Question

In a two-dimensional velocity field with velocities u and v along the x and y directions respectively, the convective acceleration along the x-direction is given by

• A. $u\frac{\partial v}{\partial x}+v\frac{\partial u}{\partial y}$
  
• B. $u\frac{\partial u}{\partial x}+v\frac{\partial v}{\partial y}$
• C. $u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}$
• D. $v\frac{\partial u}{\partial x}+u\frac{\partial u}{\partial y}$

Answer 1

The correct option is C $u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}$

Convective acceleration is defined as the rate of change of velocity due to change of position of fluid particle in a fluid flow.
Convective acceleration along the x-direction is given by

$a_x=u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}$

for 3-D velocity field

$=u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}$

for 2-D (x and y direction) velocity field