Consider the steady, viscous, incompressible flow between two infinite plates moving in the same direction, but with different speeds. Directions: - Starting from the full incompressible Navier-Stokes Equations, determine the velocity profile of the fluid, u(y), when the pressure gradient (dp/dx) is constant. State all of your assumptions and boundary conditions and show how those assumptions apply to the terms in the equations. -If the pressure gradient is 5.0 P a/m, the distance between the plates is 0.2 m, and the dynamic viscosity of the fluid is 1.0 × 10–3 Ns/m2 , what is the velocity at y =0.75h when the lower plate is moving at V1 = 20 m/s and the upper plate is moving at V1 = 100 m/s? -What is the shear stress acting on the bottom plate (y=0)?
Consider the steady, viscous, incompressible flow between two infinite plates moving in the same direction, but with different speeds. Directions: - Starting from the full incompressible Navier-Stokes Equations, determine the velocity profile of the fluid, u(y), when the pressure gradient (dp/dx) is constant. State all of your assumptions and boundary conditions and show how those assumptions apply to the terms in the equations. -If the pressure gradient is 5.0 P a/m, the distance between the plates is 0.2 m, and the dynamic viscosity of the fluid is 1.0 × 10–3 Ns/m2 , what is the velocity at y =0.75h when the lower plate is moving at V1 = 20 m/s and the upper plate is moving at V1 = 100 m/s? -What is the shear stress acting on the bottom plate (y=0)?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Consider the steady, viscous, incompressible flow between two infinite plates moving in the
same direction, but with different speeds.
Directions:
- Starting from the full incompressible Navier-Stokes Equations, determine the velocity profile
of the fluid, u(y), when the pressure gradient (dp/dx) is constant. State all of your assumptions
and boundary conditions and show how those assumptions apply to the terms in the equations.
-If the pressure gradient is 5.0 P a/m, the distance between the plates is 0.2 m, and the dynamic
viscosity of the fluid is 1.0 × 10–3 Ns/m2 , what is the velocity at y = 0.75h when the lower plate
is moving at V1 = 20 m/s and the upper plate is moving at V1 = 100 m/s?
-What is the shear stress acting on the bottom plate (y = 0)?
V2
u(y)
V,
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