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Problem 2: Average Velocity for Mass Balance in Flow down a Vertical Plate For a layer of liquid flowing in a laminar flow in the z direction down a vertical plate or surface, the velocity profile is: Pg8? V, = 2µ Where dis the thickness of the layer, x is the distance from the free surface of liquid toward the plate, and vz is the velocity at a distance x from the free surface. Consider the wall to have a depth of w in the y-direction and a length L in the z-direction. (a) Provide a sketch of the system described above with appropriate coordinates and origin point (b) What is the maximum velocity vz-mar? Show that the expression you get has the units of velocity. (c) Derive the expression for the average velocity vz-av and relate that to vz-max

Problem 2: Average Velocity for Mass Balance in Flow down a Vertical Plate For a layer of liquid flowing in a laminar flow in the z direction down a vertical plate or surface, the velocity profile is: Pg8? V, = 2µ Where dis the thickness of the layer, x is the distance from the free surface of liquid toward the plate, and vz is the velocity at a distance x from the free surface. Consider the wall to have a depth of w in the y-direction and a length L in the z-direction. (a) Provide a sketch of the system described above with appropriate coordinates and origin point (b) What is the maximum velocity vz-mar? Show that the expression you get has the units of velocity. (c) Derive the expression for the average velocity vz-av and relate that to vz-max

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Berlin, 1963, 67-77. 2B Problem 2: Average Velocity for Mass Balance in Flow down a Vertical Plate For a layer of liquid flowing in a laminar flow in the z direction down a vertical plate or surface, the velocity profile is: నgరా Where dis the thickness of the layer, x is the distance from the free surface of liquid toward the plate, and vz is the velocity at a distance x from the free surface. Consider the wall to have a depth of w in the y-direction and a length L in the z-direction. (a) Provide a sketch of the system described above with appropriate coordinates and origin point (b) What is the maximum velocity vz-max? Show that the expression you get has the units of velocity. (c) Derive the expression for the average velocity vz-av and relate that to Vz-max (d) Derive an expression for the total volumetric flow rate down the wall. Show that the expression you get has the units of m/s. (e) Calculate the shear acting on the x-surface at x=8. You are given the relationship between shear and velocities as: T =- What are the units of shear you obtain? %3D XZ (f) Calculate the drag force on the wall. What is the unit of drag you obtain?
Transcribed Image Text:Berlin, 1963, 67-77. 2B Problem 2: Average Velocity for Mass Balance in Flow down a Vertical Plate For a layer of liquid flowing in a laminar flow in the z direction down a vertical plate or surface, the velocity profile is: నgరా Where dis the thickness of the layer, x is the distance from the free surface of liquid toward the plate, and vz is the velocity at a distance x from the free surface. Consider the wall to have a depth of w in the y-direction and a length L in the z-direction. (a) Provide a sketch of the system described above with appropriate coordinates and origin point (b) What is the maximum velocity vz-max? Show that the expression you get has the units of velocity. (c) Derive the expression for the average velocity vz-av and relate that to Vz-max (d) Derive an expression for the total volumetric flow rate down the wall. Show that the expression you get has the units of m/s. (e) Calculate the shear acting on the x-surface at x=8. You are given the relationship between shear and velocities as: T =- What are the units of shear you obtain? %3D XZ (f) Calculate the drag force on the wall. What is the unit of drag you obtain?
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