 𝑉 𝑓
∴𝑄∝ 𝐻 𝑚 𝑁 𝐻 𝑚
∴𝑄∝ 𝐻 𝑚 3/2 𝑁 2
∴𝑄=𝐾 𝐻 𝑚 3/2 𝑁 2
Where, K = Constant of proportionality.

80. Specific Speed Model testing of Centrifugal Pumps:-
By definition, if 𝐻=1𝑚 and 𝑄=1 𝑚 3 𝑠𝑒𝑐 , 𝑁 becomes 𝑁 𝑠
Substituting these values in equation , we get,
1=𝐾× 1 𝑁 𝑠 2
∴𝐾= 𝑁 𝑠 2
Substituting value of 𝐾 in equation , we get,
𝑄= 𝑁 𝑠 2 𝐻 𝑚 3/2 𝑁 2
∴𝑁 𝑠 2 = 𝑄 𝑁 2 𝐻 𝑚 3/2
∴ 𝑵 𝒔 = 𝑵 𝑸 𝑯 𝒎 𝟑/𝟒
Model testing of Centrifugal Pumps:-

81. Examples:-
A Single Stage Centrifugal Pump with impeller diameter of 30cm rotates at r.p.m. and lifts 3m3 of water per second to a height of 30m with an efficiency of 75%. Find the number of stages and diameter of each impeller of a similar multistage pump to lift 5m3 of water per second to a height of 200meters when rotating at 1500 r.p.m.
Find the number of pumps required to take water from a deep well under a total head of 89m. All the pumps are identical and are running at 800 r.p.m. The specific speed pump is given as 25 while the rated capacity of each pump is 0.16 m3/s.
Two geometrically similar pumps are running at the same speed of r.p.m. One pump has an impeller diameter of 0.30 meter and lifts water at the rate of 20 litres per second against a head of 15 meters. Determine the head and impeller diameter of the other pump to deliver half the discharge.

82. Cavitation of Pump & Turbine
Cavitation is defined as the phenomenon of formation of vapor bubbles of a flowing liquid in a region where the pressure of the liquid falls below its vapor pressure and the sudden collapsing of these vapor bubbles in a region of higher pressure.
bubble collapse - high pressure created - cause pitting action on the surface.
Thus cavities are formed on the metallic surface and also considerable noise and vibrations are produced.
Cavitation includes formation of vapor bubbles of the flowing liquid and collapsing of the vapor bubbles.

83. Precaution against Cavitation: The following precautions should be taken against Cavitation:
The pressure of the flowing liquid should not be allowed to fall below its vapor pressure.
The special materials or coatings such as aluminum-bronze and stainless steel, which are cavitation resistant materials, should be used.
Effects of Cavitation: The following are the effects of cavitation:
The metallic surfaces are damaged and cavities are formed on the surfaces.
Due to sudden collapse of vapor bubble, considerable noise and vibrations are produced.
The efficiency of a turbine decreases due to cavitation.

84. Cavitation in Turbines
In turbines, only reaction turbines are subjected to cavitation.
In reaction turbines, the cavitation may occur at the outlet of the runner or at the inlet of the draft tube, where the pressure is considerably reduced
Due to cavitation, the metal of the runner vanes and draft tube is gradually eaten away, which results in lowering the efficiency of the turbine.
Hence the cavitation in a reaction turbine can be noted by a sudden drop in efficiency.
In order to determine whether cavitation will occur in any portion of a reaction turbine, the critical value of Thoma’s cavitation factor 𝜎 is calculated
𝜎= 𝐻 𝑏 − 𝐻 𝑠 𝐻 𝑛𝑒𝑡 = 𝐻 𝑎𝑡𝑚 − 𝐻 𝑣 − 𝐻 𝑠 𝐻 𝑛𝑒𝑡

85. Cavitation in Centrifugal Pumps
In centrifugal pumps the cavitation may occur at the inlet of the impeller of the pump, or at the suction side of the pumps, where the pressure is considerably reduced.
Hence if the pressure at the suction side of the pump drops below the vapor pressure of the liquid then the cavitation may occur.
The critical value of Thoma’s cavitation factor 𝜎 is calculated .
𝜎= 𝐻 𝑏 − 𝐻 𝑠 − ℎ 𝑓𝑠 𝐻 𝑛𝑒𝑡 = 𝐻 𝑎𝑡𝑚 − 𝐻 𝑣 − 𝐻 𝑠 − ℎ 𝑓𝑠 𝐻 𝑛𝑒𝑡
If the value of Thoma’s cavitation factor 𝜎 is greater than critical cavitation factor 𝜎 𝑐 , the cavitation will not occur in that turbine or pump. The critical cavitation factor 𝜎 𝑐 may be obtained from tables or empirical relationships.

86. Ventilation System
Ventilation is meant for supply of fresh air, and to replace the old hot Used up (exhausted) air.
The ventilation ensures the removal of bad effects of occupancy of an enclosed space:
By providing necessary oxygen to remove oxygen deficit caused by respiration;
By removing and diluting C02 in the air;
By lowering down the temperature by removing hot used up air and replacing it by colder fresh air;
By reducing humidity
By reducing body odours.

87. Requirements of ventilation system
A good ventilation system should generally fulfill the following requirements:
It should admit sufficient quantity of fresh air, and remove the requisite used up or vitiated air.
Admitted air should be properly controlled with respect to its quantity as well as velocity of movement.
The system should be capable of changing the old air thoroughly, without leaving any stagnant pockets in the room.
Should avoid draughts, for which maximum permissible velocity of admitted air should not exceed 15 m/min. i.e m/sec.
The system should admit clean and humid air.
The system should also be capable of controlling the temperature of admitted air.

88. Types 1) Natural ventilation: 2) Artificial or mechanical ventilation:
Natural ventilation is based upon providing suitable openings in a room, at lower levels for admitting free atmospheric air, and also at upper levels for removing the warmer and lighter used-up air. Doors and windows near the floor level, thus admit fresh air and ventilators near the ceiling, take out the vitiated air from a room.
2) Artificial or mechanical ventilation:
The artificial ventilation system can be broadly divided in to:
The extraction or vacuum system
The propulsion or plenum system
The air conditioning system

89. Characteristic Curves of Hydraulic Pumps
Characteristic curves of centrifugal pumps are defined those curves which are plotted from the results of a number of tests on the centrifugal pump. These curves are necessary to predict the behavior and performance of the pump when the pump is working under different flow rate, head and speed.
The followings are the important characteristic curves for pumps:
Main Characteristic Curves,
Operating Characteristic Curves and
Constant Efficiency or Muschel Curves.