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Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is 20mm with uniform velocity of 2 m/s. Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow, constant atmospheric pressure everywhere and neglecting curvature and surface tension effects, the diameter is mm of the stream 0.5m below the tap is approximately
- a)10
- b)15
- c)20
- d)25
Correct answer is option 'B'. Can you explain this answer?
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Water is coming out from a tap and falls vertically downwards. At the ...
Given:
- Diameter of the stream at the tap opening = 20 mm
- Velocity of the stream at the tap opening = 2 m/s
- Acceleration due to gravity = 9.81 m/s^2
To find:
The diameter of the stream 0.5 m below the tap.
Assumptions:
- Steady flow: The flow rate remains constant throughout.
- Inviscid flow: There is no viscosity in the fluid.
- Constant atmospheric pressure: The pressure remains the same throughout.
- Neglecting curvature and surface tension effects.
Explanation:
1. Bernoulli's Equation:
The Bernoulli's equation states that in steady, inviscid flow, the total energy per unit volume of the fluid remains constant.
2. Applying Bernoulli's Equation:
We can apply Bernoulli's equation to the stream of water at two different points - the tap opening and 0.5 m below the tap.
At the tap opening:
- Pressure = Atmospheric pressure (constant)
- Velocity = 2 m/s
- Height = 0 (since the tap opening is at the same height as the reference point)
At 0.5 m below the tap:
- Pressure = Atmospheric pressure (constant)
- Velocity = ?
- Height = -0.5 m (negative since it is below the reference point)
3. Bernoulli's Equation:
Applying Bernoulli's equation at the tap opening and 0.5 m below the tap:
At the tap opening:
P + 0.5ρv^2 + ρgh = Constant
At 0.5 m below the tap:
P + 0.5ρv'^2 + ρg(h - 0.5) = Constant
4. Simplifying the Equations:
Since the pressure and height are constant, we can cancel them out in both equations:
At the tap opening:
0.5ρv^2 = Constant
At 0.5 m below the tap:
0.5ρv'^2 + ρg(h - 0.5) = Constant
5. Diameter of the Stream:
The velocity of the stream at the tap opening is given as 2 m/s. We need to find the velocity 0.5 m below the tap, denoted as v'.
6. Using the Continuity Equation:
The continuity equation states that the mass flow rate at any point in a streamline is constant.
7. Applying the Continuity Equation:
We can apply the continuity equation to the stream of water at the tap opening and 0.5 m below the tap:
At the tap opening:
A1v1 = A2v2
At 0.5 m below the tap:
A2v2 = A3v'
8. Simplifying the Equations:
Since the stream is vertically downwards, the areas A1 and A3 will be the same (diameter of the stream at the tap opening and 0.5 m below the tap).
At the tap opening:
20 mm = d1 (diameter at the tap opening)
A1 = π(d1/2)^2
At 0.5 m below the tap:
- Diameter of the stream at the tap opening = 20 mm
- Velocity of the stream at the tap opening = 2 m/s
- Acceleration due to gravity = 9.81 m/s^2
To find:
The diameter of the stream 0.5 m below the tap.
Assumptions:
- Steady flow: The flow rate remains constant throughout.
- Inviscid flow: There is no viscosity in the fluid.
- Constant atmospheric pressure: The pressure remains the same throughout.
- Neglecting curvature and surface tension effects.
Explanation:
1. Bernoulli's Equation:
The Bernoulli's equation states that in steady, inviscid flow, the total energy per unit volume of the fluid remains constant.
2. Applying Bernoulli's Equation:
We can apply Bernoulli's equation to the stream of water at two different points - the tap opening and 0.5 m below the tap.
At the tap opening:
- Pressure = Atmospheric pressure (constant)
- Velocity = 2 m/s
- Height = 0 (since the tap opening is at the same height as the reference point)
At 0.5 m below the tap:
- Pressure = Atmospheric pressure (constant)
- Velocity = ?
- Height = -0.5 m (negative since it is below the reference point)
3. Bernoulli's Equation:
Applying Bernoulli's equation at the tap opening and 0.5 m below the tap:
At the tap opening:
P + 0.5ρv^2 + ρgh = Constant
At 0.5 m below the tap:
P + 0.5ρv'^2 + ρg(h - 0.5) = Constant
4. Simplifying the Equations:
Since the pressure and height are constant, we can cancel them out in both equations:
At the tap opening:
0.5ρv^2 = Constant
At 0.5 m below the tap:
0.5ρv'^2 + ρg(h - 0.5) = Constant
5. Diameter of the Stream:
The velocity of the stream at the tap opening is given as 2 m/s. We need to find the velocity 0.5 m below the tap, denoted as v'.
6. Using the Continuity Equation:
The continuity equation states that the mass flow rate at any point in a streamline is constant.
7. Applying the Continuity Equation:
We can apply the continuity equation to the stream of water at the tap opening and 0.5 m below the tap:
At the tap opening:
A1v1 = A2v2
At 0.5 m below the tap:
A2v2 = A3v'
8. Simplifying the Equations:
Since the stream is vertically downwards, the areas A1 and A3 will be the same (diameter of the stream at the tap opening and 0.5 m below the tap).
At the tap opening:
20 mm = d1 (diameter at the tap opening)
A1 = π(d1/2)^2
At 0.5 m below the tap:
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Water is coming out from a tap and falls vertically downwards. At the tapopening, the stream diameter is 20mm with uniform velocity of 2 m/s.Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow,constant atmospheric pressure everywhere and neglecting curvature and surfacetension effects, the diameter is mm of the stream 0.5m below the tap isapproximatelya)10b)15c)20d)25Correct answer is option 'B'. Can you explain this answer?
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Water is coming out from a tap and falls vertically downwards. At the tapopening, the stream diameter is 20mm with uniform velocity of 2 m/s.Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow,constant atmospheric pressure everywhere and neglecting curvature and surfacetension effects, the diameter is mm of the stream 0.5m below the tap isapproximatelya)10b)15c)20d)25Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Water is coming out from a tap and falls vertically downwards. At the tapopening, the stream diameter is 20mm with uniform velocity of 2 m/s.Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow,constant atmospheric pressure everywhere and neglecting curvature and surfacetension effects, the diameter is mm of the stream 0.5m below the tap isapproximatelya)10b)15c)20d)25Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is coming out from a tap and falls vertically downwards. At the tapopening, the stream diameter is 20mm with uniform velocity of 2 m/s.Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow,constant atmospheric pressure everywhere and neglecting curvature and surfacetension effects, the diameter is mm of the stream 0.5m below the tap isapproximatelya)10b)15c)20d)25Correct answer is option 'B'. Can you explain this answer?.
Water is coming out from a tap and falls vertically downwards. At the tapopening, the stream diameter is 20mm with uniform velocity of 2 m/s.Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow,constant atmospheric pressure everywhere and neglecting curvature and surfacetension effects, the diameter is mm of the stream 0.5m below the tap isapproximatelya)10b)15c)20d)25Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Water is coming out from a tap and falls vertically downwards. At the tapopening, the stream diameter is 20mm with uniform velocity of 2 m/s.Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow,constant atmospheric pressure everywhere and neglecting curvature and surfacetension effects, the diameter is mm of the stream 0.5m below the tap isapproximatelya)10b)15c)20d)25Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is coming out from a tap and falls vertically downwards. At the tapopening, the stream diameter is 20mm with uniform velocity of 2 m/s.Acceleration due to gravity is 9.81 m/s2. Assuming steady, inviscid flow,constant atmospheric pressure everywhere and neglecting curvature and surfacetension effects, the diameter is mm of the stream 0.5m below the tap isapproximatelya)10b)15c)20d)25Correct answer is option 'B'. Can you explain this answer?.
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