Classification of Hydraulic Turbines  Turbines that use water as the working fluid for the production of power are known as hydraulic turbines.  Main categories are impulse and reaction turbines (based on the interaction of the fluid on the blades)  Can further be classified on the basis of head available at the inlet, specific speed, and according to flow direction 1. Action of water on the runner (the rotating element of turbine)—impulse and reaction 2. Direction of flow—tangential flow, radial flow, axial flow, and mixed (radial + axial) flow 3. Available head—high head (H > 300 m), medium head (50 m < H < 300 m), and low head (H < 50 m) 4. Specific speed is the speed of geometrically similar turbine which produces unit power when operated under unit head— low, medium, and high specific speed turbines Heads and Efficiencies  Two types of heads as far as turbines are concerned—gross head and net head.  Gross head indicates the difference in head and tail race levels.  Net head is the actual head available at the turbine inlet and is computed as gross head minus frictional losses in the penstock

1. Hydraulic Turbines
Dr.Thilaksiri Bandara

2. Classification of HydraulicTurbines
 Turbines that use water as the working fluid
for the production of power are known as
hydraulic turbines.
 Main categories are impulse and reaction
turbines (based on the interaction of the
fluid on the blades)
 Can further be classified on the basis of
head available at the inlet, specific speed, and
according to flow direction

3. Classification of hydraulic turbines
Turbine Action
of water
Flow
direction
Availab
le head
Specific
speed
Pelton Impulse Tangential flow H>300m 8-50
Francis Reaction Mixed flow 50m<H
<300m
50-250
Kaplan/P
ropeller
Reaction Axial flow H<50m 250-850
1. Action of water on the runner (the rotating element of
turbine)—impulse and reaction
2. Direction of flow—tangential flow, radial flow, axial flow, and
mixed (radial + axial) flow
3. Available head—high head (H > 300 m), medium head (50 m
< H < 300 m), and low head (H < 50 m)
4. Specific speed is the speed of geometrically similar turbine
which produces unit power when operated under unit head—
low, medium, and high specific speed turbines

4. Heads and Efficiencies
 Two types of heads as far as turbines
are concerned—gross head and net
head.
 Gross head indicates the difference in
head and tail race levels.
 Net head is the actual head available at
the turbine inlet and is computed as
gross head minus frictional losses in the
penstock

5.  𝐻 𝑔 = 𝐻 𝑛𝑒𝑡 + 𝐻𝑓
 𝐻 𝑓 = 4𝑓𝐿𝑣2/2𝐷𝑔

6.  Efficiency is usually defined as the ratio of
output to the input
 The power input to the system is in the
form of hydraulic energy of the stored
water (equivalent to the net head) and the
output is in the form of electrical energy.
 Losses in different components of the
hydroelectric power plant

8. Reynolds TransportTheorem
 The Reynolds transport theorem is a tool
that relates a change in the extensive
property in a system to the change in the
corresponding intensive property for the
control volume.
 If is the extensive property and η is the
corresponding intensive property such
that 𝞰

9.  The expression for the Reynolds
transport theorem is
change in
the extensive
property of a
system
(subscripts s is
used for system
and CV for
control volume)
change in the
extensive
property inside
the control
volume
change in the
extensive
property due to
the net efflux of
fluid through the
control surface

10. proof
System and control volume at different
times

11.  To prove this theorem, let us consider a
system and control volume of same size
placed in a flow field represented by
velocity vector 𝑉 = 𝑢 Ƹ𝑖 + 𝑣 Ƹ𝑗 + 𝑤෠𝑘.
 Figure shows the positions of system and
control volume at time 𝑡 = 𝑡0 and time
𝑡 = 𝑡0 + Δ𝑡.
 The control volume is fixed in space
whereas the system will move with the
flow field
 The system does not allow mass to enter
or leave through its boundary

12.  In other words, a system will have the same
fluid particles at any time
 The system boundary is represented by a
solid line and the control surface by a
dashed (porous) line to complement their
definitions
 At time 𝑡 = 𝑡0, both system and control
volume are overlapping. Further, at time 𝑡 =
𝑡0 + Δ𝑡, the system gets displaced by𝑉Δ𝑡.
 At this time, together system and control
volume can be thought to have three
different regions, viz.A, C, and B; C is the
region common to both system and control
volume.

13.  From the first principle
 However, at and
at
 In addition -

14.  The extensive property can be expressed in
terms of intensive property for control
volume in the following manner:
 where ∆𝑠 is the length of the streamline intercepted
in the sub-region B.Therefore the length of the
element in sub-region B is ∆𝑠 𝑐𝑜𝑠𝜃 and the volume
of the element is Δ𝑠 cos 𝜃𝑑𝐴.
 In addition,

15.  In a similar fashion
 It must be noted that area 𝑑 Ԧ𝐴 is a vector quantity whose
direction is vertically outward, as shown in Fig.
 This area is the elemental area on the control surface of
the control volume intercepted by the sub-region or the
cross-sectional of the elemental sub-region.
 It must also be noted that the length of the intercepted
streamline segment will be the same in the two sub-
regions A and B as the system, as a whole, is displaced by
an amount 𝑉∆𝑡.
 Therefore, the equation can be written as

16.  Together regions A and B represent the
entire control surface of the control volume,

17. The mass conservation principle
 The mass conservation law for a system
state that the total mass of the system
remains constant, that is, there will be no
change in mass of the system with time.
Mathematically,
 Using Reynolds transport theorem, the mass
conservation principle for control
 volume can be obtained by substituting
and 𝜂 = 1,

18.  Therefore, the mass conservation equation
or continuity equation in integral form is
given by

19. Impact of a jet
 When a high-velocity jet impinges on a
surface (fixed or moving), it exerts a force
known as impact of jet.
 The computation of this force on the runner
helps in determining the power produced by
the runner. In this section, the jet impact
(force) is computed for the following
different cases:

20. Stationary flat vertical plate
 If the friction is ignored,
the magnitude of the jet
velocity will not change
before and after the
impact, there will be a
change in direction
only.
 The force on the plate
is calculated by applying
the momentum eqn on
the control volume
(CV)

21.  𝑥 and 𝑦 component form for steady flow
can be written as
 where ሶ𝑚 represents the mass flow rate.
Subscripts 1 and 2 represent inlet and
outlet of the CV as shown in Figure
 Considering y-direction momentum

22.  (as there is no inflow in y-direction, that
is, 𝑉 𝑦1 = 0 )
 Considering 𝑥-direction momentum,
 (as there is no outflow in 𝑥-direction, that
is, 𝑉 𝑥2 = 0)

23.  For a given liquid jet, the impact force is
directly proportional to the jet’s cross-
sectional area and the square of jet
velocity.
 This means a slight increase in jet velocity
V results in substantial increase in impact
force F.
 The force varies linearly with the jet’s
cross-sectional area.