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a) Given the stream function = x² + y³, provide an equation for the streamline that passes through the point (x, y) = (1,2). What is the speed and direction of the fluid at this point? Is the speed zero at any point on this streamline? b) A velocity field has the following form in cylindrical coordinates: v=Kr. Compute the angular velocity, the vorticity vector, and the rate of strain tensor for this flow. For what value of n is the flow irrotational? For what value of n is the strain identically zero? c) For 0≤ y ≤8, the velocity of a fluid near a horizontal wall has the form У uuo 2 v = 0 Determine the vorticity vector, the rate of strain tensor, and the stream function. Show that the velocity potential does not exist. For an initially-square fluid element at y = 8/2, sketch its shape a short time later.

a) Given the stream function = x² + y³, provide an equation for the streamline that passes through the point (x, y) = (1,2). What is the speed and direction of the fluid at this point? Is the speed zero at any point on this streamline? b) A velocity field has the following form in cylindrical coordinates: v=Kr. Compute the angular velocity, the vorticity vector, and the rate of strain tensor for this flow. For what value of n is the flow irrotational? For what value of n is the strain identically zero? c) For 0≤ y ≤8, the velocity of a fluid near a horizontal wall has the form У uuo 2 v = 0 Determine the vorticity vector, the rate of strain tensor, and the stream function. Show that the velocity potential does not exist. For an initially-square fluid element at y = 8/2, sketch its shape a short time later.

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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Please show all work,  for a,b, and c!!!

a) Given the stream function = x² + y³, provide an equation for the streamline that passes through the point (x, y) = (1,2). What is the speed and direction of the fluid at this point? Is the speed zero at any point on this streamline? b) A velocity field has the following form in cylindrical coordinates: v=Kr. Compute the angular velocity, the vorticity vector, and the rate of strain tensor for this flow. For what value of n is the flow irrotational? For what value of n is the strain identically zero? c) For 0≤ y ≤8, the velocity of a fluid near a horizontal wall has the form У uuo 2 v = 0 Determine the vorticity vector, the rate of strain tensor, and the stream function. Show that the velocity potential does not exist. For an initially-square fluid element at y = 8/2, sketch its shape a short time later.
Transcribed Image Text:a) Given the stream function = x² + y³, provide an equation for the streamline that passes through the point (x, y) = (1,2). What is the speed and direction of the fluid at this point? Is the speed zero at any point on this streamline? b) A velocity field has the following form in cylindrical coordinates: v=Kr. Compute the angular velocity, the vorticity vector, and the rate of strain tensor for this flow. For what value of n is the flow irrotational? For what value of n is the strain identically zero? c) For 0≤ y ≤8, the velocity of a fluid near a horizontal wall has the form У uuo 2 v = 0 Determine the vorticity vector, the rate of strain tensor, and the stream function. Show that the velocity potential does not exist. For an initially-square fluid element at y = 8/2, sketch its shape a short time later.
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