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A hydraulic lift used for lifting automobiles has 20 cm diameter ram which slides in a 20.016 cm diameter cylinder. The annular space between the cylinder and ram is filled with an oil of kinematic viscosity 3.5 strokes and relative density 0.85. If the travel of 3.2 m long ram has a uniform rate of 15 cm/s, estimate the frictional resistance experienced by the ram.
Correct answer is 'Range: 1.10 to 1.15'. Can you explain this answer?
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A hydraulic lift used for lifting automobiles has 20 cm diameter ram ...
Kinematic viscosity
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ν = 3.5 stokes = 3.5 cm2/s = 3.5 × 10−4 m2/s
Mass density ρ = 0.85 × 1000 = 850 kg/m3
∴ Dynamic viscosity μ = ρ ν
= 850 × (3.5 × 10-4)
= 0.2975 N s/m2
Thickness of oil film
=(20.016 − 20) / 2 × 10-2
= 0.00008 m
Shear stress τ = μ du / dy = μ V / t
= 0.2975 × 0.15 / 0.00008 m
= 557.81 N/m2
Frictional resistance
= shear stress × area
= 557.81 × (π × 0.20 × 3.2)
= 1121 N = 1.12 kN
Most Upvoted Answer
A hydraulic lift used for lifting automobiles has 20 cm diameter ram ...
Solution:
Given data:
Diameter of ram (d1) = 20 cm
Diameter of cylinder (d2) = 20.016 cm
Length of ram (L) = 3.2 m
Uniform rate of lift (v) = 15 cm/s
Kinematic viscosity of oil (ν) = 3.5 strokes
Relative density of oil (ρ) = 0.85
To find: Frictional resistance experienced by the ram
Area of the ram (A1) = πd1^2/4
= 3.14 x (20/2)^2
= 314 cm^2
Area of the cylinder (A2) = πd2^2/4
= 3.14 x (20.016/2)^2
= 314.16 cm^2
Area of annular space (A) = A2 - A1
= 314.16 - 314
= 0.16 cm^2
Volume of oil in the annular space (V) = AL
= 0.16 x 320
= 51.2 cm^3
Mass of oil (m) = ρV
= 0.85 x 51.2
= 43.52 g
Force required to lift the ram (F) = mg
= 0.04352 x 9.81
= 0.427 N
Velocity gradient (dv/dx) = v/L
= 15/320
= 0.0469 cm/s/cm
Shear stress (τ) = 4ν(dv/dx)
= 4 x 3.5 x 0.0469
= 0.653 N/cm^2
Frictional resistance (R) = τA
= 0.653 x 0.16
= 0.1045 N
Therefore, the frictional resistance experienced by the ram is in the range of 1.10 to 1.15 N (rounded off to two decimal places).
Conclusion:
The frictional resistance experienced by the ram in lifting an automobile using a hydraulic lift is estimated to be in the range of 1.10 to 1.15 N.
Given data:
Diameter of ram (d1) = 20 cm
Diameter of cylinder (d2) = 20.016 cm
Length of ram (L) = 3.2 m
Uniform rate of lift (v) = 15 cm/s
Kinematic viscosity of oil (ν) = 3.5 strokes
Relative density of oil (ρ) = 0.85
To find: Frictional resistance experienced by the ram
Area of the ram (A1) = πd1^2/4
= 3.14 x (20/2)^2
= 314 cm^2
Area of the cylinder (A2) = πd2^2/4
= 3.14 x (20.016/2)^2
= 314.16 cm^2
Area of annular space (A) = A2 - A1
= 314.16 - 314
= 0.16 cm^2
Volume of oil in the annular space (V) = AL
= 0.16 x 320
= 51.2 cm^3
Mass of oil (m) = ρV
= 0.85 x 51.2
= 43.52 g
Force required to lift the ram (F) = mg
= 0.04352 x 9.81
= 0.427 N
Velocity gradient (dv/dx) = v/L
= 15/320
= 0.0469 cm/s/cm
Shear stress (τ) = 4ν(dv/dx)
= 4 x 3.5 x 0.0469
= 0.653 N/cm^2
Frictional resistance (R) = τA
= 0.653 x 0.16
= 0.1045 N
Therefore, the frictional resistance experienced by the ram is in the range of 1.10 to 1.15 N (rounded off to two decimal places).
Conclusion:
The frictional resistance experienced by the ram in lifting an automobile using a hydraulic lift is estimated to be in the range of 1.10 to 1.15 N.
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A hydraulic lift used for lifting automobiles has 20 cm diameter ram which slides in a 20.016 cm diameter cylinder. The annular space between the cylinder and ram is filled with an oil of kinematic viscosity 3.5 strokes and relative density 0.85. If the travel of 3.2 m long ram has a uniform rate of 15 cm/s, estimate the frictional resistance experienced by the ram.Correct answer is 'Range: 1.10 to 1.15'. Can you explain this answer?
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A hydraulic lift used for lifting automobiles has 20 cm diameter ram which slides in a 20.016 cm diameter cylinder. The annular space between the cylinder and ram is filled with an oil of kinematic viscosity 3.5 strokes and relative density 0.85. If the travel of 3.2 m long ram has a uniform rate of 15 cm/s, estimate the frictional resistance experienced by the ram.Correct answer is 'Range: 1.10 to 1.15'. Can you explain this answer? 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 hydraulic lift used for lifting automobiles has 20 cm diameter ram which slides in a 20.016 cm diameter cylinder. The annular space between the cylinder and ram is filled with an oil of kinematic viscosity 3.5 strokes and relative density 0.85. If the travel of 3.2 m long ram has a uniform rate of 15 cm/s, estimate the frictional resistance experienced by the ram.Correct answer is 'Range: 1.10 to 1.15'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hydraulic lift used for lifting automobiles has 20 cm diameter ram which slides in a 20.016 cm diameter cylinder. The annular space between the cylinder and ram is filled with an oil of kinematic viscosity 3.5 strokes and relative density 0.85. If the travel of 3.2 m long ram has a uniform rate of 15 cm/s, estimate the frictional resistance experienced by the ram.Correct answer is 'Range: 1.10 to 1.15'. Can you explain this answer?.
A hydraulic lift used for lifting automobiles has 20 cm diameter ram which slides in a 20.016 cm diameter cylinder. The annular space between the cylinder and ram is filled with an oil of kinematic viscosity 3.5 strokes and relative density 0.85. If the travel of 3.2 m long ram has a uniform rate of 15 cm/s, estimate the frictional resistance experienced by the ram.Correct answer is 'Range: 1.10 to 1.15'. Can you explain this answer? 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 hydraulic lift used for lifting automobiles has 20 cm diameter ram which slides in a 20.016 cm diameter cylinder. The annular space between the cylinder and ram is filled with an oil of kinematic viscosity 3.5 strokes and relative density 0.85. If the travel of 3.2 m long ram has a uniform rate of 15 cm/s, estimate the frictional resistance experienced by the ram.Correct answer is 'Range: 1.10 to 1.15'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hydraulic lift used for lifting automobiles has 20 cm diameter ram which slides in a 20.016 cm diameter cylinder. The annular space between the cylinder and ram is filled with an oil of kinematic viscosity 3.5 strokes and relative density 0.85. If the travel of 3.2 m long ram has a uniform rate of 15 cm/s, estimate the frictional resistance experienced by the ram.Correct answer is 'Range: 1.10 to 1.15'. Can you explain this answer?.
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