Consider the flow field represented by the velocity potential φ = Ax+Bx2−By2, where A = 1...
Consider the flow field represented by the velocity potential φ = Ax+Bx2−By2, where A = 1 m/s, B = 1 s−1, and the coordinates are measured in meters. Obtain expressions forthe velocity field and the stream function. Using water as the working fluid, calculate the pressure difference between the origin and the point (x,y) = (1,2). What is the volume flow rate (per unit depth) between streamlines passing through these two points?
Homework Answers
Add Answer to:
Consider the flow field represented by the velocity potential φ
= Ax+Bx2−By2, where A = 1...
help 1. A 2D inviscid flow field is represented by the velocity potential function: ° =...
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)...
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a sour...
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink in a uniform stream, separated by a fixed distance. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink...
2. The velocity potential for a spiral vortex flow is given by φ-2nInr-2-9, where A (positive)...
2. The velocity potential for a spiral vortex flow is given by φ-2nInr-2-9, where A (positive) is the sink strength and Γ is the vortex strength (1) Find the expression of stream function. (2) The plot of stream function is shown in the following figure. Prove the angle,a, between the 2Tt velocity vector and the radial direction is constant throughout the flow field. (FYI, this spiral is called Logarithmic spiral.) .y
The y component of velocity in a steady, incompressible flow field in the xy plane is...
The y component of velocity in a steady, incompressible flow field in the xy plane is v = -Bxy3, where B = 0.7 m-3 · s-1, and x and y are measured in meters. (a) Find the simplest x component of velocity for this flow field. (b) Find the equation of the streamlines for this flow (use C as constant).
Consider the flow field with velocity given by: V = [A(y2-x2)-Bx] i + [2Axy+By] j, where...
Consider the flow field with velocity given by: V = [A(y2-x2)-Bx] i + [2Axy+By] j, where A = 4 m-1s -1 and B = 4 m-1s -1. The coordinates are measured in meters. The density is 1,000 kg/m3, and gravity acts in the negative y-direction Calculate the acceleration of a fluid particle and the pressure gradient at point (x, y) = (1, 1).
1) The velocity components in a 2-D incompressible flow are expressed as; u =(y/3 + 2x...
1) The velocity components in a 2-D incompressible flow are expressed as; u =(y/3 + 2x - x’y) m/s and v = (xy? - 2y - x®/3) m/s a) Determine the velocity and acceleration at point P (1, 3). (1 point) b) Is the flow physically possible? (Proof needed) (1 point) c) Obtain an expression for the stream function. () (1 point) d) What is the discharge between the streamlines passing through (1, 3) and (2, 3). (1 point) e)...
Please answer without using previously posted answers. Thanks Let F(x, y) be a two-dimensional vector field. Spose further that there exists a scalar function, o, such that Then, F(x,y) is called a g...
Please answer without using previously posted answers.
Thanks
Let F(x, y) be a two-dimensional vector field. Spose further that there exists a scalar function, o, such that Then, F(x,y) is called a gradient field, and φ s called a potential function. Ideal Fluid Flow Let F represent the two-dimensional velocity field of an inviscid fluid that is incompressible, ie. . F-0 (or divergence-free). F can be represented by (1), where ф is called the velocity potential-show that o is harmonic....
1) A velocity field is given by V = ax?i-bxyl, where a = 2 m-'s-1 and...
1) A velocity field is given by V = ax?i-bxyl, where a = 2 m-'s-1 and b = 4 m-'s-1. (5 points) is the flow field one, two, or three-dimensional? Why? Is it steady? Why? (15 points) Find the equation of the streamline passing through the point (x,y) = (2,1).
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 you...
Consider the velocity field V - A(4- 6x2y2 +y4)i+ A(4xy3 - 4x3y) j in the xy...
Consider the velocity field V - A(4- 6x2y2 +y4)i+ A(4xy3 - 4x3y) j in the xy plane, where A 0.28 m3.s1, and the coordinates are measured in meters. (a) Is this a possible incompressible flow field? (b) Calculate thex component and (c) y-component of the acceleration of a fluid particle at point (x,y)-(2, 3) b) -119 m/s 2 120 (c) ay - m/s2
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)...
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink in a uniform stream, separated by a fixed distance. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink...
2. The velocity potential for a spiral vortex flow is given by φ-2nInr-2-9, where A (positive) is the sink strength and Γ is the vortex strength (1) Find the expression of stream function. (2) The plot of stream function is shown in the following figure. Prove the angle,a, between the 2Tt velocity vector and the radial direction is constant throughout the flow field. (FYI, this spiral is called Logarithmic spiral.) .y
1) The velocity components in a 2-D incompressible flow are expressed as; u =(y/3 + 2x - x’y) m/s and v = (xy? - 2y - x®/3) m/s a) Determine the velocity and acceleration at point P (1, 3). (1 point) b) Is the flow physically possible? (Proof needed) (1 point) c) Obtain an expression for the stream function. () (1 point) d) What is the discharge between the streamlines passing through (1, 3) and (2, 3). (1 point) e)...
Please answer without using previously posted answers.
Thanks
Let F(x, y) be a two-dimensional vector field. Spose further that there exists a scalar function, o, such that Then, F(x,y) is called a gradient field, and φ s called a potential function. Ideal Fluid Flow Let F represent the two-dimensional velocity field of an inviscid fluid that is incompressible, ie. . F-0 (or divergence-free). F can be represented by (1), where ф is called the velocity potential-show that o is harmonic....
1) A velocity field is given by V = ax?i-bxyl, where a = 2 m-'s-1 and b = 4 m-'s-1. (5 points) is the flow field one, two, or three-dimensional? Why? Is it steady? Why? (15 points) Find the equation of the streamline passing through the point (x,y) = (2,1).
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 you...
Consider the velocity field V - A(4- 6x2y2 +y4)i+ A(4xy3 - 4x3y) j in the xy plane, where A 0.28 m3.s1, and the coordinates are measured in meters. (a) Is this a possible incompressible flow field? (b) Calculate thex component and (c) y-component of the acceleration of a fluid particle at point (x,y)-(2, 3) b) -119 m/s 2 120 (c) ay - m/s2
Most questions answered within 3 hours.
-
Living in a group could bring several disadvantages to an
individual. What are some of the...
asked 11 minutes ago -
Complete and balance the following reactions. In case of no
reaction occurring write NR.
Mix #1:...
asked 17 minutes ago -
If an economy consumes 75% of any increase in income, then an
increase in autonomous investment...
asked 20 minutes ago -
A shotputter throws the shot with an initial speed of 15.8 m/s
at a 38.0 ∘...
asked 36 minutes ago -
Debra and Merina sell electronic equipment and supplies through
their partnership. They wish to expand their...
asked 37 minutes ago -
How does a linear regression allow you to better estimate
trends, costs, and other factors in...
asked 45 minutes ago -
1. (15%) Describe the difference between a pull (Kanban), push
and CONWIP production systems.
asked 41 minutes ago -
QUESTION 5
The total area under the Z distribution curve is equal to:
a.
10
b....
asked 50 minutes ago -
Using Python
The variables x and y refer to numbers. Write a code segment
that prompts...
asked 1 hour ago -
If
the coefficient of static friction between a box and the floor is
0.35 with what...
asked 1 hour ago -
A die is designed to punch holes with a radius of 1.08 10-2 m in
a...
asked 1 hour ago -
government can increase import through
a. export subsidies
b. tax breaks
c. increase import tax
d....
asked 1 hour ago