The circulation $^{'} Γ^{'}$ around a circle of radius 2 units for the velocity field $u = 2 x + 3 y a n d v = - 2 y i s$

- 6 π

units

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- 12 π

units

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- 18 π

units

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- 24 π

units

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Solution

The correct option is B $- 12 π$ units
Circulation = Vorticity × Area
$= (\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}) \times a r e a$
$= (0 - 3) \times π \times (2)^{2}$
$= - 12 π u n i t s$

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Similar questions

Γ

x = 1, y = 1, x = 5 a n d y = 4

v = 2 x = 3 y a n d v = 2 y

\to V = (8 x - 6 y)^i + (2 y - x)^j

y = 1, x = 3, y = 3

x = 4

u = 3 y

v = 3 x

u = 3 x t

v = 3 y t

u = x y + y^{2} t

v = x y + x^{4} t

u = 4 x^{2} y^{3}

v = - 2 x y^{4}

The lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 154 square units. The equation of the circle is

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