Turbines are hydraulic machines which convert hydraulic energy into mechanical energy.
Efficiency to Turbines
Hydraulic efficiency (hh)
Classification of Turbines on the basis of energy at inlet
Ex. : Pelton Wheel, Gurard Turbine, Banki Turbine, Jonval Turbine, Turgo Impulse Wheel.
Ex. : Francis Turbine, Propeller Turbine, Kaplan Turbine, Thomson Turbine, Furneyron Turbine.
Classification of Turbines on the basis of type of flow within turbine
Ex. : Pelton Wheel, Turgo Impulse Wheel.
Ex. : Inward-radial flow turbines are Francis turbine, Thomson Turbine, Guard Turbine. Outwardradial
flow turbine is Fourneyron turbine
Ex. : Jonval Turbine, Propeller Turbine, Kaplan Turbine
Ex. : Modern Francis Turbine
|Turbine||Specific Speed (MKS Unit)|
|Pelton Turbine||10 to 35|
|Francis Turbine||60 to 300|
|Kaplan & Propeller Turbine||300 to 1000|
|Pelton Turbine||above 250 m|
|Francis Turbine||60 m to 250 m|
|Kaplan & Propeller Turbine||Below 60 m|
V1 = Velocity of jet coming out of nozzle
u1 = u2 = u = tangential velocity of vane
k = Bucket friction coefficient
(i) Nozzle efficiency
(ii) Hydraulic efficiency
(iii) Mechanical efficiency
(iv) Overall efficiency
ho = hN × hh × hmech
Cv = coeff of velocity = 0.97 – 0.99
Ku = 0.43 – 0.47
A jet ratio of 12 is normally adopted
=18 to 25
This formula is called Tygun formula.
Purpose of draft tube
(i) Permits the negative suction head to establish at the runner exit
(ii) It acts as a recuperator of pressure energy.
The angle of straight divergent type draft tube should not be more than 8° otherwise eddies will be formed
& efficiency will be reduced.
i.e., work done per sec (Q/g)Vw1u1
V w1 & Vw2 are whirl velocities at inlet and outlet
u1 & u2 are peripheral velocities of blades at inlet and outlet.
= 0.15 0.30
Q = pD1 B1 Vf1
= pD2 B2 Vf2
B1, B2 are width of inlet & outlet
D1, D2 are diameter at inlet & outlet
Vf1 ,Vf2 are velocities of flow at inlet & outlet
= 0.35 to 0.61
u1= u2 =
Do = outer diameter of runner
Db = inner diameter or diameter of boss or hub
For a turbine working under maximum head & full gate opening, if the external load suddenly drops to almost
zero value and at the same time, governing mechanism fail, turbine runner will tend to race up and attains
maximum possible speed. This limiting speed of turbine is known as runaway speed.
For Pelton Turbine, Runaway speed is 1.8-1.9 times of normal speed.
For Francis Turbine, Runaway speed is 2-2.2 times of normal speed
For Kaplan Turbine, Runaway speed is 2.5-3 times of normal speed
The concept of unit quantities is required to
(i) predict the behaviour of turbines working under different conditions.
(ii) make comparison between the same type but different size of turbines.
(iii) co-relation and use of experimental data.
Note that specific speed is not a dimensions parameter, its unit is [M1/2L–1/4T–5/2]
S = 9.6 × 10–4Ns
Q μ N........1st Fan law
= is called flow coefficient.or capacites co-efficient
H μ N2........2nd Fanlaw
= is called head coefficient.
P μ N3........3rd Fan law
= is called power coefficient.
Note : Similarity of model and prototype turbines are based on the assumption that efficiency of model is equal
to that of the prototype. But the efficiency of prototype is higher than the models efficiency. This is known as
Ha = Atmospheric head
Hv = Vapour pressure head
hs = Suction head (at the outlet of reaction turbine)
H = Working head
NPSH = Net Positive Suction Head
(i) For Francis Turbine,
(ii) For Propeller Turbine,
(iii) For Kaplan Turbine,sc is 10% higher than sc for properller turbine.