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Question 1 (10 points) Rotational Flow and Vorticity The velocity components for a two-dimensional flow are...
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 +
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...
Consider a two-dimensional ?ow with velocity components .Find expressions for the vorticity and the strain rate...
Consider a two-dimensional ?ow with velocity
components
.Find expressions for the
vorticity and the strain rate tensor.
V1 = CT1, 12 = -CT2
. 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
1) What is the equation for the volumetric strain rate? (Hint: Uses dot product). incompressible flow be determined...
1) What is the equation for the volumetric strain rate? (Hint: Uses dot product). incompressible flow be determined from the volumetric strain rate? Given the velocity field V= (u, v) (0.75+1.2x) +(2.25-1.2y ), determine if the flow is incompressible or compressible. (20 pts) How can 2) What is the equation for vorticity? (Hint: Uses cross product). How can irrotational flow be determined from vorticity? Given the velocity field V = (u, v) (0.75+ 1.2x)t+ (2.25 1.2y), determine if the flow...
The velocity component of a two-dimensional flow in an inviscid fluid is . (a) Does this flow not...
The velocity component of a two-dimensional flow in an inviscid
fluid is .
(a) Does this flow not divergent?
(b) Is the flow irrotational?
(c) Draw two lines passing through two points A and B with the
following coordinates:
A: x=1, z=1 ; B:x=1, z=2
Kx u= Kz w=
Kx u= Kz w=
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
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...
Problem M.7 The velocity and pressure are given at two points in the flow field. Assume...
Problem M.7 The velocity and pressure are given at two points in the flow field. Assume that the two points lie in a horizontal plane and that the fluid density is uniform in the flow field and is equal to 1000 kg/m3. Assume steady flow. Do necessary computation, then determine which of the following statements is true (a) The flow in the contraction is nonuniform and irrotational. (b) The flow in the contraction is uniform and irrotational. (c) The flow...
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 +
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...
Consider a two-dimensional ?ow with velocity
components
.Find expressions for the
vorticity and the strain rate tensor.
V1 = CT1, 12 = -CT2
1) What is the equation for the volumetric strain rate? (Hint: Uses dot product). incompressible flow be determined from the volumetric strain rate? Given the velocity field V= (u, v) (0.75+1.2x) +(2.25-1.2y ), determine if the flow is incompressible or compressible. (20 pts) How can 2) What is the equation for vorticity? (Hint: Uses cross product). How can irrotational flow be determined from vorticity? Given the velocity field V = (u, v) (0.75+ 1.2x)t+ (2.25 1.2y), determine if the flow...
The velocity component of a two-dimensional flow in an inviscid
fluid is .
(a) Does this flow not divergent?
(b) Is the flow irrotational?
(c) Draw two lines passing through two points A and B with the
following coordinates:
A: x=1, z=1 ; B:x=1, z=2
Kx u= Kz w=
Kx u= Kz w=
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
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...
Problem M.7 The velocity and pressure are given at two points in the flow field. Assume that the two points lie in a horizontal plane and that the fluid density is uniform in the flow field and is equal to 1000 kg/m3. Assume steady flow. Do necessary computation, then determine which of the following statements is true (a) The flow in the contraction is nonuniform and irrotational. (b) The flow in the contraction is uniform and irrotational. (c) The flow...
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