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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...
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 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.
W The stream function « in a two-dimensional flow field is given as Q = 4x...
W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
Q1.a) Consider a two dimensional, incompressible flow in cylindirical coordianates; the tangential velocity component is uq K/r, where K is a constant. Generate an expression for the other veloci...
Q1.a) Consider a two dimensional, incompressible flow in cylindirical coordianates; the tangential velocity component is uq K/r, where K is a constant. Generate an expression for the other velocity components, u.. b) Velocity profile in the pipe flow is given Determine; i) Potential and stream functions, ii) Define the stream function at the wall iii) Draw the stream and potential lines in the pipe flow
Q1.a) Consider a two dimensional, incompressible flow in cylindirical coordianates; the tangential velocity component is...
Question 1 (10 points) Rotational Flow and Vorticity The velocity components for a two-dimensional flow are...
Question 1 (10 points) Rotational Flow and Vorticity The velocity components for a two-dimensional flow are u = ln hie) v = created where C is a constant. Is the flow irrotational?
1. The velocity in a certain two-dimensional flow field is given by the equation -= 2zt의...
1. The velocity in a certain two-dimensional flow field is given by the equation -= 2zt의 _ 2yte2 where the velocity is in ft/s when x, y, and t are in feet and seconds, respectively. Determine expressions for the local and convective components of acceleration in the x and y direc tions. What is the magnitude and direction of the velocity and the acceleration at the point x = y = 2 ft at the time t = 0.
. 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
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.
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...
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
W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
Q1.a) Consider a two dimensional, incompressible flow in cylindirical coordianates; the tangential velocity component is uq K/r, where K is a constant. Generate an expression for the other velocity components, u.. b) Velocity profile in the pipe flow is given Determine; i) Potential and stream functions, ii) Define the stream function at the wall iii) Draw the stream and potential lines in the pipe flow
Q1.a) Consider a two dimensional, incompressible flow in cylindirical coordianates; the tangential velocity component is...
Question 1 (10 points) Rotational Flow and Vorticity The velocity components for a two-dimensional flow are u = ln hie) v = created where C is a constant. Is the flow irrotational?
1. The velocity in a certain two-dimensional flow field is given by the equation -= 2zt의 _ 2yte2 where the velocity is in ft/s when x, y, and t are in feet and seconds, respectively. Determine expressions for the local and convective components of acceleration in the x and y direc tions. What is the magnitude and direction of the velocity and the acceleration at the point x = y = 2 ft at the time t = 0.
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