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### Velocity Diagrams For Simple and Multistage Turbines

The simple impulse (DE LAVAL) turbine:

• The first commercial steam turbine is the De Laval impulse turbine, which in its elementary form consists of one ring of moving blades, mounted around the periphery of a wheel. The velocity of steam is increased by passing the steam through a group of nozzle placed partially around the periphery of the wheel where expansion takes place from boiler pressure down to exhaust pressure.
•  The high velocity steam when allowed to impinge on the moving blades exerts a force on the blades and produces shaft work. Since the primary force on the blades is due to the high velocity steam jet, this type of turbine is classified as an impulse turbine. The pressure and velocity variation of steam during its flow through the nozzle and the turbine are also indicated in the figure.
Velocity diagram

• The adiabatic flow of fluid through the blades of a turbine is governed by the bladesof a turbine is governed by the continuity, energy and momentum equations.  Theyare , respectively ,

• The momentum equation is particularly important in determining the net force on the moving blades due to a change in fluid velocity. It is to be noted that since velocity is a vector quantity having magnitude as well as direction, the change in fluid velocity must be determined vectorally.
• For the construction of vector diagrams the following notations are followed in this text
V= Absolute velocity of fluid
Vr= Relative velocity of fluid
Vw= Whirl velocity
Va= Axial velocity of flow
u = Velocity of the moving blades.

• The suffix ‘1’ or ‘2’ denotes the corresponding quantity at inlet or outlet as the case may be. The velocity diagrams are constructed by setting off absolute vectors from a selected origin. The velocity diagrams at inlet and exit of the moving blades are shown in figure.
• The jet of steam strikes the moving blade with an absolute velocity of V1 at an angle of a1 to the tangent, a1 being termed as the nozzle angle, the tangential component Vw1 at inlet does work on the moving blades as it is the same direction of motion.
• The axial component Va1 is perpendicular to the direction of motion and hence, does no work on the blades. But the velocity of flow causes steam to flow through the turbine axially and due to this component there will be axial thrust on the rotor.
• Since the blade is moving with a velocity of u, the stream jet reaches the blade with a relative velocity of Vr1 and is obtained by vectorial subtraction, as shown. The angle between the relative velocity and the tangent is b1, the entrance angle of moving blade required for shockless flow of steam.

• The jet leaves the moving blades with a relative velocity of Vr2 whose direction for
shockless exit, is at an angle b2 to the tangent. The absolute velocity V2 of the stream
with the relative velocity Vr2. a2 is the angle between the absolute velocity V2 and
the tangent.

• The tangential component of V2 is Vw2, which is the whirl velocity at exit of the moving blade. Since the blade velocity u is common for both, it is usual to combine the entrance and exit velocity triangles on this common base and figure shows this.