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Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is
2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly to
- a)192 kN/m2
- b)150 kN/m2
- c)165 kN/m2
- d)175 kN/m2
Correct answer is option 'C'. Can you explain this answer?
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Water flows through a vertical contraction from a pipe of diameter d t...
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Water flows through a vertical contraction from a pipe of diameter d t...
Given:
Inlet velocity at the inlet to contraction (v1) = 2 m/s
Pressure at the inlet to contraction (P1) = 200 kN/m2
Height of contraction (h) = 2 m
Diameter of the pipe at the inlet (D1) = d
Diameter of the pipe at the outlet (D2) = d/2
To find:
Pressure at the exit of contraction (P2)
Assumptions:
- The flow is steady and incompressible.
- The fluid is ideal and follows Bernoulli's principle.
- There are no losses due to friction or other factors.
Bernoulli's principle states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume of a fluid is constant along a streamline.
Applying Bernoulli's equation to the inlet and exit of the contraction:
At the inlet:
P1 + 1/2 * ρ * v1^2 + ρ * g * h = constant
At the exit:
P2 + 1/2 * ρ * v2^2 + ρ * g * h = constant
Since the height of the contraction is the same at both the inlet and exit, the potential energy terms cancel out.
Simplifying the equations:
P1 + 1/2 * ρ * v1^2 = P2 + 1/2 * ρ * v2^2
Since the fluid is incompressible, the density (ρ) is constant.
Substituting the given values:
200 kN/m2 + 1/2 * ρ * (2 m/s)^2 = P2 + 1/2 * ρ * v2^2
Simplifying further:
200 kN/m2 + 2 kN/m2 = P2 + 1/2 * ρ * v2^2
As the height of the contraction (h) is the same as the pressure difference, the pressure at the exit of the contraction is equal to the pressure at the inlet plus the pressure difference due to the change in velocity.
Result:
P2 = 200 kN/m2 + 2 kN/m2 = 202 kN/m2
Therefore, the pressure at the exit of the contraction will be approximately 202 kN/m2, which is closest to option C (165 kN/m2).
Inlet velocity at the inlet to contraction (v1) = 2 m/s
Pressure at the inlet to contraction (P1) = 200 kN/m2
Height of contraction (h) = 2 m
Diameter of the pipe at the inlet (D1) = d
Diameter of the pipe at the outlet (D2) = d/2
To find:
Pressure at the exit of contraction (P2)
Assumptions:
- The flow is steady and incompressible.
- The fluid is ideal and follows Bernoulli's principle.
- There are no losses due to friction or other factors.
Bernoulli's principle states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume of a fluid is constant along a streamline.
Applying Bernoulli's equation to the inlet and exit of the contraction:
At the inlet:
P1 + 1/2 * ρ * v1^2 + ρ * g * h = constant
At the exit:
P2 + 1/2 * ρ * v2^2 + ρ * g * h = constant
Since the height of the contraction is the same at both the inlet and exit, the potential energy terms cancel out.
Simplifying the equations:
P1 + 1/2 * ρ * v1^2 = P2 + 1/2 * ρ * v2^2
Since the fluid is incompressible, the density (ρ) is constant.
Substituting the given values:
200 kN/m2 + 1/2 * ρ * (2 m/s)^2 = P2 + 1/2 * ρ * v2^2
Simplifying further:
200 kN/m2 + 2 kN/m2 = P2 + 1/2 * ρ * v2^2
As the height of the contraction (h) is the same as the pressure difference, the pressure at the exit of the contraction is equal to the pressure at the inlet plus the pressure difference due to the change in velocity.
Result:
P2 = 200 kN/m2 + 2 kN/m2 = 202 kN/m2
Therefore, the pressure at the exit of the contraction will be approximately 202 kN/m2, which is closest to option C (165 kN/m2).
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Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly toa)192 kN/m2b)150 kN/m2c)165 kN/m2d)175 kN/m2Correct answer is option 'C'. Can you explain this answer?
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Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly toa)192 kN/m2b)150 kN/m2c)165 kN/m2d)175 kN/m2Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly toa)192 kN/m2b)150 kN/m2c)165 kN/m2d)175 kN/m2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly toa)192 kN/m2b)150 kN/m2c)165 kN/m2d)175 kN/m2Correct answer is option 'C'. Can you explain this answer?.
Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly toa)192 kN/m2b)150 kN/m2c)165 kN/m2d)175 kN/m2Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly toa)192 kN/m2b)150 kN/m2c)165 kN/m2d)175 kN/m2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly toa)192 kN/m2b)150 kN/m2c)165 kN/m2d)175 kN/m2Correct answer is option 'C'. Can you explain this answer?.
Solutions for Water flows through a vertical contraction from a pipe of diameter d to another of diameter of d/2. Inlet velocity at inlet to contraction is2 m/s and pressure 200 kN/m2. If height of contraction measures 2 m/s, the pressure at exit of contraction will be nearly toa)192 kN/m2b)150 kN/m2c)165 kN/m2d)175 kN/m2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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