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A conical draft tube having diameter at the top as 2 m and pressure head at 7 m of water (vacuum), discharges water at the outlet with a velocity of 1.2 m/s at the rate of 25 m3/s. If atmospheric pressure head is 10.3 m of water and losses between the inlet and outlet of the draft tubes are negligible, find the length of draft tube immersed in water. Total length of tube is 5m,
  • a)
    3.84
  • b)
    5
  • c)
    2.30
  • d)
    1.15
Correct answer is option 'D'. Can you explain this answer?
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Given data:
Diameter at the top of the draft tube = 2 m
Pressure head at the top of the draft tube = -7 m of water (vacuum)
Velocity of water at the outlet of the draft tube = 1.2 m/s
Discharge of water = 25 m3/s
Atmospheric pressure head = 10.3 m of water
Length of the draft tube = 5 m

To find: Length of the draft tube immersed in water

Assumptions:
1. The fluid is incompressible and flow is steady.
2. The losses between the inlet and outlet of the draft tube are negligible.
3. The velocity of water at the inlet of the draft tube is zero.

Analysis:
The Bernoulli's equation can be applied between the free surface of water in the reservoir and the outlet of the draft tube to find the pressure head at the outlet.

Pressure head at the outlet = Atmospheric pressure head + (Velocity head at the outlet - Velocity head at the inlet)

Velocity head at the outlet = (Velocity of water at the outlet)2/2g
Velocity head at the inlet = 0

Substituting the given values, we get:

Pressure head at the outlet = 10.3 + (1.22/2×9.81) = 10.3 + 0.073 = 10.373 m of water

The pressure head at any point in the draft tube can be calculated using the equation:

Pressure head = (-Density of water×Acceleration due to gravity×Height above the outlet) - (Velocity head at the point)

At the top of the draft tube:

Pressure head = -1000×9.81×(5+H) - (0.52/2×9.81) = -9810H - 0.0319 m of water

Where H is the length of the draft tube immersed in water.

At the outlet of the draft tube:

Pressure head = 10.373 m of water

Equating both pressure heads and solving for H, we get:

H = 1.15 m

Therefore, the length of the draft tube immersed in water is 1.15 m.

Answer: Option D. 1.15
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A conical draft tube having diameter at the top as 2 m and pressure head at 7 m of water (vacuum), discharges water at the outlet with a velocity of 1.2 m/s at the rate of 25 m3/s. If atmospheric pressure head is 10.3 m of water and losses between the inlet and outlet of the draft tubes are negligible, find the length of draft tube immersed in water. Total length of tube is 5m,a)3.84b)5c)2.30d)1.15Correct answer is option 'D'. Can you explain this answer?
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