Consider the following statements in respect of two-dimensional incompressible flow with velocity components u and v in x and y directions respectively-1- The continuity equation is - u- x- v- y2- The acceleration in x-direction is ax- u- t-u- u- x-v- u- y3- The condition of irrotationality is - u- y- v- x4- The equation of a streamline is udy - -vdxWhich of these statement are correct-

(a) For two dimensional incompressible flow. (i) the continuity equation is ∂ u∂ x+∂ v∂ y=0 (ii) the equation of a stream line in vdx udy = 0 nbsp; ...

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Fluid Mechanics

Velocity and Acceleration-I

Consider the ...

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Consider the following statements in respect of two-dimensional incompressible flow with velocity components u and v in x and y directions respectively:
1. $T h e c o n t i n u i t y e q u a t i o n i s \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}$
2. $T h e a c c e l e r a t i o n i n x - d i r e c t i o n i s a_{x} = \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y}$
3. $T h e c o n d i t i o n o f i r r o t a t i o n a l i t y i s \frac{\partial u}{\partial y} = \frac{\partial v}{\partial x}$
4. The equation of a streamline is udy = -vdx

Which of these statement are correct?

2 and 3 only

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1 and 2 only

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1, 2, and 3

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3 and 4

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Solution

The correct option is A 2 and 3 only
(a)
For two dimensional incompressible flow.

(i) the continuity equation is $\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0$

(ii) the equation of a stream line in vdx-udy = 0

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The correct option is A 2 and 3 only (a) For two dimensional incompressible flow. (i) the continuity equation is ∂u∂x+∂v∂y=0 (ii) the equation of a stream line in vdx-udy = 0

The correct option is A 2 and 3 only
(a)
For two dimensional incompressible flow.

(i) the continuity equation is $\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0$

(ii) the equation of a stream line in vdx-udy = 0