Question

The velocity v in a fluid in a two dimensional model at any point (x,y) in...

The velocity v in a fluid in a two dimensional model at any point (x,y) in the flow is given by the function below.


v=4x2y−32xy+48y−24x

Find the stationary points for this function

(I)

Find the x coordinate of the stationary point with the larger x coordinate. Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Type in the number only ie leave out the "x=" (4 marks)



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(II)

Find the corresponding y coordinate of the stationary point whose x coordinate you have given in (i). Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Type in the number only ie leave out the "y=" (4 marks)



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(III)

What is the nature of this stationary point?
Saddle (enter 1)
Maximum (enter 2)
Minimum (enter 3) (2 marks)



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(IV)

Find the value of the velocity at this stationary point. Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Type in the number only ie leave out the "v=" (2 marks)



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(V)

Find the x coordinate of the stationary point with the smaller x coordinate. Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Type in the number only ie leave out the "x=" (4 marks)



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(VI)

Find the corresponding y coordinate of the stationary point whose x coordinate you have given in (v). Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Type in the number only ie leave out the "y=" (4 marks)



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(VII)

What is the nature of this stationary point?
Saddle (enter 1)
Maximum (enter 2)
Minimum (enter 3) (2 marks)



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(VIII)

Find the value of the velocity at this stationary point. Give your answer to AT LEAST FOUR PLACES OF DECIMALS. Type in the number only ie leave out the "v=" (2 marks)

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Answer #1

V(x,y) = 4*?y - 32xy +494 - 24% Ver de = fxy – 32y – 24 Bu y = 4x² – 32x tag Vy - To get stationary points Vx= 0 ? Vy- o Sxy-(6,3/2) NXX = $(3/2) = 12 ; Vyy=0; Vey = 8(6) -32 = 16 H = (12)(0) - (163 = -25540. - H2O =) (6, 7) is a seedle point (1) x =

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