# turbines numericals

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• 8/10/2019 Turbines Numericals

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1 PELTON TURBINE VELOCITY TRIANGLES

A 137 mm diameter jet of water issuing from a nozzle impinges on

the buckets of a Pelton turbine, and is deflected through an angle of

165 0 by the buckets. Head available at the nozzle is 400 m.

Assume: C v = 0.97, speed ratio = 0.46; reduction in relative velocity

= 15 . Determine

a) Force developed by the jet on the runner

b) Power developed

c) Hydraulic efficiency of the turbine

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2 PELTON TURBINE VELOCITY TRIANGLES

A Pelton Turbine works under a gross head of 400 m. The jet

diameter is 80 mm and the penstock diameter is 0.6m with length

of 4 km. The buckets deflects the jet through 165 and reduces

the relative velocity by 15 . Assume mechanical efficiency of 90 ,

determine:

a) Flow rate

b) Shaft power developed by the pump

c) Overall efficiency

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PELTON TURBINE DESIGN

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3 PELTON TURBINE DESIGN

A Pelton Turbine is required to drive a generator to develop 10 MW

of power. Available head at the nozzle is 760 m. Assume electricgeneration efficiency of 95 and Pelton wheel efficiency of 87 .

The jet after striking the blades, deflects by 165 0 with a 15 loss

in velocity due to blade friction. Assume C v = 0.97 and K u = 0.46.

Determine:

a) Flow through Nozzle

b) Diameter of the jet

c) Force exerted by Jet on the bucketd) Best synchronous speed for generation at 50 Hz;

Corresponding bucket diameter (Jet ratio = 10)

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4 PELTON TURBINE DESIGN

Design a Pelton Turbine for the following specifications:

SHP = 9560 kWHead = 350 m

Speed = 750 rpm

Overall Efficiency = 85

Jet ratio (m) = 1/6

Cv = 0.985

Ku = 0.45

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5 FRANCIS TURBINE VELOCITY TRIANGLES

Francis Turbine Inward Flow Reaction Turbine

An inward flow reaction turbine has external and internal diametersas 0.9 and 0.45 m. Turbine is running at 200 rpm, width of the

turbine at inlet is 200 mm. Velocity of flow through the runner is

constant, and is 1.8 m/s. Guide blades makes an angle of 10 0 at

the inlet, and discharge at the outlet of the turbine is radial. Find:

a) Components of velocity triangle at inlet and outlet

b) Power developed by the runner

c) Hydraulic efficiency

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6 FRANCIS TURBINE DESIGN

Francis Turbine Inward Flow Reaction Turbine

Design a Francis Turbine for following specifications:Net head = 60 m

Speed = 700 rpm

Shaft Power = 294.3 kW

Overall Eff. = 84 ; Hyd. Efficiency = 93

Flow ratio = 0.2

Outlet Dia = 0.5 Inlet diaVane thickness = 5 of runner circumference

Velocity of flow at inlet and out are the same

Discharge is radial at the outlet

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GEOMETRICALLY SIMILAR TURBINES

Specific Speed of a Turbine The speed of a turbine which is

identical in shape geometric dimension blade angle gateopening etc. but of such a size that it develops unit power when

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FOR THE SAME TURBINE DIFFERENT CONDITIONS

Unit Speed (N u) = /

Unit Discharge (Q u) = /

Unit Power (P u) = /

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7 UNIT QUANTITIES

A Turbine is to operate under a head of 25 m at 200 rpm. The

discharge is 9 cumecs. If the overall efficiency is 90 , determine

the performance of the turbine under a head of 20 m.

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8 DRAFT TUBE

In a Francis turbine ,the velocity at the entrance and exit of the

draft tube are 6 m/s and 1.2 m/s. For a friction loss of 0.1 m,

and a tail water of 5 m below the entrance of the draft tube,

determine the pressure at inlet of the draft tube.