The velocity field of an incompressible flow in a Cartesian system is represented byV -2x2-y2i-v-3k-Which one of the following expressions for V is valid-

V =(2x^2 2y^2)î+vĵ+3k̂ For incompressible flow, continuity equation: ∂ u∂ x+∂ v∂ y+∂ w∂ z=0 4x+∂ v∂ y=0 ∂ v∂ y= 4x v= 4xy+f(x,z) Option "a" is the appropriate ...

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Fluid Mechanics

Velocity and Acceleration-II

The velocity ...

Question

The velocity field of an incompressible flow in a Cartesian system is represented by
$- \to V = 2 (x^{2} - y^{2}) i + v^j + 3^k$
Which one of the following expressions for $- \to V$ is valid?

-4xy-4xz

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-4xy-6xy

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4xy+4xz

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4xz+6xz

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Solution

The correct option is A -4xy-4xz
$- \to V = (2 x^{2} - 2 y^{2})^i + v^j + 3^k$
For incompressible flow, continuity equation:
$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$
$4 x + \frac{\partial v}{\partial y} = 0$
$\frac{\partial v}{\partial y} = - 4 x$
v= -4xy+f(x,z)
Option "a" is the appropriate answer

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The velocity field of an incompressible flow in a Cartesian system is represented by −→ V =2(x2−y2)i+v^j+3^k Which one of the following expressions for −→ V is valid?

The correct option is A -4xy-4xz−→ V =(2x2−2y2)^i+v^j+3^k For incompressible flow, continuity equation: ∂u∂x+∂v∂y+∂w∂z=0 4x+∂v∂y=0 ∂v∂y=−4x v= -4xy+f(x,z) Option "a" is the appropriate answer

The velocity field of an incompressible flow in a Cartesian system is represented by
$- \to V = 2 (x^{2} - y^{2}) i + v^j + 3^k$
Which one of the following expressions for $- \to V$ is valid?