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3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above?
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3.Two large plane surfaces are 20mm apart and the gap contains oil of ...
Problem Statement:
Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s. A thin plate of area 0.5m² is to be pulled through the gap at a constant velocity of 0.6m/s. The location of the plate will have to be such that it is 8mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is
Solution:
Given parameters are:
- Distance between the surfaces (d) = 20 mm = 0.02 m
- Dynamic viscosity of oil (μ) = 0.6 Pa.s
- Area of the plate (A) = 0.5 m²
- Velocity of the plate (V) = 0.6 m/s
- Distance of plate from one of the surfaces (h) = 8 mm = 0.008 m
We need to calculate the force required to pull the plate through the gap.
Calculation:
- Calculation of shear stress (τ):
The shear stress (τ) can be calculated using the formula:
τ = μ x (V/d)
τ = 0.6 x (0.6/0.02) = 18 Pa
- Calculation of force (F):
The force (F) required to pull the plate can be calculated using the formula:
F = τ x A
F = 18 x 0.5 = 9 N
- Calculation of effective area (A'):
The effective area (A') can be calculated using the formula:
A' = A - h x L
where L is the length of the plate in the direction of motion.
Here, L = 0.5/0.008 = 62.5 m
A' = 0.5 - 0.008 x 62.5 = 0.004 m²
- Calculation of force (F) with effective area (A'):
The force (F) required to pull the plate with effective area (A') can be calculated using the formula:
F = τ x A'
F = 18 x 0.004 = 0.72 N
Therefore, the force required to pull the plate through the gap is 0.72 N which is not given in the options. Hence, the answer is (d) None of the above.
Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s. A thin plate of area 0.5m² is to be pulled through the gap at a constant velocity of 0.6m/s. The location of the plate will have to be such that it is 8mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is
Solution:
Given parameters are:
- Distance between the surfaces (d) = 20 mm = 0.02 m
- Dynamic viscosity of oil (μ) = 0.6 Pa.s
- Area of the plate (A) = 0.5 m²
- Velocity of the plate (V) = 0.6 m/s
- Distance of plate from one of the surfaces (h) = 8 mm = 0.008 m
We need to calculate the force required to pull the plate through the gap.
Calculation:
- Calculation of shear stress (τ):
The shear stress (τ) can be calculated using the formula:
τ = μ x (V/d)
τ = 0.6 x (0.6/0.02) = 18 Pa
- Calculation of force (F):
The force (F) required to pull the plate can be calculated using the formula:
F = τ x A
F = 18 x 0.5 = 9 N
- Calculation of effective area (A'):
The effective area (A') can be calculated using the formula:
A' = A - h x L
where L is the length of the plate in the direction of motion.
Here, L = 0.5/0.008 = 62.5 m
A' = 0.5 - 0.008 x 62.5 = 0.004 m²
- Calculation of force (F) with effective area (A'):
The force (F) required to pull the plate with effective area (A') can be calculated using the formula:
F = τ x A'
F = 18 x 0.004 = 0.72 N
Therefore, the force required to pull the plate through the gap is 0.72 N which is not given in the options. Hence, the answer is (d) None of the above.
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3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above?
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3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above?.
3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above?.
Solutions for 3.Two large plane surfaces are 20mm apart and the gap contains oil of dynamic viscosity 0.6Pa.s.A thin plate of area 0.5m² is to be pulled through the gap at at constant velocity of 0.6m/s.The location of the plate will have to be such that it is 8 mm from one of the surfaces. Neglecting edge effects, the force required for pulling the plate is a) 37.5 N b) 75 N c) 30N d) None of the above? in English & in Hindi are available as part of our courses for GATE.
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