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In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.?
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In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter...
Given information:
- Length of the journal bearing (L): 60 mm
- Diameter of the shaft (D): 30 mm
- Rotational speed of the shaft (N): 500 rpm
- Clearance between the journal and bearing at concentric condition (C): 0.12 mm
- Viscosity of the Newtonian fluid (μ): 0.5 Ns/m^2
Frictional torque:
The frictional torque can be calculated using the following equation:
T = μ * A * N * (dL/dx)
Where:
- T is the frictional torque
- μ is the viscosity of the fluid
- A is the area of the bearing
- N is the rotational speed of the shaft
- (dL/dx) is the velocity gradient
Area of the bearing:
The area of the bearing can be calculated using the formula for the surface area of a cylinder:
A = π * D * L
Where:
- A is the area of the bearing
- π is a mathematical constant (approximately 3.14159)
- D is the diameter of the shaft
- L is the length of the journal bearing
Velocity gradient:
The velocity gradient can be calculated using the linear velocity variation in the fluid:
(dL/dx) = (V2 - V1) / (x2 - x1)
Where:
- (dL/dx) is the velocity gradient
- V2 is the velocity at x2
- V1 is the velocity at x1
- x2 is the outer radius of the bearing (D/2 + C)
- x1 is the inner radius of the bearing (D/2)
Calculating the frictional torque:
1. Calculate the area of the bearing using the given values:
- D = 30 mm
- L = 60 mm
- A = π * D * L
2. Calculate the velocity gradient using the linear velocity variation:
- x2 = (D/2 + C)
- x1 = (D/2)
- (dL/dx) = (V2 - V1) / (x2 - x1)
3. Substitute the calculated values into the frictional torque equation:
- T = μ * A * N * (dL/dx)
Calculating the power loss:
The power loss can be calculated using the following equation:
Power Loss = T * 2π * N / 60
Where:
- Power Loss is the amount of power lost due to friction
- T is the frictional torque
- π is a mathematical constant (approximately 3.14159)
- N is the rotational speed of the shaft
Final answer:
The frictional torque overcome by the journal is determined using the given values and equations. The corresponding power loss can also be calculated using the frictional torque.
- Length of the journal bearing (L): 60 mm
- Diameter of the shaft (D): 30 mm
- Rotational speed of the shaft (N): 500 rpm
- Clearance between the journal and bearing at concentric condition (C): 0.12 mm
- Viscosity of the Newtonian fluid (μ): 0.5 Ns/m^2
Frictional torque:
The frictional torque can be calculated using the following equation:
T = μ * A * N * (dL/dx)
Where:
- T is the frictional torque
- μ is the viscosity of the fluid
- A is the area of the bearing
- N is the rotational speed of the shaft
- (dL/dx) is the velocity gradient
Area of the bearing:
The area of the bearing can be calculated using the formula for the surface area of a cylinder:
A = π * D * L
Where:
- A is the area of the bearing
- π is a mathematical constant (approximately 3.14159)
- D is the diameter of the shaft
- L is the length of the journal bearing
Velocity gradient:
The velocity gradient can be calculated using the linear velocity variation in the fluid:
(dL/dx) = (V2 - V1) / (x2 - x1)
Where:
- (dL/dx) is the velocity gradient
- V2 is the velocity at x2
- V1 is the velocity at x1
- x2 is the outer radius of the bearing (D/2 + C)
- x1 is the inner radius of the bearing (D/2)
Calculating the frictional torque:
1. Calculate the area of the bearing using the given values:
- D = 30 mm
- L = 60 mm
- A = π * D * L
2. Calculate the velocity gradient using the linear velocity variation:
- x2 = (D/2 + C)
- x1 = (D/2)
- (dL/dx) = (V2 - V1) / (x2 - x1)
3. Substitute the calculated values into the frictional torque equation:
- T = μ * A * N * (dL/dx)
Calculating the power loss:
The power loss can be calculated using the following equation:
Power Loss = T * 2π * N / 60
Where:
- Power Loss is the amount of power lost due to friction
- T is the frictional torque
- π is a mathematical constant (approximately 3.14159)
- N is the rotational speed of the shaft
Final answer:
The frictional torque overcome by the journal is determined using the given values and equations. The corresponding power loss can also be calculated using the frictional torque.
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In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.?
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In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.?.
In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.?.
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In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.?, a detailed solution for In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.? has been provided alongside types of In a 60 mm long journal bearing arrangement, a shaft of 30 mm diameter rotates at 500 rpm. The clearance between the journal and bearing at concentric condition is flled with a Newtonian fluid of thickness 0.12 mm having viscosity of 0.5 Ns/m2. If velocity variation in the fluid is linear, then determine frictional torque overcome by the journal and the corresponding power loss.? theory, EduRev gives you an
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