ME161P POWER PLANT
DESIGN WITH
RENEWABLE ENERGY
WEEK 8 – CAVITATION
1T/2022-2023
10/10/2023
Prepared by:
Engr. Manuel B. Rustria
1
October 10, 2023
 Define cavitation and cite its effects on hydraulic turbines.
 Identify factors that contribute to cavitation on hydraulic turbines.
 Explain how to locate reaction turbines above or below tail water elevation
to prevent cavitation.
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 Cavitation is a phenomenon that involves the implosion of vapor bubbles
in a liquid.
These bubbles are formed by the flashing of some of the liquid into vapor
caused by a reduction of the liquid pressure below the vapor pressure.
When the liquid pressure is then increased above vapor pressure, the
bubbles implode with a release of large amounts of energy.
Some small amount of this energy is dissipated as sound.
The remaining energy causes vibration of the equipment and also tears
away part of the surface of the metal boundary.
 When cavitation occurs in pumps and turbines, the metal becomes pitted
or honeycombed. The efficiency and maximum power of a unit may be
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badly
impaired by severe cavitation.
 Cavitation is most likely to occur on the outer edge of the back of Francis
and propeller-runner blades and on the band of Francis runners.
 Because propeller runners operate at high specific speeds, they must be
set lower to avoid cavitation.
 Cavitation of the runner can be controlled by the elevation of the runner
above (or below) tailwater level.
 Other points at which cavitation can occur are on draft-tube walls, at sharp
corners or restrictions, and on the needle and deflectors of impulse
turbines.
 Impulse runners may encounter cavitation of the back edge of the bucket
lip.
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 Tests of model runners are the most reliable means of predicting
cavitation.
 From these tests the proper elevation of the bottom of a Francis wheel or
the centerline of a propeller wheel can be determined.
 This elevation is one of the most important dimensions that must be
determined for the plant and involves the use of the sigma function (σ).
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 However, preliminary calculations may be made by establishing the
minimum permissible pressure at the wheel as being equal to the vapor
pressure (Hvap); some manufacturers use an arbitrary value of 0.6 ft for
Hvap.
 This will be equal to the barometric pressure (Hb), less the pressure due to
the elevation of the wheel above tail-water level (He), less the velocity
head at the wheel outlet (Hv), all expressed in feet of water; or,
Hvap = Hb – He – Hv
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16-5
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 The velocity head at the runner outlet is proportional to the square of the
velocity at this point.
 In turn, the velocity is proportional to the volume of water flowing, so that
the velocity head is proportional to square of the flow.
 But the square of the flow is proportional to the turbine net head (Hn).
 Therefore, the velocity head is proportional to net head.
 Then, taking σ as the constant proportionality,
Hv = σHn
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Hv = σHn
16-6
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 Combining Eqs. (16-5) and (16-6).
Hb – He – Hvap
σ=
Hn
16-7a
Thus, the elevation of hydraulic turbine runner or wheel with respect to
tailwater elevation is
He = Hb – Hvap – σHn
16-7b
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 If the runner is above tailwater level, He is positive; if the runner is below
tailwater level, He is negative.
 Values of the vapor pressure may be obtained from the steam tables and
converted into feet of water for the summer water temperature.
 Barometric pressure is that existing at the plant elevation and not the
barometric pressures corrected to sea level.
 For most purposes, it is satisfactory to assume the barometric pressure as
34 ft of water less 1.13 ft for each 1000-ft increase in elevation above sea
level.
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 The constant of proportionality, σ, is called the cavitation factor and is
assumed to be constant for all heads on a given runner and for all
proportionality similar (homologous) runners.
 Actually, σ varies with gate and blade angle.
 The minimum σ necessary to prevent cavitation is the critical σ.
 The operating σ is the value at which the turbine actually operates and
should exceed critical σ by an ample margin to prevent cavitation due to
unforeseeable variation in equipment manufacture and in operating
conditions.
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 Approximate values of σ suitable for the solution or problems may be
obtained from the following equations:
 For propeller turbines,
σ=
(Ns)2
15,000
– 0.2
16-8
 For Francis turbines,
σ=
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(Ns)2
15,000
16-9
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 Some metals are more subject to the pitting effects of cavitation than
others, porous materials being the most susceptible.
 Cast iron, which is used for small, low-head turbines of all three types, is
the most susceptible to cavitation pitting.
 Some bronze have about one-third the rate of pitting of cast iron, while
cast carbon-steel exhibits only one-eighth the rate of pitting of cast iron.
 Cast stainless-steel (18% Cr, 8% Ni) aluminum bronze has about onesixtieth the rate of cast iron.
 Most runners today are made of cast steel, and many are protected with a
welded-on layer of stainless steel over the are more likely to be subjected
to pitting due to cavitation.
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EXAMPLE 16-2
 For the 30,000-hp, 50-ft head, 90 rpm Kaplan unit of the preceeding
example, determine the elevation of the propeller for a 3000-ft elevation
and 80 °F water.
Solution
 For the actual speed of 90 rpm, the specific speed from Eq. (13-3) would
be
90(30,000)1/2
Ns =
= 117.2
5/4
(50)
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 From Eq. (16-8),
σ=
(117.2)2
15,000
– 0.2 = 0.717
 Barometric pressure equals 34 – 1.13 × (3000/1000), say, 30.6 ft.
 At 80 °F, from the steam tables, the vapor pressure is 1.0321 in. Hg or
(1.0321/12) (0.01608/0.001183) = 1.17 ft of water (0.01608 is the specific
volume of water at 80 °F).
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 From Eq. (16-7b),
He = 30.6 – 1.17 – 0.717 × 50 = -6.4 ft
 Since this is a minus value, the centerline of the runner should be set to at
least 6.4 ft below the minimum tail-water level that can occur when the
turbine is developing 30,000 hp.
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P1. Determine the maximum elevation of the runner above (or
minimum below) tail-water level in feet of water for the following
data:
Type of runner: Francis
Elevation above sea level: 2, 260 ft
Water temperature: 80 oF
Horsepower: 150, 500
Net Head: 425 ft
Actual speed: 130 rpm
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P2. Determine the maximum elevation of the runner above (or
minimum below) tail-water level in feet of water for the following
data:
Type of runner: Kaplan
Elevation above sea level: 2, 260 ft
Water temperature: 80 oF
Horsepower: 150, 500
Net Head: 425 ft
Actual speed: 130 rpm
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P3. Determine the maximum elevation of the runner above (or
minimum below) tail-water level in feet of water for the following
data:
Type of runner: Pelton
Elevation above sea level: 2, 260 ft
Water temperature: 80 oF
Horsepower: 150, 500
Net Head: 425 ft
Actual speed: 130 rpm
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P4.
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P5.
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P6.
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P7.
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 Potter, Philip J. Power Plant Design. 2nd ed. New York, The Ronald Press
Company.
 https://www.youtube.com/watch?v=UuUYCFDTrc&ab_channel=IETInstituteforEnergyTechnology
 https://www.youtube.com/watch?v=ON_irzFAU9c&ab_channel=DanSt
efanescu
 https://www.brighthubengineering.com/fluid-mechanicshydraulics/27427-cavitation-in-hydraulic-turbines-causes-and-effects/
 https://aulti.bbcollab.com/recording/39617982a49f4bd983b49d090b031467
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A wise man is full of strength, and a man of knowledge
enhances his might.
Prov. 24:5 (ESV)
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