Question
In: Mechanical Engineering
In a two-dimensional vortex flow, the fluid flows in circular paths around the center of the...
In a two-dimensional vortex flow, the fluid flows in circular paths around the center of the vortex. The magnitude of the velocity decreases with distance from the center. The stream function for a two-dimensional vortex centered at the origin is ψ=ln sqrt(x^2+y^2) where the x--y plane is horizontal and x and y are in meters. Show that continuity of the flow is satisfied and determine the magnitude of the horizontal velocity at A, where x=−0.2m, y=0.4m. Express your answer in m/s to three significant figures
Solutions
samet mamat answered 2 years agoRelated Solutions
for a two dimensional flow u =[Sx,Sy,0]^T, show that the fluid element which was initially circular...
for a two dimensional flow u =[Sx,Sy,0]^T, show that the fluid
element which was initially circular in shape will be deformed into
an ellipse with major axes aligned pi/4 with positive x-axis and
justify if this prediction is consistent with the streamline.(need
to provide asketch off the streamlines)
This is a fluid dynamics problem. specially vortex dynamics. Please, Explain how a secondary flow and...
This is a fluid dynamics problem. specially vortex
dynamics.
Please, Explain how a secondary flow and vortex turning
are related in an open channel flow.
please help to me using picture &
equation.
In the steady flow of a Newtonian fluid through a long uniform circular tube, if NRe...
In the steady flow of a Newtonian fluid through a long uniform
circular tube, if NRe <2100 the flow is laminar and
the fluid elements move in smooth, straight, parallel lines. Under
these conditions, it is known that the relation between the flow
rate and the pressure drop in the pipe does not depend upon the
fluid density or the pipe wall material.
Perform a dimensional analysis of this system to determine the
dimensionless groups that apply. Express your result...
An incompressible, Newtonian fluid is flowing through a vertical circular conduit (a pipe). The flow is...
An incompressible, Newtonian fluid is
flowing through a vertical circular conduit (a pipe). The flow is
laminar.
What is the velocity at the inner wall of the pipe? How do you
know?
The pipe has diameter a. The velocity profile in the
pipe is vz = b – c r2.
Please express c in terms of a and b.
(You are applying a boundary condition to solve this problem.)
Where in the pipe is the velocity a maximum?
Please express...
examine the uniform flow and the double flow superposition (flow over the cylinder) for the two-dimensional,...
examine the uniform flow and the double flow
superposition (flow over the cylinder) for the two-dimensional,
incompressible, irrotational flow.
A) flow funcion and velocity potantial.
B) velocity field.
C) stopping points.
D) roller surface.
E) surface pressure distribution.
F) tensile force on the circular cylinder.
G) lifting force on the circular cylinder.
Two satellites are in circular orbits around the earth. The orbit for satellite A is at...
Two satellites are in circular orbits around the earth. The
orbit for satellite A is at a height of 555 km above the earth’s
surface, while that for satellite B is at a height of 778 km. Find
the orbital speed for (a) satellite A and (b) satellite B.
Two satellites are in circular orbits around the earth. The orbit for satellite A is at...
Two satellites are in circular orbits around the earth. The
orbit for satellite A is at a height of 458 km above the earth’s
surface, while that for satellite B is at a height of 732 km. Find
the orbital speed for (a) satellite A and
(b) satellite B.
A two dimensional transverse water waves spread in circular ripples a) show that the amplitude at...
A two dimensional transverse water waves spread in circular
ripples a) show that the amplitude at distance r from the intial
disturbance is proportional to sqrt of r b) the intensity of the
above wave at distant r=2m is 10^-4 W. what is the intensity at 4m
distance?
The stream function in cylindrical coordinates for a two-dimensional flow is given by:  
The stream function in cylindrical
coordinates for a two-dimensional flow is given by:
Ψ = [(a)(r) + (b)/(r)] Sin ϴ
Where “a” and “b” are constants.
a)Does this flow satisfy the continuity?
b)Determine the corresponding velocity
potential in the polar coordinate system.
c) Is this flow irrotational? Why?
The stream function ?? in a two-dimensional flow field is given as ?? = 4?? −...
The stream function ?? in a two-dimensional flow field is given
as ?? = 4?? − 3?? + 7???? (a) Prove that this flow field is
irrotational and that it satisfies the continuity equation. (b) Find the potential flow function Ф(??, ??) for this flow
field with boundary condition Ф = 0 at x = 2, y = 1.
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