. 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
Homework Answers
Add Answer to:
. Consider the following two dimensional velocity field ~v(x, y)
= −xy3ˆi + y 4 ˆj....
The velocity in a certain two-dimensional flow field is given by the equation: ✓ = 2xti...
The velocity in a certain two-dimensional flow field is given by the equation: ✓ = 2xti – 2 yı where the velocity is in ft/s when x, y, and t are in feet and seconds, respectively. (a) Is flow steady or unsteady (b) Determine the expression of acceleration (c) Check if the flow is compressible or incompressible (d) Check if the flow is rotational or irrotational (e) Sketch the streamlines of t= ls on a x-y plane W
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.
Consider the following steady, two-dimensional, incompressible velocity field V - (10x +2) i+ (-10y -4) j....
Consider the following steady, two-dimensional, incompressible velocity field V - (10x +2) i+ (-10y -4) j. Is this flow field irrotational? If so, generate an expression for the velocity potential function. 5.
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...
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this...
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
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...
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.
Question 3 4-73 Solution For a given velocity field we are to calculate the vorticity Analysis...
Question 3 4-73 Solution For a given velocity field we are to calculate the vorticity Analysis The velocity field is V = (u, v, w)-(3.0+ 2.Ox-y)--(2.0-2.01.) j+10.5ryk Question 4 4-97 Solution For a given velocity field we are to determine if the flow is rotational or irrotational. 1 The flow is steady. 2 The flow is two-dimensional in the r-eplane. The velocity components for flow over a circular cylinder of radiur are Assumptions Analysis 11,--r sin θ| 1 +
H08.2 (2 points) Given the vector velocity field V(x, y, z, t) = 4t i +...
H08.2 (2 points) Given the vector velocity field V(x, y, z, t) = 4t i + xz j + 2ty3 k a) Is this a valid incompressible flow field? b) Is this flow field irrotational?
The velocity in a certain two-dimensional flow field is given by the equation: ✓ = 2xti – 2 yı where the velocity is in ft/s when x, y, and t are in feet and seconds, respectively. (a) Is flow steady or unsteady (b) Determine the expression of acceleration (c) Check if the flow is compressible or incompressible (d) Check if the flow is rotational or irrotational (e) Sketch the streamlines of t= ls on a x-y plane W
Consider the following steady, two-dimensional, incompressible velocity field V - (10x +2) i+ (-10y -4) j. Is this flow field irrotational? If so, generate an expression for the velocity potential function. 5.
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...
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
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...
Question 3 4-73 Solution For a given velocity field we are to calculate the vorticity Analysis The velocity field is V = (u, v, w)-(3.0+ 2.Ox-y)--(2.0-2.01.) j+10.5ryk Question 4 4-97 Solution For a given velocity field we are to determine if the flow is rotational or irrotational. 1 The flow is steady. 2 The flow is two-dimensional in the r-eplane. The velocity components for flow over a circular cylinder of radiur are Assumptions Analysis 11,--r sin θ| 1 +
H08.2 (2 points) Given the vector velocity field V(x, y, z, t) = 4t i + xz j + 2ty3 k a) Is this a valid incompressible flow field? b) Is this flow field irrotational?
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