A belt moves upward at velocity V, dragging a film of viscous liquid of thickness h as shown in the figure. Gravity is aligned with negative y direction. Near the belt, the fluid moves upward due to no-slip. At its outer edge, the film has a free surface (i.e. no shear stress) Assuming that the only non-zero velocity is v(x), with zero shear stress at the outer film edge. The fluid has viscosity u and density p. Assuming steady flow, no pressure gradient, fully developed flow. Please answer the following: What assumptions can be made about this flow scenario? Write out the N.S. equation governing this flow along the flow direction, and A). C). reduce this equation to a second order ordinary differential equation. D). Find the solution of v(x) to this ODE using appropriate Boundary Conditions.
A belt moves upward at velocity V, dragging a film of viscous liquid of thickness h as shown in the figure. Gravity is aligned with negative y direction. Near the belt, the fluid moves upward due to no-slip. At its outer edge, the film has a free surface (i.e. no shear stress) Assuming that the only non-zero velocity is v(x), with zero shear stress at the outer film edge. The fluid has viscosity u and density p. Assuming steady flow, no pressure gradient, fully developed flow. Please answer the following: What assumptions can be made about this flow scenario? Write out the N.S. equation governing this flow along the flow direction, and A). C). reduce this equation to a second order ordinary differential equation. D). Find the solution of v(x) to this ODE using appropriate Boundary Conditions.
Related questions
Question

Transcribed Image Text:A belt moves upward at velocity V, dragging a film of viscous liquid of thickness h,
as shown in the figure. Gravity is aligned with negative y direction. Near the belt, the fluid
moves upward due to no-slip. At its outer edge, the film has a free surface (i.e. no shear stress).
Assuming that the only non-zero velocity is v(x), with zero shear stress at the outer film edge.
The fluid has viscosity µu and density p. Assuming steady flow, no pressure gradient, fully
developed flow. Please answer the following:
What assumptions can be made about this flow scenario?
Write out the N.S. equation governing this flow along the flow direction, and
A).
C).
reduce this equation to a second order ordinary differential equation.
D).
E).
Find the solution of v(x) to this ODE using appropriate Boundary Conditions.
Find the average velocity Vave in the film.
h s const
y,v
х, и
P.
BELT
2.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
