Fluid flowing has a velocity field given by V =u, sin[a(t – ý/v.F +v,j on=4 %3D where uo Vo, and @ are constants. (a) Determine the streamline that passes through the origin at t 0; at t = 1/20.
Fluid flowing has a velocity field given by V =u, sin[a(t – ý/v.F +v,j on=4 %3D where uo Vo, and @ are constants. (a) Determine the streamline that passes through the origin at t 0; at t = 1/20.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Fluid Mechanics want an answer to the question when it is cos ?
![nepartment of Mathematics
Faculty of Science,
Fluid Mechanics
Prof./ Abo-el-nour Abd-alla
Example 6C9)
Fluid flowing has a velocity field given by
V =u, sin[a(t- ý/v. +vj
where uo Vo, and O are constants.
(a) Determine the streamline that passes through the origin at t = 0; at t =
T/20.
(b) Determine the path line of the particle that was at the origin at t=0: at t
Επ / 2ω .
Solution:
(a) Since u = uo sin[w(t-y/v] and v = vo it follows from Eq. 4.1 that
streamlines are given by the solution of
dy
vo
dx
uo sin[w(t – y/vo)]
и
n which the variables can be separated and the equation integrated (for any
given time f) to give
uo ſsin[w(t-)ky=voſdx
Vo](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb80b8497-29c6-4d7e-bc49-a597db54d2dc%2F6f563d99-9c95-4bfb-be63-8988e90ed162%2Fwawt02a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:nepartment of Mathematics
Faculty of Science,
Fluid Mechanics
Prof./ Abo-el-nour Abd-alla
Example 6C9)
Fluid flowing has a velocity field given by
V =u, sin[a(t- ý/v. +vj
where uo Vo, and O are constants.
(a) Determine the streamline that passes through the origin at t = 0; at t =
T/20.
(b) Determine the path line of the particle that was at the origin at t=0: at t
Επ / 2ω .
Solution:
(a) Since u = uo sin[w(t-y/v] and v = vo it follows from Eq. 4.1 that
streamlines are given by the solution of
dy
vo
dx
uo sin[w(t – y/vo)]
и
n which the variables can be separated and the equation integrated (for any
given time f) to give
uo ſsin[w(t-)ky=voſdx
Vo
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