2. Consider a stream function given by = (²+x²).(a) Does this flow satisfy conservation of mass? Show your work.(b) Plot the streamlines for this flow. Let K= 2. Be sure to indicate the direction of the flow.(c) Is this flow irrotational? If so, find the velocity potential for this flow. If not, show that avelocity potential does not exist.(d) Describe the flow represented by this stream function.

Given: Stream function: To find: Does it satisfy conservation of mass Plot streamline of flow Is…

Consider a stream function given by = (²+x²). (a) Does this flow satisfy conservation of mass? Show your work. (b) Plot the streamlines for this flow. Let K = 2. Be sure to indicate the direction of the flow. (e) Is this flow irrotational? If so, find the velocity potential for this flow. If not, show that a velocity potential does not exist. (d) Describe the flow represented by this stream function.

Consider a stream function given by = (²+x²). (a) Does this flow satisfy conservation of mass? Show your work. (b) Plot the streamlines for this flow. Let K = 2. Be sure to indicate the direction of the flow. (e) Is this flow irrotational? If so, find the velocity potential for this flow. If not, show that a velocity potential does not exist. (d) Describe the flow represented by this stream function.

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

See similar textbooks

Similar questions

Consider steady flow of water through an axisymmetric garden hose nozzle. The axial component of velocity increases linearly from uz, entrance to uz, exit as sketched. Between z = 0 and z = L, the axial velocity component is given by uz = uz,entrance + [(uz,exit − uz,entrance)/L]z. Generate an expression for the radial velocity component ur between z = 0 and z = L. You may ignore frictional effects on the walls.
Problem 1 Given a steady flow, where the velocity is described by: u = 3 cos(x) + 2ry v = 3 sin(y) + 2?y !! !! a) Find the stream function if it exists. b) Find the potential function if it exists. c) For a square with opposite diagonal corners at (0,0) and (47, 27), evaluate the circu- lation I = - f V.ds where c is a closed path around the square. d) Calculate the substantial derivative of velocity at the center of the same box.
QI A/ The inviscid, steady, and incompressible 2D flows are given by (a) o =x- 3xy (b) y = x-2xy-y? In each case, find the components of velocity in x- and y-directions.
In plane stagnation flow, an incompressible fluid occupying the space y>0 has one velocity component given by Vx-x. The flow is two-dimensional and steady, such that V₂=0 and nothing depends on z or time t. (a) Use the continuity equation to determine Vy(x,y), given that Vy(x,0) =0. (This condition for Vy corresponds to the plane y=0 being an impenetrable boundary.) (b) is arbitrary, so you may set Y=0 at any convenient location.) Determine the stream function for this flow, (x,y). (The absolute value of
In two dimensions along the converging nozzle, stable, considering incompressible flow. The velocity on the horizontal centerline (x-axis) is given as V=V1(1+x/L)i Derive an equation for the acceleration of a particle moving along the centerline using (a) Euler's approximation and (b) Lagrangian approximation. Discuss the acceleration for the particle being at the beginning and end of the channel.
3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at 150°. The intent is to use this cylinder as a stream velocimeter, i.e. a device to determine the velocity of a stream by measuring the pressures at the two taps. The fluid is incompressible with a density of p. Figure for Part (a) U Figure for Part (b) 30 a) Using potential flow approximation, derive a formula for calculating U from the measured pressure difference at the two pressure taps. Note that for accurate measurement, the velocimeter must be aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: 2|Aptaps|/p ) b) Suppose the velocimeter has been misaligned by ổ degrees so that the two pressure taps are now at 180° + 8 and 150° + 8. Derive an expression for the percent error in stream velocity measurement. Then, calculate the error for 8 = 5°,10° and –10°. (Ans: [2/(sin2(150 + 8) – sin²(180 + 8) )– 1] × 100 )
Velocity components in the flow of an ideal fluid in a horizontal plane; Given as u = 16 y - 12 x , v = 12 y - 9 x a) Is the current continuous?(YES OR NO) b) Can the potential function be defined?(YES OR NO) c) Find the unit width flow passing between the origin and the point A(2,4). (y(0,0)=0) d) Calculate the pressure difference between the origin and the point B(3;3).
The velocity of flow of fluid is represented by the equation: V=2xi +3vj. The equation of the stream line passing through the point (4,3) is (A) 0.72x = 1,2 (B)¹ = 0.72x¹/² (C) 0.72x2=2 (D) None of these
For a flow in the xy plane, the x component of the velocity is u=3x2y-y3is given. Determine the y component for steady state and incompressible flow. Does this result also apply to unstable, incompressible flow? Why is that? How many possible y components are there? Discuss.
1. Find the stream function for a parallel flow of uniform velocity V0 making an angle α with the x-axis. 2. A certain flow field is described by the stream function ψ = xy. (a) Sketch the flow field. (b) Find the x and y velocity components at [0, 0], [1, 1], [∞, 0], and [4, 1]. (c) Find the volume flow rate per unit width flowing between the streamlines passing through points [0, 0] and [1, 1], and points [1, 2] and [5, 3].
1. For incompressible flows, their velocity field 2. In the case of axisymmetric 2D incompressible flows, where is Stokes' stream function, and u = VXS, S(r, z, t) = Uz = where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence 1 Ꭷ r dr 1 dy r dz Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads Y(R, 0, t) R sin 0 S(R, 0, t) UR uo Y(r, z, t) r = = -eq, and Up = = 1 ay R2 sin Ꮎ ᎧᎾ 1 ƏY R sin Ꮎ ᎧR -eq 2 (1) (2) (3)
Q.5 A stream function is given by Y = (x² – y2). The Velocity potential function (b) of the flow will be A 2xy + f(x) B -2xy + constant © 2(x2 -y2) D 2xy + f(y)