This set of Hydraulic Machines Multiple Choice Questions & Answers (MCQs) focuses on “Efficiency of Francis Turbine”.

1. Which of the following efficiencies for Francis Turbine is described as the ratio between the power produced by runner to the power supplied by water at the inlet?

a) Hydraulic efficiency

b) Volumetric efficiency

c) Mechanical efficiency

d) Overall efficiency

View Answer

Explanation: The definition of Hydraulic efficiency in a Francis turbine states that it is the ratio between the Runner power to the shaft power. Hence, the correct option is Hydraulic efficiency.

2. Which of the following efficiencies for Francis Turbine is described as the ratio between total quantity of water over runner blades to total quantity of water supplied to turbine?

a) Hydraulic efficiency

b) Volumetric efficiency

c) Mechanical efficiency

d) Overall efficiency

View Answer

Explanation: The definition of volumetric efficiency in a Francis turbine states that it is the ratio between the total volume of water flowing over the runner blades to the volume of water entering the turbine. Hence, the correct option is volumetric efficiency.

3. Which of the following efficiencies for Francis Turbine is defined as the ratio between the power available at the shaft of the turbine to the power produced by the runner?

a) Hydraulic efficiency

b) Volumetric efficiency

c) Mechanical efficiency

d) Overall efficiency

View Answer

Explanation: The definition of Mechanical efficiency in a Francis turbine states that it is the ratio between the Shaft power to the Runner power. Hence, the correct option is Mechanical efficiency.

4. Which of the following efficiencies for Francis Turbine is defined as the ratio between the power available at the shaft to the power supplied by water at the inlet?

a) Hydraulic efficiency

b) Volumetric efficiency

c) Mechanical efficiency

d) Overall efficiency

View Answer

Explanation: The definition of Overall efficiency in a Francis turbine states that it is the ratio between the Shaft power to the Water power. Hence, the correct option is Overall efficiency.

5. The whirl velocity at inlet of Francis turbine is given to be 20 m/s. The blade velocity is given as 35 m/s. What is the hydraulic efficiency for a head of 100 m?

a) 80%

b) 90%

c) 70%

d) 98%

View Answer

Explanation: The hydraulic efficiency of a Francis turbine is given by ηh = Vw1.u1/ gH. Substituting the values of the given parameters in the equation, we get hydraulic efficiency = 70%.

6. The desired hydraulic efficiency of a turbine is 80% at a whirl velocity of 20 m/s and a head of 100 m. What should be the blade velocity of the turbine at inlet in m/s?

a) 40

b) 60

c) 80

d) 25

View Answer

Explanation: The hydraulic efficiency of a Francis turbine is given by ηh = Vw1.u1/ gH. Substituting the values of the given parameters in the equation, we get blade velocity at the inlet as 40 m/s.

7. The input water power of the Francis turbine is 1.25 times the runner power. What would be the hydraulic efficiency of the turbine (in %)?

a) 60

b) 70

c) 80

d) 90

View Answer

Explanation: The definition of Hydraulic efficiency in a Francis turbine states that it is the ratio between the Runner power to the shaft power. If input water power is 1.25 times the runner power, the runner power is 1/1.25 = 0.8 Times the water power. Hence, hydraulic efficiency = 80%.

8. The volume flow rate into a Francis turbine is Q m3/s. 0.25Q m3/s volume of water do not flow over the runner blades. What is the mechanical efficiency of the turbine (in %)?

a) 65

b) 75

c) 80

d) Mechanical efficiency cannot be found out from the given information

View Answer

Explanation: With the given information, we can find the volumetric efficiency and not the mechanical efficiency. If you got this question wrong, its advised to read the question carefully before answering.

9. The volumetric efficiency of a Francis turbine is given to be 90%. If the volume flow rate through the turbine is 25 m^{3}/s. What is the flow rate of water over the runner blades (in m^{3}/s)?

a) 20

b) 25

c) 22.5

d) 21.5

View Answer

Explanation: The definition of volumetric efficiency in a Francis turbine states that it is the ratio between the total volume of water flowing over the runner blades to the volume of water entering the turbine. Hence, if Q = 25 m3/s, the volume of water over runner blades = 0.9*25 = 22.5 m

^{3}/s.

10. The volumetric efficiency of a given turbine is 80%. If volume flow rate of water in given to be 30 m^{3}/s, find the volume of water (m^{3}) NOT flowing over the runner blades per second?

a) 5

b) 6

c) 10

d) 12

View Answer

Explanation: The volume of water flowing over runner blades = 0.8*30 = 24 m

^{3}/s. The volume of water NOT flowing over the runner blades would then be 30 – 24 = 6 m

^{3}/s.

11. The power available at the shaft of a Francis turbine is 1 MW. The volume flow rate of water in 25 m^{3}/s, whirl velocity at inlet is 10 m/s and blade velocity is 5 m/s. Find the mechanical efficiency (in %)?

a) 65

b) 75

c) 80

d) 90

View Answer

Explanation: Mechanical efficiency is given by ηm = shaft power / ρQVw1u1. Substituting the given values into this equation, we get mechanical efficiency = 80%.

12. The whirl velocity at inlet is 15 m/s and blade velocity is 10 m/s. The volume flow rate of water in 20 m^{3}/s. Find the power output available at the shaft if the mechanical efficiency is 95% (in MW)?

a) 2.85

b) 3.075

c) 6.55

d) 0.285

View Answer

Explanation: Mechanical efficiency is given by ηm = shaft power / ρQV

_{w1u1}. Substituting the given values into this equation, we get shaft power = 2.85 MW.

13. The power output of the shaft is 5 MW. The volume flow rate of water in 10 m^{3}/s at an available head of 60 m. Find the overall efficiency of the turbine in % (g = 10 m/s^{2})?

a) 80

b) 82.5

c) 83.3

d) 85

View Answer

Explanation: The overall efficiency of a Francis turbine is given by ηo = shaft power/ ρQgH. Substituting the given values in this equation, we get overall efficiency = 83.33 %.

14. The volume flow rate of water in 10 m^{3}/s at an available head of 60 m (g = 10 m/s^{3}). Find the shaft power (in MW) if the overall efficiency of the turbine is 90%.

a) 54

b) 5.4

c) 540

d) 0.54

View Answer

Explanation: The overall efficiency of a Francis turbine is given by ηo = shaft power/ ρQgH. Substituting the given values in this equation, we get shaft power = 5.4 MW.

15. The hydraulic efficiency of a Francis turbine is 90%, the mechanical efficiency is 95% and the volumetric efficiency is assumed to be 100%. Fine the overall efficiency (in %)?

a) 80

b) 85.5

c) 87.5

d) 83.3

View Answer

Explanation: Overall efficiency is also given by ηo = ηh*ηm*ηv. So, ηo = 0.90*0.95*1 = 0.855 = 85.5%.

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