Basics of Hydraulic Machines

Hydraulic Machines :- Branch of Engineering science which deals with the machines run by water under some head or raising the water to higher level.


 Force exerted by a jet of water impinging normally on fixed plate,

 Fx = waV2/g (In Newton)

Where, w = Specific weight of water

a = Cross-sectional area of jet

V = Velocity of jet

 Force exerted by jet of water impinging normally on fixed plate inclined at an angle θ,

 FN = waV2/g x sin θ

 Force exerted by jet in direction of flow

 Fx = FN sin θ

 Force exerted by jet in direction normal to the flow

 Fy = FN cos θ

 When curved fixed plate is used, Force jet of water along normal to the plate,

 F = (waV2/g) (cos α + cos β)


 The hydraulic turbines are also known as Water Turbines.

 A hydraulic turbine is a machine which converts the hydraulic energy into mechanical energy.

 Two Types of Turbine:-

1. Impulse Turbine

2. Reaction Turbine

 Impulse Turbine (I.T)

 Total Energy at the inlet of a turbine is only Kinetic Energy.

 The pressure of water both at entering and leaving the vanes is Atmospheric.

 Used for High Head of Water.

 Breaking jet in an I.T is used to bring the runner to rest in short time.

 Hydraulic Efficiency = Work done on the wheel/The energy of the jet

Hydraulic Efficiency of I.T is Maximum when the velocity of wheel is one-half the velocity of jet of water at inlet.

 Maximum Hydraulic Efficiency

Ƞ max = 1+cos∅2 Where, ∅ = Angle of blade tip at outlet

 Mechanical Efficiency = Actual work available at the turbine/Energy imparted to the wheel

 Overall Efficiency = Actual power produced by turbine/Energy actually supplied to by turbine

 Pelton Wheel I.T.

 Pelton Wheel is Tangential flow Impulse turbine.

 Width of Bucket for Pelton wheel = 5 times the diameter of jet.

 Depth of Bucket for Pelton wheel = 1.2 times the diameter of jet.

 Number of Bucket on periphery of Pelton Wheel is given by D2d+ 15

 Jet ratio = Diameter of pelton wheel/Diameter of jet = Dd

 Maximum number of jets employed on Pelton wheel = 6.

 Reaction Turbine (R.T)

 In R.T, water enters the wheel under pressure and flow over the vanes.

 Function of Guide vanes in R.T,

 Allow water to enter the runner without shock.

 Allow water to flow over them without forming eddies.

 Allow the required quantity of water to enter the turbine.

 Hydraulic Efficiency = Work done on the wheel Energy actually supplied to the turbine

 Overall Efficiency = Power produced by the turbine/Energy actually supplied by turbine

 Kaplan Turbine = Axial Flow R.T.

 In Axial flow R.T., water flows parallel to the axis of wheel.

 Number of Blade in Kaplan Turbine Runner = 4 to 8.

 Francis Turbine = Outward Flow R.T.

 In Outward flow R.T., water enters at the centre of the wheel and then flows towards the other periphery of the wheel.

 Number of Blade in Francis Turbine Runner = 16 to 24.

 Flow Ratio for Francis Turbine = Velocity of flow at inlet/Theoretical jet velocity = 0.15 to 3.

 In Inward flow R.T., water enters the wheel at the outer periphery and then flows towards the centre of the wheel.


 Draft tube is a pipe of gradually increasing area used for discharging water from the exit of reaction turbines.

 Draft tube in R.T., To increase the head of water by an amount equal to the height of the runner outlet above the tail race.

 Integral part of Mixed and Axial Turbines.

 Because of Draft tube, it is possible to have the pressure at runner outlet much below the atmospheric.

 Efficiency of Draft Tube = Net gain in pressure head Velocity head at entrance of draft tube


 The speed of an imaginary turbine, identical with the given turbine, which develops unit power under unit head.

 Ns = (N √P)/(H5/4 )

 Play important role in Selection of Type of Turbine.

 By knowing specific speed, Performance of turbine can also be predicted.

 Low Specific Speed of Turbine = Impulse Turbine

 High Specific Speed of Turbine = Propeller Turbine


 Speed of the turbine operating under one metre head.

 Nu = N /√H


 Discharge through a turbine when the head on the turbine is unity.

 Qu = Q/√ H


 Power developed by turbine when the head on turbine is unity.

 Pu = P/H3/2


 The formation, growth and collapse of vapour filled cavities or bubbles in a flowing liquid due to local fall in fluid pressure are called Cavitation.

 Cavitation in hydraulic machines mainly due to low pressure.

 It affects in hydraulic machine,

 Causes noise and vibration of various parts.

 Makes surface rough.

 Reduce the discharge of turbine.

 Causes sudden drop in power output and efficiency.

 Cavitation in R.T. can be avoided

 By installing the turbine below the tail race level.

 By using stainless steel runner of the turbine.

 By providing highly polished blades to the runner.

 By running the turbine runner to the designed speed.

 To Avoid Cavitation in centrifugal pump, the suction pressure should be High.


 A machine which converts the kinetic energy of the water into pressure energy before the water leaves its casing.

 Liquid enter the centrifugal pump at centre.

 The flow of water leaving the impeller is free water.

 Impeller of pump may have Volute casing, Vortex casing & Volute casing with guide vanes.

 For C.P. impeller, Maximum value of vane exit angle = 20° to 25°.

 In C.P., Regulating valve is provided on the delivery pipe.

 Foot valve is provided in C.P.

 Manometric Head is actual head of water against which a centrifugal pump has to work.

 Manometric Head = Work done per kg of water – Losses within the impeller = Energy per kg at outlet of impeller – Energy per kg at inlet of impeller.

 Discharge of centrifugal pump

Q = π D b Vf

Where, D = Diameter of impeller at inlet

b = Width of impeller at inlet

Vf = Velocity of flow at inlet

 Power required to drive C.P

P = ω Q Hmo

Where, ω = Specific speed of water

Q = Discharge of the pump

Hm = Manometric head in m

ƞo = Overall efficiency of the pump

 C.P. takes too much power due to air in water.

 Manometric Efficiency = Manometric Head/Energy supplied by the impeller

Mechanical Efficiency = Energy supplied to the pump at the impeller/Energy supplied to the pump by prime mover

 Overall Efficiency = Energy supplied to the pump/Energy available at the impeller

 Efficiency of C.P. will be Maximum, when the blades are bent backward.


Pumps are those which have two or more identical impellers mounted on the same shaft or on different shafts.

 Used produce high heads or to discharge a large quantity of liquid.

 To obtain high head, Number of impeller are mounted in series.

 To obtain discharge a large quantity of liquid, the impellers are connected in parallel.


 The speed of an imaginary pump identical with the given pump which will discharge 1

litre of water, while it is being raised through head of one metre.

 Ns = N √Q/H3/4m

 Low specific speed of pump = Centrifugal Pump.

Type of Pump Specific Speed(r.p.m.)
Slow speed with radial flow at outlet 10-30
Medium speed with radial flow at outlet 30-50
High speed with radial flow at outlet 50-80
High speed with mixed flow at outlet 80-160
High speed with axial flow at outlet 160-500

 Difference between net inlet head and head corresponding to the vapour pressure of the liquid.

 It may be noted that when the pressure at the suction falls below the vapour pressure of the liquid, then cavitation will be formed.


 Ratio of all the corresponding linear dimensions of the model and the prototype

are equal, then they are said Geometric Similarity.

 In other word, If Model & Prototype are identical in shape but differ only in size.

 Ratio of corresponding velocities at corresponding points is equal, and then the model and prototype are Kinematic Similarity.

 Ratio of corresponding forces acting at corresponding points is equal then the model & prototype are said to have Dynamic Similarity.


 Known as Positive Displacement Pump.

 It discharges a definite quantity of liquid during the displacement of its piston or plunger which executes a reciprocating motion in a closely fitting cylinder.

 Best suited for Less Discharge, High Heads & High Pressure.

 Discharge through Reciprocating Pump

Q = LAN/60 for single acting.

Q = 2LAN/60 for double acting.

Where, L = Length of stroke in m.

A = Cross-sectional area of the piston in m2

N = Speed of the crank in r.p.m.

 Power required to drive Reciprocating Pump

P = wQ (Hs + Hd) (Both for single & double acting)

 Difference between the theoretical discharge and the actual discharge is called Slip of the pump.

 Slip of R.P is Negative, when suction pipe is long and delivery pipe is short and pump is running at high speed.


 Air vessels in R.P is cast iron closed chamber having an opening at its base.

 It fitted to the suction pipe and delivery pipe close to the cylinder of the pump.

 Used to get continuous supply of liquid at a uniform rate & to save the power required to drive the pump.

 Because of this in R.P, Acceleration & Friction heads are reduced.

 Because of this in R.P, the saving of work & power is about 84.8% in single acting R.P & 39.2% in double acting R.P.


 Device used to lift larger load by the application of comparatively much smaller force.

 Based on Pascal’s Law.

 Efficiency = Ƞ = WP ×aA


 Device used to lift small quantity of water to a greater height when a large quantity of water is available at smaller height.

 Work on principle of water hammer.


Device used to store pressure energy which may be supplied to hydraulic machines such as presses, lifts and cranes.


Device used to increase the intensity of pressure of water by means of energy available from a large quantity of water at low pressure.


Device used to lift heavy loads.

Widely used in docks for loading and unloading ships, ware houses and heavy industries.


Device used for carrying persons and loads from one floor to another in multi-storeyed building.


 Device used for transmitting increased or decreased torque to the driven shaft.

Hydraulic Coupling is Energy Transfer Machines.

 Normal force of jet of water on plate inclined at an angle of 30°Normal force of jet of water on plate normal to jet = 12


 Principle of jet propulsion is used in driving the ships and aeroplanes.

 Efficiency of jet propulsion for ship with inlet orifices at right angles to the direction of motion of ship will be maximum, When Relative velocity of the jet and ship is equal to 2 x the velocity of ship.

 Maximum efficiency if jet propulsion of the ship with inlet orifices at right angles to the direction of ship is 50%.

Undershot water wheels are those in which the wheel runs entirely by the impulse of water.

 Breast water wheels are those in which the wheel runs partly by the weight of water and partly by the impulse of water.

 Overshot water wheels are those in which the wheel runs entirely by the weight of water.

 Runway speed of turbine:- The speed at which the turbine will run freely without load.

Turbine Specific Speed Head of water
Francis 60 to 300 r.p.m 25 to 250 m
Kaplan 300 to 1000 r.p.m 0 to 25 m

Pump used to pump highly viscous fluid = Screw Pump.

 Jet Pump is used to lifting water to the boilers & turbines.

 Air lift pump is used to lifting water from deep wells.