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In a circular pipe of certain length carrying oil at a Reynolds number 100, it is proposed to triple the discharge. If the viscosity remains unchanged, the power input will have to be?
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In a circular pipe of certain length carrying oil at a Reynolds number...
Solution:
Given data:
Length of the pipe (L) = ?
Reynolds number (Re) = 100
Discharge (Q) = 3Q
Viscosity (μ) = constant
To find:
Power input required to triple the discharge
Formula used:
Reynolds number (Re) = (ρVD)/μ
where,
ρ = density of fluid
V = velocity of fluid
D = diameter of pipe
μ = viscosity of fluid
Power input (P) = (ΔPQ)/(η)
where,
ΔP = pressure drop across the pipe
Q = discharge
η = efficiency of pump
Steps:
1. As the Reynolds number is given, we can find the velocity of fluid using the formula of Reynolds number.
Reynolds number (Re) = (ρVD)/μ
100 = (ρVD)/μ
V = (100μ)/(ρD)
2. As the discharge is tripled, the velocity of fluid will also increase by a factor of 3.
V = (3Q)/(πD^2/4)
V = (12Q)/(πD^2)
3. Equating the above two equations, we get the diameter of the pipe.
(100μ)/(ρD) = (12Q)/(πD^2)
D^3 = (12QρDμ)/(100π)
D = [12Qρμ/(100π)]^(1/3)
4. Using the above equation, we can find the diameter of the pipe.
5. As the viscosity is constant, the pressure drop remains the same.
6. As the discharge is tripled, the power input required to maintain the flow rate also increases by a factor of 27.
P = (ΔPQ)/(η)
P' = (ΔP(3Q))/η
P' = 27P
Answer:
Therefore, the power input required to triple the discharge is 27 times the original power input.
Given data:
Length of the pipe (L) = ?
Reynolds number (Re) = 100
Discharge (Q) = 3Q
Viscosity (μ) = constant
To find:
Power input required to triple the discharge
Formula used:
Reynolds number (Re) = (ρVD)/μ
where,
ρ = density of fluid
V = velocity of fluid
D = diameter of pipe
μ = viscosity of fluid
Power input (P) = (ΔPQ)/(η)
where,
ΔP = pressure drop across the pipe
Q = discharge
η = efficiency of pump
Steps:
1. As the Reynolds number is given, we can find the velocity of fluid using the formula of Reynolds number.
Reynolds number (Re) = (ρVD)/μ
100 = (ρVD)/μ
V = (100μ)/(ρD)
2. As the discharge is tripled, the velocity of fluid will also increase by a factor of 3.
V = (3Q)/(πD^2/4)
V = (12Q)/(πD^2)
3. Equating the above two equations, we get the diameter of the pipe.
(100μ)/(ρD) = (12Q)/(πD^2)
D^3 = (12QρDμ)/(100π)
D = [12Qρμ/(100π)]^(1/3)
4. Using the above equation, we can find the diameter of the pipe.
5. As the viscosity is constant, the pressure drop remains the same.
6. As the discharge is tripled, the power input required to maintain the flow rate also increases by a factor of 27.
P = (ΔPQ)/(η)
P' = (ΔP(3Q))/η
P' = 27P
Answer:
Therefore, the power input required to triple the discharge is 27 times the original power input.
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In a circular pipe of certain length carrying oil at a Reynolds number 100, it is proposed to triple the discharge. If the viscosity remains unchanged, the power input will have to be?
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In a circular pipe of certain length carrying oil at a Reynolds number 100, it is proposed to triple the discharge. If the viscosity remains unchanged, the power input will have to be? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a circular pipe of certain length carrying oil at a Reynolds number 100, it is proposed to triple the discharge. If the viscosity remains unchanged, the power input will have to be? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a circular pipe of certain length carrying oil at a Reynolds number 100, it is proposed to triple the discharge. If the viscosity remains unchanged, the power input will have to be?.
In a circular pipe of certain length carrying oil at a Reynolds number 100, it is proposed to triple the discharge. If the viscosity remains unchanged, the power input will have to be? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a circular pipe of certain length carrying oil at a Reynolds number 100, it is proposed to triple the discharge. If the viscosity remains unchanged, the power input will have to be? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a circular pipe of certain length carrying oil at a Reynolds number 100, it is proposed to triple the discharge. If the viscosity remains unchanged, the power input will have to be?.
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