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Problem M.7 The velocity and pressure are given at two points in the flow field. Assume...
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
help 1. A 2D inviscid flow field is represented by the velocity potential function: ° =...
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1. A 2D inviscid flow field is represented by the velocity potential function: ° = Ax + Bx2 – By2. Where A = 1m/s, B = 15-7, and the coordinates are measured in meters. The flow density is p = 1.2 kg/m3. (a) (2 points) Calculate the velocity field. (b) (2 points) Verify that the flow is irrotational. (c) (2 points) Verify that the flow is incompressible. (d) (2 points) Obtain the expression of stream function. (e) (2 points)...
A 2D flow has the pressure and velocity fields given below. Calculate the total force, pressure...
A 2D flow has the pressure and velocity fields given below. Calculate the total force, pressure force, viscous force, and body force acting on a fluid particle located at (?,?)=(2,−2) m. Assume that the density and dynamic viscosity are constant and given by 1000 kg/m3 and 10-3 kg/(m s), respectively. ?̅ =(1+?2)?̂+(1−?2)? ̂ m/s ?=(?+?) kPa
Given the velocity field V =107 +(x + y2)7-2xyk [m/s] Is the flow steady or unsteady?...
Given the velocity field V =107 +(x + y2)7-2xyk [m/s] Is the flow steady or unsteady? Is this motion kinematically possible for an incompressible fluid? Do you think that velocity field can represent a potential flow at specific positions of (x, y)? What is the acceleration of a particle at position (x, y, z) = (3, 1, 0) m?
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...
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?
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...
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 +
11) (6 points) Given the velocity field V =101 +(x2 + y2); -2xy [m/s] a) b)...
11) (6 points) Given the velocity field V =101 +(x2 + y2); -2xy [m/s] a) b) c) Is the flow steady or unsteady? Is this motion kinematically possible for an incompressible fluid? Do you think that velocity field can represent a potential flow at specific positions of (x, y)? What is the acceleration of a particle at position (x, y, z) = (3, 1, 0) m? d)
6-7. Oil flows through the 100-mm-diameter pipe with a velocity of 8 m/s. If the pressure...
6-7. Oil flows through the 100-mm-diameter pipe with a velocity of 8 m/s. If the pressure in the pipe at A and B is assumed to be 60 kPa, determine the x and y components of force the flow exerts on the elbow. The flow occurs in the horizontal plane. Take ρο -900 kg/m3 8 m/s 30° 100 mm 100 mm
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
help
1. A 2D inviscid flow field is represented by the velocity potential function: ° = Ax + Bx2 – By2. Where A = 1m/s, B = 15-7, and the coordinates are measured in meters. The flow density is p = 1.2 kg/m3. (a) (2 points) Calculate the velocity field. (b) (2 points) Verify that the flow is irrotational. (c) (2 points) Verify that the flow is incompressible. (d) (2 points) Obtain the expression of stream function. (e) (2 points)...
Given the velocity field V =107 +(x + y2)7-2xyk [m/s] Is the flow steady or unsteady? Is this motion kinematically possible for an incompressible fluid? Do you think that velocity field can represent a potential flow at specific positions of (x, y)? What is the acceleration of a particle at position (x, y, z) = (3, 1, 0) m?
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 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?
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...
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 +
11) (6 points) Given the velocity field V =101 +(x2 + y2); -2xy [m/s] a) b) c) Is the flow steady or unsteady? Is this motion kinematically possible for an incompressible fluid? Do you think that velocity field can represent a potential flow at specific positions of (x, y)? What is the acceleration of a particle at position (x, y, z) = (3, 1, 0) m? d)
6-7. Oil flows through the 100-mm-diameter pipe with a velocity of 8 m/s. If the pressure in the pipe at A and B is assumed to be 60 kPa, determine the x and y components of force the flow exerts on the elbow. The flow occurs in the horizontal plane. Take ρο -900 kg/m3 8 m/s 30° 100 mm 100 mm
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