FLUID MACHINES

TURBINE

Turbine is a prime mover to subtract energy

from fluid. Energy from water will be changed to

mechanical energy. Turbines are subdivided into

impulse and reaction machines.

In impulse turbines, the total head available

is first converted into the kinetic energy. The

fluid energy which is reduced on passing through

the runner in entirely kinetic, it follows that the

absolute velocity at outlet is smaller than the

absolute velocity at inlet (jet velocity). The fluid

pressure is atmospheric throughout and the

velocity is constant except for a slight reduction

due to friction.

Example : Pelton wheel

Part four : Reaction Turbine – Francis Turbine 1

FLUID MACHINES

In the reaction turbines, the fluid passes

first through a ring of stationary guide vanes in

which only part of the available total head is

converted into kinetic energy. The guide vanes

discharge directly into the runner along the

whole of its periphery, so that the fluid entering

the runner has pressure energy as well as

kinetic energy. The pressure energy is converted

into kinetic energy in the runner. Therefore, the

relative velocity is not constant but increases

through the runner. There is, therefore, a

pressure difference across the runner.

Example : Francis turbine

Part four : Reaction Turbine – Francis Turbine 2

FLUID MACHINES

FRANCIS TURBINE Main parts :

1. spiral

2. guide vanes

3. runner / impeller

4. draft tube

Part four : Reaction Turbine – Francis Turbine 3

FLUID MACHINES

Net head :

iii

input Zg

Vg

PHH ++==2

2

ρ

Part four : Reaction Turbine – Francis Turbine 4

FLUID MACHINES

Velocity triangle :

Part four : Reaction Turbine – Francis Turbine 5

FLUID MACHINES

Part four : Reaction Turbine – Francis Turbine 6

FLUID MACHINES

Euler’s head :

gUVH w

E11=

Hydraulic efficiency :

gHUVUV ww

h2211 −

=η

Mechanical efficiency :

( )[ ]22111 UVUVgQ

P

wwg

omech −

=ρ

η

Overall efficiency :

gQHPo

o ρη =

Part four : Reaction Turbine – Francis Turbine 7

FLUID MACHINES

PELTON WHEEL Main parts :

1. jet nozzle

2. runner / impeller

3. bucket

Part four : Impulse Turbine – Pelton Wheel 1

FLUID MACHINES

Velocity triangle :

at inlet :

111 UVVr −= and 11 VVw =

at outlet :

12 rr VkV ⋅=

)180cos(122 θ−⋅−= rw VkUV

Power : )]180cos(1)[( 1 θρ −+−= kUVQUP

Part four : Impulse Turbine – Pelton Wheel 2

FLUID MACHINES

EFFICIENCY OF PELTON WHEEL

1. hydraulic efficiency

21

1 )]180cos(1)[(2V

kUVUh

θη −+−=

velocity at maximum hydraulic efficiency :

21VU =

Part four : Impulse Turbine – Pelton Wheel 3

FLUID MACHINES

maximum hydraulic efficiency :

2)180cos(1 θη −+

=k

h

power at max hydraulic efficiency :

)]180cos(1[4

21

max θρ −+⎟⎟⎠

⎞⎜⎜⎝

⎛= k

VQP

Part four : Impulse Turbine – Pelton Wheel 4

FLUID MACHINES

2. mechanical efficiency

)]180cos(1)[( 1 θρη

−+−=

kUVQUP

mech

3. volumetric efficiency

QQa

v =η

4. overall efficiency

gQHP

o ρη =

Part four : Impulse Turbine – Pelton Wheel 5

FLUID MACHINES

Hydraulic efficiency :

gHUVUV ww

h2211 −

=η

Mechanical efficiency :

( )[ ]22111 UVUVgQ

P

wwg

omech −

=ρ

η

Overall efficiency :

gQHPo

o ρη =

Part four : Impulse Turbine – Pelton Wheel 6