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Tests were conducted on a francis turbine of 0.8 m diameter under a head of 9m. The turbine running at 240 rpm develops 84.5 kW and the water consumption was 1.2 m3/s. If the some turbine operated under a head of 16 m, the new discharge will be
  • a)
    1.4 m3/s
  • b)
    1.6 m3/s
  • c)
    1.8 m 3/s
  • d)
    2 m3/s
Correct answer is option 'B'. Can you explain this answer?
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Given data:
Diameter of Francis turbine (D) = 0.8 m
Head (H1) = 9 m
Turbine speed (N1) = 240 rpm
Power developed (P1) = 84.5 kW
Water consumption (Q1) = 1.2 m^3/s

To find:
New discharge (Q2) when the turbine operates under a head of 16 m.

Formula:
The power developed by a Francis turbine is given by the equation:
P = ρ * g * Q * H * η
where,
P = Power developed (kW)
ρ = Density of water (1000 kg/m^3)
g = Acceleration due to gravity (9.81 m/s^2)
Q = Discharge (m^3/s)
H = Head (m)
η = Efficiency of the turbine

The specific speed (Ns) of a turbine is given by the equation:
Ns = N * √Q / √H
where,
Ns = Specific speed
N = Turbine speed (rpm)

The specific speed is constant for a turbine, so we can use it to find the new discharge.

Calculation:
1. Specific speed (Ns1) for the given turbine:
Ns1 = N1 * √Q1 / √H1

2. Specific speed (Ns2) for the turbine operating under a head of 16 m:
Ns2 = N1 * √Q2 / √H2

Since the specific speed is constant, we can equate Ns1 and Ns2:
Ns1 = Ns2

3. Substituting the values in the equation:
N1 * √Q1 / √H1 = N1 * √Q2 / √H2

4. Simplifying the equation:
√Q2 / √H2 = √Q1 / √H1

5. Cross-multiplying the equation:
√Q2 * √H1 = √Q1 * √H2

6. Squaring both sides of the equation:
Q2 * H1 = Q1 * H2

7. Solving for Q2:
Q2 = (Q1 * H2) / H1

8. Substituting the given values:
Q2 = (1.2 * 16) / 9
Q2 ≈ 2.133 m^3/s

Therefore, the new discharge (Q2) when the turbine operates under a head of 16 m is approximately 2.133 m^3/s.

Hence, the correct answer is option 'B' (1.6 m^3/s).
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Tests were conducted on a francis turbine of 0.8 m diameter under a head of 9m. The turbine running at 240 rpm develops 84.5 kW and the water consumption was 1.2 m3/s. If the some turbine operated under a head of 16 m, the new discharge will bea)1.4 m3/sb)1.6 m3/sc)1.8 m 3/sd)2 m3/sCorrect answer is option 'B'. Can you explain this answer?
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Tests were conducted on a francis turbine of 0.8 m diameter under a head of 9m. The turbine running at 240 rpm develops 84.5 kW and the water consumption was 1.2 m3/s. If the some turbine operated under a head of 16 m, the new discharge will bea)1.4 m3/sb)1.6 m3/sc)1.8 m 3/sd)2 m3/sCorrect answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Tests were conducted on a francis turbine of 0.8 m diameter under a head of 9m. The turbine running at 240 rpm develops 84.5 kW and the water consumption was 1.2 m3/s. If the some turbine operated under a head of 16 m, the new discharge will bea)1.4 m3/sb)1.6 m3/sc)1.8 m 3/sd)2 m3/sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Tests were conducted on a francis turbine of 0.8 m diameter under a head of 9m. The turbine running at 240 rpm develops 84.5 kW and the water consumption was 1.2 m3/s. If the some turbine operated under a head of 16 m, the new discharge will bea)1.4 m3/sb)1.6 m3/sc)1.8 m 3/sd)2 m3/sCorrect answer is option 'B'. Can you explain this answer?.
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