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For the given 2D flow fields:Find the divergenceSketch the velocity fielda) v(x,y)=(vx(x,y), vy(x,y))=(x,y)b) v(x,y)=(vx(x,y), vy(x,y))= (y1/2,0)c) v(x,y)=(vx(x,y), vy(x,y)= (-y,x)

Question

For the given 2D flow fields:

  • Find the divergence
  • Sketch the velocity field

a) v(x,y)=(vx(x,y), vy(x,y))=(x,y)

b) v(x,y)=(vx(x,y), vy(x,y))= (y1/2,0)

c) v(x,y)=(vx(x,y), vy(x,y)= (-y,x)

check_circleAnswer
Step 1

To find the divergence and sketch the velocity field of the following 2D flow fields.

(a) v(x,y)=(vx(x,y), vy(x,y))=(x,y)

Divergence, Vv=,
ax
ôy
(x)+y)
=1+1
= 2
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Image Transcriptionclose

Divergence, Vv=, ax ôy (x)+y) =1+1 = 2

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Step 2

The velocity field is as follows.

10
10
-10
5
0
5
-10
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Image Transcriptionclose

10 10 -10 5 0 5 -10

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Step 3

(b) v(x,y)=(vx(x,y), vy(x,y))...

Divergence, Vv=-
ax
(0)
+
ax
=00
=0
help_outline

Image Transcriptionclose

Divergence, Vv=- ax (0) + ax =00 =0

fullscreen

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Math

Calculus

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