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A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.
Correct answer is '87'. Can you explain this answer?
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A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The len...
Given d = 150 mm, N = 2000 rpm, p = 1 N/mm2
l = 1.4d = 210 mm
μ = 0.005, t = 15°C, S = 1900 J/kg°C
Load on the bearing, F = dlp = 150 x 210 x 1 = 31500 N
Rubbing velocity, V = πdN/60 = π/60 x 150/1000 x 2000 = 15.71 m/s
Heat generated at the bearing, Hg = μFV = 0.005 x 31500 x 15.71 = 2474.33 W
Heat generated at the bearing is entirely removed by the coolant oil.
⇒ Hg = mSt
2474.33 = m x 1900 x 15
⇒ m = 0.887 kg/s
= 87 g/s
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A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The len...
Given data:
- Diameter of the shaft (d) = 150 mm
- Rotational speed of the shaft (N) = 2000 rpm
- Length of the bearing (L) = 1.4 times its diameter = 1.4d = 1.4 * 150 mm
- Bearing pressure (P) = 1 N/mm^2
- Coefficient of friction at the bearing surface (μ) = 0.005
- Temperature difference across the bearing (ΔT) = 15°C
- Specific heat of the oil (C) = 1900 J/kg°C
- Required amount of coolant oil per second = ?
Calculating the bearing speed:
The bearing speed can be calculated using the formula:
V = π * d * N / 60
where V is the speed of the shaft in mm/s, d is the diameter of the shaft in mm, and N is the rotational speed of the shaft in rpm.
Substituting the given values, we get:
V = π * 150 mm * 2000 rpm / 60
V ≈ 15708.04 mm/s
Calculating the frictional force:
The frictional force can be calculated using the formula:
F = P * A
where F is the frictional force in N, P is the bearing pressure in N/mm^2, and A is the bearing area in mm^2.
The bearing area can be calculated using the formula:
A = L * d
where L is the length of the bearing in mm and d is the diameter of the shaft in mm.
Substituting the given values, we get:
A = 1.4d * d = 1.4 * 150 mm * 150 mm
A ≈ 31500 mm^2
Substituting the bearing pressure and bearing area, we get:
F = 1 N/mm^2 * 31500 mm^2
F = 31500 N
Calculating the power loss:
The power loss due to friction can be calculated using the formula:
P_loss = F * V / 1000
where P_loss is the power loss in watts, F is the frictional force in N, and V is the speed of the shaft in mm/s.
Substituting the given values, we get:
P_loss = 31500 N * 15708.04 mm/s / 1000
P_loss ≈ 496.05 watts
Calculating the heat generated:
The heat generated can be calculated using the formula:
Q = P_loss * t
where Q is the heat generated in joules, P_loss is the power loss in watts, and t is the time in seconds.
Assuming the time is 1 second, we get:
Q = 496.05 watts * 1 s
Q = 496.05 joules
Calculating the mass of the oil:
The mass of the oil can be calculated using the formula:
m = Q / (C * ΔT)
where m is the mass of the oil in kg, Q is the heat generated in joules, C is the specific heat of the oil in J/kg°C, and ΔT is the temperature difference across the bearing in °C.
Substituting the given values
- Diameter of the shaft (d) = 150 mm
- Rotational speed of the shaft (N) = 2000 rpm
- Length of the bearing (L) = 1.4 times its diameter = 1.4d = 1.4 * 150 mm
- Bearing pressure (P) = 1 N/mm^2
- Coefficient of friction at the bearing surface (μ) = 0.005
- Temperature difference across the bearing (ΔT) = 15°C
- Specific heat of the oil (C) = 1900 J/kg°C
- Required amount of coolant oil per second = ?
Calculating the bearing speed:
The bearing speed can be calculated using the formula:
V = π * d * N / 60
where V is the speed of the shaft in mm/s, d is the diameter of the shaft in mm, and N is the rotational speed of the shaft in rpm.
Substituting the given values, we get:
V = π * 150 mm * 2000 rpm / 60
V ≈ 15708.04 mm/s
Calculating the frictional force:
The frictional force can be calculated using the formula:
F = P * A
where F is the frictional force in N, P is the bearing pressure in N/mm^2, and A is the bearing area in mm^2.
The bearing area can be calculated using the formula:
A = L * d
where L is the length of the bearing in mm and d is the diameter of the shaft in mm.
Substituting the given values, we get:
A = 1.4d * d = 1.4 * 150 mm * 150 mm
A ≈ 31500 mm^2
Substituting the bearing pressure and bearing area, we get:
F = 1 N/mm^2 * 31500 mm^2
F = 31500 N
Calculating the power loss:
The power loss due to friction can be calculated using the formula:
P_loss = F * V / 1000
where P_loss is the power loss in watts, F is the frictional force in N, and V is the speed of the shaft in mm/s.
Substituting the given values, we get:
P_loss = 31500 N * 15708.04 mm/s / 1000
P_loss ≈ 496.05 watts
Calculating the heat generated:
The heat generated can be calculated using the formula:
Q = P_loss * t
where Q is the heat generated in joules, P_loss is the power loss in watts, and t is the time in seconds.
Assuming the time is 1 second, we get:
Q = 496.05 watts * 1 s
Q = 496.05 joules
Calculating the mass of the oil:
The mass of the oil can be calculated using the formula:
m = Q / (C * ΔT)
where m is the mass of the oil in kg, Q is the heat generated in joules, C is the specific heat of the oil in J/kg°C, and ΔT is the temperature difference across the bearing in °C.
Substituting the given values
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A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. Can you explain this answer?
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A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. 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 A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. 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 A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. Can you explain this answer?.
A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. 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 A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. 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 A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. Can you explain this answer?.
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A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. Can you explain this answer?, a detailed solution for A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. Can you explain this answer? has been provided alongside types of A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A shaft 150 mm in diameter, rotates in a bearing at 2000 rpm. The length of the bearing is 1.4 times its diameter. The bearing pressure is 1 N/mm2 and the coefficient of friction at the bearing surface is 0.005. The temperature of the bearing is entirely controlled by the flow of oil through the bearing. The difference between the outlet and the inlet temperature is 15°C. If the specific heat of the oil is 1900 J/kg°C, the required amount of coolant oil (in g /s) is___________.Correct answer is '87'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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