Francis and Kaplan turbines

QUESTION 1
For the following questions mention the correct option(s) in the manuscript.
i. The spin rate of a turbine decreases by a factor of 3. Under these conditions, its
a. Power output decreases by a factor of 9
b. Power output decreases by a factor of 27
c. Volume flow rate decreases by a factor of 3
d. Volume flow rate decreases by a factor of 9
[1 mark]
ii. Consider gas flow through a converging-diverging nozzle. Of the five statements
below, select the incorrect option(s):
a. The fluid velocity at the throat can never exceed the speed of sound.
b. If the fluid velocity at the throat is below the speed of sound, the diverging
section will act like a diffuser.
c. If the fluid enters the diverging section with a Mach number greater than
one, the flow at the nozzle exit will be supersonic.
d. There will be no flow through the nozzle if the back pressure equals the
stagnation pressure.
[1 mark]
iii. Which of the following principles are true for the design, operation, and selection of
pumps:
a. The vapour pressure of the fluid is irrelevant.
b. The net positive suction head is an important consideration.
c. The setup and application should lead to no cavitation.
d. Pumps always lead to an increase in outgoing fluid velocity.
[1 mark]
iv. Francis and Kaplan turbines are often provided with a draft tube, which lead the exit
flow into the tailrace region. For this aspect, which of the following are true:
a. The draft tube helps in increasing the pressure at the runner outlet.
b. The draft tube helps in decreasing the pressure at the runner outlet
c. The design of draft tubes must consider the vapour pressure of the fluid in
the turbine.
d. The draft tube increases fluid velocities so that kinetic energy can be
extracted by the turbine.
[1 mark]
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Page 3 of 11
v. The capacity coefficient and head coefficients for a pump operation are 256 and 16,
respectively. Which type of pump would you recommend for this application
a. Positive displacement pump.
b. Centrifugal flow pump.
c. Mixed flow pump.
d. Axial flow pump.
[1 mark]
vi. Consider a converging nozzle with a low velocity at the inlet and sonic velocity at the
exit plane. Now the nozzle exit diameter is reduced by half while the nozzle inlet
temperature and pressure are maintained the same. The nozzle exit velocity will
a. remain the same
b. double
c. quadruple
d. go down by half
[1 mark]
vii. Which of the following are true for isentropic flow and its analysis for ideal gases?
a. Energy conservation implies stagnation enthalpy remains constant if
potential energy is additionally neglected.
b. The stagnation temperature never changes in isentropic flow.
c. The stagnation state properties will satisfy the ideal gas equation, even if the
stagnation state never realised anywhere in the fluid domain.
d. The relation � = � �!/#, where � is a constant and �, �, and � are gas
density, pressure, and ratio of specific heats, respectively, applies to all
states.
[1 mark]
viii. Which of the following are true for Rayleigh flow:
a. Entropy of the fluid remains constant.
b. The stagnation properties of the fluid remain constant.
c. Through heating supersonic flow cannot be achieved.
d. Through cooling all gases in supersonic flow can be cooled to an absolute
zero temperature.
[1 mark]
ix. In Rayleigh flow, for an ideal with k = 1.6, at Ma = 0.9, a small amount of heating will:
a. Lead to an increase in Mach number.
b. Lead to a decrease in temperature.
c. Lead to an increase in stagnation temperature.
d. Lead to reduction in entropy. [1 mark]
TURN OVER
Page 4 of 11
x. A poorly designed propeller has no twist (constant pitch). For such a propeller
a. The angle of attack remains constant as radius increases.
b. The angle of attack increases as radius increases.
c. Then angle of attack decreases as radius increases.
d. The change in the angle of attack is non-linear as radius increases