Given a velocity field as V(x, y, z) = axî – ayĵ With units of velocity in m/sec; x and y in meters; and the constant coefficient a = 0.1 sec-. a) Determine the equation for the streamline passing through the point (x, y, 0) = (2, 8, 0). %3D b) Determine the velocity of a particle at the point (2, 8, 0). c) If we mark the particle passing through the point (Xo, Yo, 0) at to = 0, determine the location of the particle at time t = 20 sec. %3D
Given a velocity field as V(x, y, z) = axî – ayĵ With units of velocity in m/sec; x and y in meters; and the constant coefficient a = 0.1 sec-. a) Determine the equation for the streamline passing through the point (x, y, 0) = (2, 8, 0). %3D b) Determine the velocity of a particle at the point (2, 8, 0). c) If we mark the particle passing through the point (Xo, Yo, 0) at to = 0, determine the location of the particle at time t = 20 sec. %3D
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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![Given a velocity field as
\[ \vec{V}(x, y, z) = ax\hat{i} - ay\hat{j} \]
With units of velocity in m/sec; \( x \) and \( y \) in meters; and the constant coefficient \( a = 0.1 \, \text{sec}^{-1} \).
a) Determine the equation for the streamline passing through the point \( (x, y, 0) = (2, 8, 0) \).
b) Determine the velocity of a particle at the point \( (2, 8, 0) \).
c) If we mark the particle passing through the point \( (x_0, y_0, 0) \) at \( t_0 = 0 \), determine the location of the particle at time \( t = 20 \, \text{sec} \).
d) Show that the equation of the particle path (the pathline) matches the equation of the streamline.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56f48589-eb2d-462d-97e2-ddaf1b0fdc8f%2F56c7cccf-e0b2-4ebc-a7e6-b45f6829a869%2Fkeyo9f2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given a velocity field as
\[ \vec{V}(x, y, z) = ax\hat{i} - ay\hat{j} \]
With units of velocity in m/sec; \( x \) and \( y \) in meters; and the constant coefficient \( a = 0.1 \, \text{sec}^{-1} \).
a) Determine the equation for the streamline passing through the point \( (x, y, 0) = (2, 8, 0) \).
b) Determine the velocity of a particle at the point \( (2, 8, 0) \).
c) If we mark the particle passing through the point \( (x_0, y_0, 0) \) at \( t_0 = 0 \), determine the location of the particle at time \( t = 20 \, \text{sec} \).
d) Show that the equation of the particle path (the pathline) matches the equation of the streamline.
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