USEFUL EQUATION FOR TURBINE

USEFUL EQUATIONS FOR TURBINEIMPULSE TURBINE

It consists of one or more stationary inlet nozzles (Spear nozzles), a runner, and a casing. The runner has multiple buckets mounted on a rotating wheel. The pressure head upstream of the nozzle is converted into kinetic energy contained in the water jet leaving the nozzle. As the jet strikes the rotating bucket, the kinetic energy is converted into a rotating torque.

a) Torque delivered to the wheel by the liquid jet

(1)

Where Q is the discharge from all the jets and and friction is neglected.

b) The jet velocity V1

(2)

The velocity coefficient accounts for the nozzle losses.

c) Power delivered by the fluid to the turbine runner

(3)

d) Condition for Maximum Power

(4)

e) Turbine Efficiency

(5)

REACTION TURBINE

For Velocity triangle at inlet

= Runner vane velocity OR Tangential velocity of Runner OR vane peripheral velocity at inlet

= Absolute velocity of water (leaving the guide vane) at inlet

= Velocity of water relative to runner vane (Relative velocity of water) at inlet

= Guide vane angle

= Tangential component of the absolute velocity at inlet OR Velocity of whirl at inlet OR Swirl at inlet

= Runner vane angle at inlet (Vane angle at inlet)

= Velocity of flow (flow velocity) at inlet OR Radial velocity at inlet

For velocity triangle at outlet

= Runner vane velocity OR Tangential velocity of Runner OR vane peripheral velocity at outlet

= Absolute velocity of water at outlet

= Velocity of water relative to runner vane (Relative velocity of water) at outlet

= Tangential component of the absolute velocity at outlet OR Velocity of whirl at outlet OR Swirl at outlet

= Runner vane angle at outlet (Vane angle at outlet)

= Velocity of flow (flow velocity) at outlet OR Radial velocity at outlet

i) Discharge

(6)

ii) Theoretical torque delivered to the shaft

(7)

iii) Power delivered to the shaft

(8)iv) Power input to the turbine (Water Power)

(9)

where HT is the actual head drop across the turbine.

v) Overall Turbine Efficiency

(10)

vi) Guide vane angle

(11)

AXIAL FLOW TURBINE

(12)

At maximum efficiency and V2 = Vf, it follows that the energy transferred by the fluid to the turbine per unit weight of the fluid

In which . Since E should be the same at the blade tip and at the hub, but U is grater at the tip, it follows that must be reduced. Similarly, the velocity of flow Vf should remain constant along the blade and, therefore, must be reduced towards the tip of the blade. Thus, has to be reduced and, consequently, the blade must be twisted so that it makes a greater angle with the axix at the tip than it does at the hub.GENERAL RELATIONSHIPSvii) Net Positive Suction Head

(13)

viii) Thoma Cavitation Number

(14)

ix) Flow Rate Coefficient

(15)

x) Power Coefficient

(16)xi) Head Coefficient

(17)

xii) NPSH Coefficient

(18)

xiii) Similarity Rules

POWER:

(19)

HEAD:

(20)

DISCHARGE:

(21)

xiv) SPECIFIC SPEED (Turbine)

(22)xv) SPEED FACTOR

CLASSIFICATION OF PUMPS AND TURBINES

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