Problem 1. For uniform flow over a flat plate, a useful approximation for the x-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 = 8) = U. The equation for the profile is given by u/U = 2 (y/d) – (y/8)², where d = cx 1/2 and c is a constant - (a) Show that the simplest expression for the y-component of velocity is (b) Plot u/U and v/U versus y/d at x = separate graphs. 2 *=4[4(9)²¯ +(9)*] = 0.50 m where = 5.0 mm. Use the x-axis for velocity and plot on (c) Find the maximum value for v/U at this location and discuss its magnitude compared to u/U. АУ u(x, y) U
Problem 1. For uniform flow over a flat plate, a useful approximation for the x-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 = 8) = U. The equation for the profile is given by u/U = 2 (y/d) – (y/8)², where d = cx 1/2 and c is a constant - (a) Show that the simplest expression for the y-component of velocity is (b) Plot u/U and v/U versus y/d at x = separate graphs. 2 *=4[4(9)²¯ +(9)*] = 0.50 m where = 5.0 mm. Use the x-axis for velocity and plot on (c) Find the maximum value for v/U at this location and discuss its magnitude compared to u/U. АУ u(x, y) U
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 x-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 = 8) = U. The
equation for the profile is given by
u/U = 2 (y/d) – (y/8)², where d = cx 1/2 and c is a constant
-
(a) Show that the simplest expression for the y-component of velocity is
(b) Plot u/U and v/U versus y/d at x =
separate graphs.
2
*=4[4(9)²¯ +(9)*]
= 0.50 m where = 5.0 mm. Use the x-axis for velocity and plot on
(c) Find the maximum value for v/U at this location and discuss its magnitude compared to u/U.
АУ
u(x, y)
U](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb7a04db-8f0c-4d5a-b7e2-400f7abcc7d1%2Fe8e085be-c028-48c9-ae0a-ea4332b23b19%2F14erwa9_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1. For uniform flow over a flat plate, a useful approximation for the x-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 = 8) = U. The
equation for the profile is given by
u/U = 2 (y/d) – (y/8)², where d = cx 1/2 and c is a constant
-
(a) Show that the simplest expression for the y-component of velocity is
(b) Plot u/U and v/U versus y/d at x =
separate graphs.
2
*=4[4(9)²¯ +(9)*]
= 0.50 m where = 5.0 mm. Use the x-axis for velocity and plot on
(c) Find the maximum value for v/U at this location and discuss its magnitude compared to u/U.
АУ
u(x, y)
U
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