Channel flow The flow in a long shallow channel is modeled by the velocity field F = ⟨0, 1 - x2⟩, where R = {(x, y): | x | ≤ 1 and | y | < 5}.a. Sketch R and several streamlines of F.b. Evaluate the curl of F on the lines x = 0, x = 1/4, x = 1/2, and x = 1.c. Compute the circulation on the boundary of the region R.d. How do you explain the fact that the curl of F is nonzero atpoints of R, but the circulation is zero?
Channel flow The flow in a long shallow channel is modeled by the velocity field F = ⟨0, 1 - x2⟩, where R = {(x, y): | x | ≤ 1 and | y | < 5}.a. Sketch R and several streamlines of F.b. Evaluate the curl of F on the lines x = 0, x = 1/4, x = 1/2, and x = 1.c. Compute the circulation on the boundary of the region R.d. How do you explain the fact that the curl of F is nonzero atpoints of R, but the circulation is zero?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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Channel flow The flow in a long shallow channel is modeled by the velocity field F = ⟨0, 1 - x2⟩, where R = {(x, y): | x | ≤ 1 and | y | < 5}.
a. Sketch R and several streamlines of F.
b. Evaluate the curl of F on the lines x = 0, x = 1/4, x = 1/2, and x = 1.
c. Compute the circulation on the boundary of the region R.
d. How do you explain the fact that the curl of F is nonzero at
points of R, but the circulation is zero?
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