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Oil of viscosity μ = 0.0357 Pa's and density p = 0.796 kg/m³ is sandwiched in the small gap between two very large parallel flat plates. A third flat plate of surface area A = 20. 0 cm x 20. 0 cm (on one side) is dragged through the oil at steady velocity V = 1.00 m/s to the right as sketched. The top plate is stationary, but the bottom plate is moving at velocity V = 0.300 m/s to the left as sketched. The heights are h₁ = 1.00 mm and h2 = 1.65 mm. The force required to pull the plate through the oil is F. (a) Sketch the velocity profiles and calculate the distance ya where the velocity is zero. Hint: Since the gaps are small and the oil is very viscous, the velocity profiles are linear in both gaps. Use the no-slip conditions at the walls to determine the velocity profile in each gap. (b) Calculate force F in newtons (N) required to keep the middle plate moving at constant speed. Oil Oil H, P H, P h₁ h₂ Area = A Area = A УА V = 1.00 m/s Vw = 0.300 m/s F

Oil of viscosity μ = 0.0357 Pa's and density p = 0.796 kg/m³ is sandwiched in the small gap between two very large parallel flat plates. A third flat plate of surface area A = 20. 0 cm x 20. 0 cm (on one side) is dragged through the oil at steady velocity V = 1.00 m/s to the right as sketched. The top plate is stationary, but the bottom plate is moving at velocity V = 0.300 m/s to the left as sketched. The heights are h₁ = 1.00 mm and h2 = 1.65 mm. The force required to pull the plate through the oil is F. (a) Sketch the velocity profiles and calculate the distance ya where the velocity is zero. Hint: Since the gaps are small and the oil is very viscous, the velocity profiles are linear in both gaps. Use the no-slip conditions at the walls to determine the velocity profile in each gap. (b) Calculate force F in newtons (N) required to keep the middle plate moving at constant speed. Oil Oil H, P H, P h₁ h₂ Area = A Area = A УА V = 1.00 m/s Vw = 0.300 m/s F

Fundamentals of Geotechnical Engineering (MindTap Course List)
Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN:9781305635180
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Braja M. Das, Nagaratnam Sivakugan
Chapter7: Seepage
Section: Chapter Questions
Problem 7.1P
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Oil of viscosity μ = 0.0357 Pa's and density p = 0.796 kg/m³ is sandwiched in the small gap between two very large parallel flat plates. A third flat plate of surface area A = 20. 0 cm x 20. 0 cm (on one side) is dragged through the oil at steady velocity V= 1.00 m/s to the right as sketched. The top plate is stationary, but the bottom plate is moving at velocity V = 0.300 m/s to the left as sketched. The heights are h₁ = 1.00 mm and h2 = 1.65 mm. The force required to pull the plate through the oil is F. (a) Sketch the velocity profiles and calculate the distance ya where the velocity is zero. Hint: Since the gaps are small and the oil is very viscous, the velocity profiles are linear in both gaps. Use the no-slip conditions at the walls to determine the velocity profile in each gap. (b) Calculate force F in newtons (N) required to keep the middle plate moving at constant speed. Oil Oil H, P H₂ P h₁ h₂ Area = A Area = A УА V = 1.00 m/s V₁ = 0.300 m/s F
Transcribed Image Text:Oil of viscosity μ = 0.0357 Pa's and density p = 0.796 kg/m³ is sandwiched in the small gap between two very large parallel flat plates. A third flat plate of surface area A = 20. 0 cm x 20. 0 cm (on one side) is dragged through the oil at steady velocity V= 1.00 m/s to the right as sketched. The top plate is stationary, but the bottom plate is moving at velocity V = 0.300 m/s to the left as sketched. The heights are h₁ = 1.00 mm and h2 = 1.65 mm. The force required to pull the plate through the oil is F. (a) Sketch the velocity profiles and calculate the distance ya where the velocity is zero. Hint: Since the gaps are small and the oil is very viscous, the velocity profiles are linear in both gaps. Use the no-slip conditions at the walls to determine the velocity profile in each gap. (b) Calculate force F in newtons (N) required to keep the middle plate moving at constant speed. Oil Oil H, P H₂ P h₁ h₂ Area = A Area = A УА V = 1.00 m/s V₁ = 0.300 m/s F
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