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Problem 1. For uniform flow over a flat plate, a useful approximation for the z-component of velocity in an incompressible laminar boundary layer is a parabolic variation from the velocity at the surface, u (y - 0) = 0 due to no- slip condition, to the free-stream velocity at the edge of the boundary layer, u (y- 6) - U. The equation for the profile is given by u/U = 2 (y/6) - (w/5)², where & - cz!/? and c is a constant (a) Show that the simplest expression for the y-component of velocity is tb) Plot u/U and e/U versus y/6 at z= 0.50 m where & = 5.0 mm. Use the z-axis for velocity and plot on separate graphs. ) Find the maximum value for e/U at this location and discuss its magnitude compared to u/U. u(z, y)

Problem 1. For uniform flow over a flat plate, a useful approximation for the z-component of velocity in an incompressible laminar boundary layer is a parabolic variation from the velocity at the surface, u (y - 0) = 0 due to no- slip condition, to the free-stream velocity at the edge of the boundary layer, u (y- 6) - U. The equation for the profile is given by u/U = 2 (y/6) - (w/5)², where & - cz!/? and c is a constant (a) Show that the simplest expression for the y-component of velocity is tb) Plot u/U and e/U versus y/6 at z= 0.50 m where & = 5.0 mm. Use the z-axis for velocity and plot on separate graphs. ) Find the maximum value for e/U at this location and discuss its magnitude compared to u/U. u(z, y)

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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Problem 1. For uniform flow over a flat plate, a useful approximation for the z-component of velocity in an incompressible laminar boundary layer is a parabolic variation from the velocity at the surface, u (y - 0) = 0 due to no- slip condition, to the free-stream velocity at the edge of the boundary layer, u (y- 6) - U. The equation for the profile is given by u/U = 2 (y/6) - (w/5)², where & - cz!/? and c is a constant (a) Show that the simplest expression for the y-component of velocity is tb) Plot u/U and e/U versus y/6 at z= 0.50 m where & = 5.0 mm. Use the z-axis for velocity and plot on separate graphs. ) Find the maximum value for e/U at this location and discuss its magnitude compared to u/U. u(z, y)
Transcribed Image Text:Problem 1. For uniform flow over a flat plate, a useful approximation for the z-component of velocity in an incompressible laminar boundary layer is a parabolic variation from the velocity at the surface, u (y - 0) = 0 due to no- slip condition, to the free-stream velocity at the edge of the boundary layer, u (y- 6) - U. The equation for the profile is given by u/U = 2 (y/6) - (w/5)², where & - cz!/? and c is a constant (a) Show that the simplest expression for the y-component of velocity is tb) Plot u/U and e/U versus y/6 at z= 0.50 m where & = 5.0 mm. Use the z-axis for velocity and plot on separate graphs. ) Find the maximum value for e/U at this location and discuss its magnitude compared to u/U. u(z, y)
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