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A shaft of diameter 120mm is rotating inside a sleeve at a speed of 360 rpm. The space between the shaft and the sleeve is filled with of viscosity 6 poise. Find the power absorbed in the oil ifthe length of the sleeve is 100mm and thickness of oil is 1.5mm?
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A shaft of diameter 120mm is rotating inside a sleeve at a speed of 36...
Given:
- Diameter of the shaft (D) = 120 mm
- Speed of rotation (N) = 360 rpm
- Viscosity of the oil (μ) = 6 poise
- Length of the sleeve (L) = 100 mm
- Thickness of oil (h) = 1.5 mm
To find:
- Power absorbed in the oil
Solution:
Step 1: Convert units
- Convert the diameter of the shaft from mm to m: D = 120 mm = 0.12 m
- Convert the speed of rotation from rpm to rad/s: N = 360 rpm = (360/60) rad/s = 6 rad/s
- Convert the viscosity of the oil from poise to Ns/m²: μ = 6 poise = 0.6 Ns/m²
- Convert the length of the sleeve from mm to m: L = 100 mm = 0.1 m
- Convert the thickness of the oil from mm to m: h = 1.5 mm = 0.0015 m
Step 2: Calculate the area of the oil film
- The area of the oil film can be approximated as the product of the length of the sleeve and the thickness of the oil: A = L * h
Step 3: Calculate the velocity of the oil film
- The velocity of the oil film can be calculated using the formula: V = (π * N * D) / 60
- Substituting the given values: V = (π * 6 * 0.12) / 60 = 0.03768 m/s
Step 4: Calculate the shear stress on the oil film
- The shear stress on the oil film can be calculated using the formula: τ = μ * (V / h)
- Substituting the given values: τ = 0.6 * (0.03768 / 0.0015) = 15.12 N/m²
Step 5: Calculate the power absorbed in the oil
- The power absorbed in the oil can be calculated using the formula: P = τ * A * V
- Substituting the calculated values: P = 15.12 * (0.1 * 0.0015) * 0.03768 = 0.00907 W
Answer:
The power absorbed in the oil is 0.00907 W.
- Diameter of the shaft (D) = 120 mm
- Speed of rotation (N) = 360 rpm
- Viscosity of the oil (μ) = 6 poise
- Length of the sleeve (L) = 100 mm
- Thickness of oil (h) = 1.5 mm
To find:
- Power absorbed in the oil
Solution:
Step 1: Convert units
- Convert the diameter of the shaft from mm to m: D = 120 mm = 0.12 m
- Convert the speed of rotation from rpm to rad/s: N = 360 rpm = (360/60) rad/s = 6 rad/s
- Convert the viscosity of the oil from poise to Ns/m²: μ = 6 poise = 0.6 Ns/m²
- Convert the length of the sleeve from mm to m: L = 100 mm = 0.1 m
- Convert the thickness of the oil from mm to m: h = 1.5 mm = 0.0015 m
Step 2: Calculate the area of the oil film
- The area of the oil film can be approximated as the product of the length of the sleeve and the thickness of the oil: A = L * h
Step 3: Calculate the velocity of the oil film
- The velocity of the oil film can be calculated using the formula: V = (π * N * D) / 60
- Substituting the given values: V = (π * 6 * 0.12) / 60 = 0.03768 m/s
Step 4: Calculate the shear stress on the oil film
- The shear stress on the oil film can be calculated using the formula: τ = μ * (V / h)
- Substituting the given values: τ = 0.6 * (0.03768 / 0.0015) = 15.12 N/m²
Step 5: Calculate the power absorbed in the oil
- The power absorbed in the oil can be calculated using the formula: P = τ * A * V
- Substituting the calculated values: P = 15.12 * (0.1 * 0.0015) * 0.03768 = 0.00907 W
Answer:
The power absorbed in the oil is 0.00907 W.
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A shaft of diameter 120mm is rotating inside a sleeve at a speed of 360 rpm. The space between the shaft and the sleeve is filled with of viscosity 6 poise. Find the power absorbed in the oil ifthe length of the sleeve is 100mm and thickness of oil is 1.5mm?
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A shaft of diameter 120mm is rotating inside a sleeve at a speed of 360 rpm. The space between the shaft and the sleeve is filled with of viscosity 6 poise. Find the power absorbed in the oil ifthe length of the sleeve is 100mm and thickness of oil is 1.5mm? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A shaft of diameter 120mm is rotating inside a sleeve at a speed of 360 rpm. The space between the shaft and the sleeve is filled with of viscosity 6 poise. Find the power absorbed in the oil ifthe length of the sleeve is 100mm and thickness of oil is 1.5mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shaft of diameter 120mm is rotating inside a sleeve at a speed of 360 rpm. The space between the shaft and the sleeve is filled with of viscosity 6 poise. Find the power absorbed in the oil ifthe length of the sleeve is 100mm and thickness of oil is 1.5mm?.
A shaft of diameter 120mm is rotating inside a sleeve at a speed of 360 rpm. The space between the shaft and the sleeve is filled with of viscosity 6 poise. Find the power absorbed in the oil ifthe length of the sleeve is 100mm and thickness of oil is 1.5mm? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A shaft of diameter 120mm is rotating inside a sleeve at a speed of 360 rpm. The space between the shaft and the sleeve is filled with of viscosity 6 poise. Find the power absorbed in the oil ifthe length of the sleeve is 100mm and thickness of oil is 1.5mm? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shaft of diameter 120mm is rotating inside a sleeve at a speed of 360 rpm. The space between the shaft and the sleeve is filled with of viscosity 6 poise. Find the power absorbed in the oil ifthe length of the sleeve is 100mm and thickness of oil is 1.5mm?.
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