To create a vertical wall along the y-axis, one can superimpose two source flows of equal...
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To create a vertical wall along the y-axis, one can superimpose two source flows of equal strength Q, centered about the origin on the x-axis at (-x0,0) and (x0,0). Given these two source flows:
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Determine the potential for this flow field in cartesian coordinates.
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Determine the streamfunction for this flow field in cartesian coordinates. What value
of y corresponds to the wall?
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Determine functions for the cartesian velocities (u,v) along the wall and show that
there is no normal (i.e., u) velocity along the wall. Use your function for v to determine the velocity at (0,x0).
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Homework Answers
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To create a vertical wall along the y-axis, one can superimpose
two source flows of equal...
4. A source is located at (x,y) = (-3,+2) next to a corner as shown. y=...
4. A source is located at (x,y) = (-3,+2) next to a corner as shown. y= +2 x axis 77 X =- (x,y) = (0,0) y axis a) what is the stream function for the entire field b) what is the velocity potential function for the entire field c) what is the u velocity component for the entire field d) what is the v velocity component for the entire field e) what is the velocity along both walls (can be...
A source of strength m, which by itself produces radial streamlines as indicated by the dashed ar...
A source of strength m, which by itself produces radial
streamlines as indicated by the dashed arrows, is placed a distance
L away from a vertical wall (occupying the yz-plane), at point S
(x=L,y= 0). To compute the flow field in the presence of the wall,
the method of images can be employed: A second source of strength m
is placed a distance L from the wall on the other side, at S′
(x=−L,y= 0). The combined flow field of...
6.102 The flow field for a plane source at a distance h above an infinite wall...
6.102 The flow field for a plane source at a distance h above an infinite wall aligned along the x axis is given by 20[x2 + y - 12|xi +(y-hil 9 2;[xi + (y + hil * 29x2 + (y + h) 21 where q is the strength of the source. The flow is irrotational and incompressible. Derive the stream function and velocity potential. By choosing suitable values for 4 and h, plot the streamlines and lines of constant velocity...
. An experimentalist has measured the u-velocity component of a steady, two- imensional flow field. It...
. An experimentalist has measured the u-velocity component of a steady, two- imensional flow field. It is approximated by u 3x2y x +10 It is also known that the v-velocity is zero along the line y-0. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, v, for this flow c) Determine the location of any stagnation points in the flow (stagnation means -0) d) Calculate the acceleration field (a and ay)...
6. An experimentalist has measured the u-velocity component of a steady, two- dimensional flow field. It...
6. An experimentalist has measured the u-velocity component of a steady, two- dimensional flow field. It is approximated by u 3x2y x 10 It is also known that the v-velocity is zero along the line y-O. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, 11, for this flow c) Determine the location of any stagnation points in the flow (stagnation means V-0) d) Calculate the acceleration field (ax and ay)...
D at the origin and continues along the negative y axis. The current in the wire is (JA and flows...
d at the origin and continues along the negative y axis. The current in the wire is (JA and flows in the positive x direction, then in the Consider a wire along the x axis and negative y direction. Calculate the magnitude of the magnetic field produced by the wire at the point (1.1). (Use Biot Savart law). The integra might be useful State your answer in terms of Ho i.e. set Ho 1 Answer The two wire parts contribute...
11. Let two rings both with radius a, be parallel to one another along the y-axis....
11. Let two rings both with radius a, be parallel to one another along the y-axis. Each ring carries a uniform charge q. What is the electric field at point along the y-axis if the rings are a distance from the origin? 12. Say we have a dipole consisting of charges -e and te separated by 0.34 nm. What is the work required to rotate the dipole from an initial parallel orientation to the electric field (E 1.1 x 103N/C)...
how to solve this probelm with draw put 25 points [velocity , acceleration] at raduis L/2...
how to solve this probelm with draw
put 25 points [velocity , acceleration] at raduis L/2 ,L ,
3/2L , 2L
H-W. 405 5 Paint Example Consider the steady, two-dimensional flow field V = (V/C)(xi – yj) Determine the acceleration field for this flow, Solution OV V [ ᎧV u + + W- In general, the acceleration is given by DV a -= +(V. (V) = + ofix by öz where the velocity is given by V = (1/0)(xi -...
A. In the table below, identify which of the circled terms of the governing equations can...
A. In the table below, identify which of the circled terms of
the governing equations can be neglected
by the given assumption. Write the number of the term in the table.
Some assumptions relate
to multiple terms, include them all.
B. Write the mathematical equations describing the
appropriate boundary conditions and identify
them in words.
C. Applying the appropriate boundary conditions,
solve the differential equation remaining after
appropriate terms have been neglected to determine the velocity
profile in the film: d^2(w)/dx^2 =...
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...
4. A source is located at (x,y) = (-3,+2) next to a corner as shown. y= +2 x axis 77 X =- (x,y) = (0,0) y axis a) what is the stream function for the entire field b) what is the velocity potential function for the entire field c) what is the u velocity component for the entire field d) what is the v velocity component for the entire field e) what is the velocity along both walls (can be...
A source of strength m, which by itself produces radial
streamlines as indicated by the dashed arrows, is placed a distance
L away from a vertical wall (occupying the yz-plane), at point S
(x=L,y= 0). To compute the flow field in the presence of the wall,
the method of images can be employed: A second source of strength m
is placed a distance L from the wall on the other side, at S′
(x=−L,y= 0). The combined flow field of...
6.102 The flow field for a plane source at a distance h above an infinite wall aligned along the x axis is given by 20[x2 + y - 12|xi +(y-hil 9 2;[xi + (y + hil * 29x2 + (y + h) 21 where q is the strength of the source. The flow is irrotational and incompressible. Derive the stream function and velocity potential. By choosing suitable values for 4 and h, plot the streamlines and lines of constant velocity...
. An experimentalist has measured the u-velocity component of a steady, two- imensional flow field. It is approximated by u 3x2y x +10 It is also known that the v-velocity is zero along the line y-0. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, v, for this flow c) Determine the location of any stagnation points in the flow (stagnation means -0) d) Calculate the acceleration field (a and ay)...
6. An experimentalist has measured the u-velocity component of a steady, two- dimensional flow field. It is approximated by u 3x2y x 10 It is also known that the v-velocity is zero along the line y-O. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, 11, for this flow c) Determine the location of any stagnation points in the flow (stagnation means V-0) d) Calculate the acceleration field (ax and ay)...
d at the origin and continues along the negative y axis. The current in the wire is (JA and flows in the positive x direction, then in the Consider a wire along the x axis and negative y direction. Calculate the magnitude of the magnetic field produced by the wire at the point (1.1). (Use Biot Savart law). The integra might be useful State your answer in terms of Ho i.e. set Ho 1 Answer The two wire parts contribute...
11. Let two rings both with radius a, be parallel to one another along the y-axis. Each ring carries a uniform charge q. What is the electric field at point along the y-axis if the rings are a distance from the origin? 12. Say we have a dipole consisting of charges -e and te separated by 0.34 nm. What is the work required to rotate the dipole from an initial parallel orientation to the electric field (E 1.1 x 103N/C)...
how to solve this probelm with draw
put 25 points [velocity , acceleration] at raduis L/2 ,L ,
3/2L , 2L
H-W. 405 5 Paint Example Consider the steady, two-dimensional flow field V = (V/C)(xi – yj) Determine the acceleration field for this flow, Solution OV V [ ᎧV u + + W- In general, the acceleration is given by DV a -= +(V. (V) = + ofix by öz where the velocity is given by V = (1/0)(xi -...
A. In the table below, identify which of the circled terms of
the governing equations can be neglected
by the given assumption. Write the number of the term in the table.
Some assumptions relate
to multiple terms, include them all.
B. Write the mathematical equations describing the
appropriate boundary conditions and identify
them in words.
C. Applying the appropriate boundary conditions,
solve the differential equation remaining after
appropriate terms have been neglected to determine the velocity
profile in the film: d^2(w)/dx^2 =...
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...
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