A two dimensional incompressible flow is given by the velocity field V = 3yi + 2xj,...
A two dimensional incompressible flow is given by the velocity field V = 3yi + 2xj, in arbitrary units. Does this flow satisfy continuity? If so, find the stream function ψ(x,y) and plot a few streamlines, with arrows.
Homework Answers
Use formula for continuity and after that stream function
equation to calculate it.then draw graph for stream lines.
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A two dimensional incompressible flow is given by the velocity
field V = 3yi + 2xj,...
Incompressible fluid flow field 2. (a) An incompressible fluid flow field is given as Vx =...
Incompressible fluid flow field
2. (a) An incompressible fluid flow field is given as Vx = x2+y+z2 and Vy=xy+yz+z, what is V?=? that satisfies continuity equation? (b) Plot the 2-D flow field represented by Vx=2y, Vy=4x. First obtain an expression for stream function, and then plot flow lines corresponding to constant stream function values.
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 -...
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
Q1. (a) The velocity components of a certain two-dimensional flow field are claimed to be given...
Q1. (a) The velocity components of a certain two-dimensional flow field are claimed to be given by u = -Cy and v = Cx , where is a constant. (i) Does this velocity distribution satisfy continuity? If yes, what is the stream function y ? (8 marks) (ii) Analyse whether the flow is rotational or irrotational. What is the velocity potential o ? (4 marks) (iii) Sketch several y and lines (if exist) of the flow field. Briefly explain how...
Q1. (a) The velocity components of a certain two-dimensional flow field are claimed to be given...
Q1. (a) The velocity components of a certain two-dimensional flow field are claimed to be given by u =-Cy and v = Cx , where is a constant. (i) Does this velocity distribution satisfy continuity? If yes, what is the stream function y? (8 marks) (ii) Analyse whether the flow is rotational or irrotational. What is the velocity potential o ? (4 marks) (iii) Sketch several y and © lines (if exist) of the flow field. Briefly explain how you...
can you solve the last question (e) Q1. Consider a steady, two-dimensional, incompressible flow field has...
can you solve the last question
(e)
Q1. Consider a steady, two-dimensional, incompressible flow field has the velocity potential a) b) c) 2 (x-7)(x+y) Determine the velocity components and verify that continuity is satisfied. [4 marks] Verify that the flow is irrotational. [2 marks] Determine the corresponding stream function. [4 marks) Now, consider a steady, two-dimensional, incompressible flow defined by velocity components u = ax + b&v=-ay + cx, where a, b and care constants. Neglect gravity. d) e) Show...
The x and y components of the velocity field of a three-dimensional incompressible flow are given...
The x and y components of the velocity field of a three-dimensional incompressible flow are given by U = xv; V = -y-1 Find the expression for the z component of the velocity that vanishes at the origin.
. Consider the following two dimensional velocity field ~v(x, y) = −xy3ˆi + y 4 ˆj....
. Consider the following two dimensional velocity field ~v(x, y) = −xy3ˆi + y 4 ˆj. (a) Sketch a figure of the streamlines for this flow field. Include arrows on your streamlines to indicate the direction of the flow. (b) Is this flow field incompressible or compressible? Show all work. (c) Derive an expression for the vorticity vector ~ζ for this flow field. (d) Is this flow field rotational or irrotational? Provide some evidence in support of your answer
ents of a steady state, incompressible two dimensional flow is given by u 2y determine the...
ents of a steady state, incompressible two dimensional flow is given by u 2y determine the corresponding stream function and sketc h the stream lines. Specify the line of (solid Boundaries) and plot all possible streamlines.
The following two-dimensional incompressible flow field is given: u = x2y v = x (1 –...
The following two-dimensional incompressible flow field is
given:
u = x2y
v = x (1 – y2)
Find pressure distribution, i.e., P=P(x,y), assuming no
gravity in x and y directions.
1) The following two-dimensional incompressible flow field is given u-xy Find pressure distribution, ie, p-P(y), assuming no gravity in x and y directions.
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y...
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y = vzt where a is a positive constant. • Sketch the streamlines for the given flow field in the xy-plane at a given time, t. Be sure to specify the direction of the streamlines in your plot. Determine if the fluid in the flow field is incompressible. Determine if the flow field is irrotational. If so, find the corresponding velocity potential and sketch a...
Incompressible fluid flow field
2. (a) An incompressible fluid flow field is given as Vx = x2+y+z2 and Vy=xy+yz+z, what is V?=? that satisfies continuity equation? (b) Plot the 2-D flow field represented by Vx=2y, Vy=4x. First obtain an expression for stream function, and then plot flow lines corresponding to constant stream function values.
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
Q1. (a) The velocity components of a certain two-dimensional flow field are claimed to be given by u = -Cy and v = Cx , where is a constant. (i) Does this velocity distribution satisfy continuity? If yes, what is the stream function y ? (8 marks) (ii) Analyse whether the flow is rotational or irrotational. What is the velocity potential o ? (4 marks) (iii) Sketch several y and lines (if exist) of the flow field. Briefly explain how...
Q1. (a) The velocity components of a certain two-dimensional flow field are claimed to be given by u =-Cy and v = Cx , where is a constant. (i) Does this velocity distribution satisfy continuity? If yes, what is the stream function y? (8 marks) (ii) Analyse whether the flow is rotational or irrotational. What is the velocity potential o ? (4 marks) (iii) Sketch several y and © lines (if exist) of the flow field. Briefly explain how you...
can you solve the last question
(e)
Q1. Consider a steady, two-dimensional, incompressible flow field has the velocity potential a) b) c) 2 (x-7)(x+y) Determine the velocity components and verify that continuity is satisfied. [4 marks] Verify that the flow is irrotational. [2 marks] Determine the corresponding stream function. [4 marks) Now, consider a steady, two-dimensional, incompressible flow defined by velocity components u = ax + b&v=-ay + cx, where a, b and care constants. Neglect gravity. d) e) Show...
ents of a steady state, incompressible two dimensional flow is given by u 2y determine the corresponding stream function and sketc h the stream lines. Specify the line of (solid Boundaries) and plot all possible streamlines.
The following two-dimensional incompressible flow field is
given:
u = x2y
v = x (1 – y2)
Find pressure distribution, i.e., P=P(x,y), assuming no
gravity in x and y directions.
1) The following two-dimensional incompressible flow field is given u-xy Find pressure distribution, ie, p-P(y), assuming no gravity in x and y directions.
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y = vzt where a is a positive constant. • Sketch the streamlines for the given flow field in the xy-plane at a given time, t. Be sure to specify the direction of the streamlines in your plot. Determine if the fluid in the flow field is incompressible. Determine if the flow field is irrotational. If so, find the corresponding velocity potential and sketch a...
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