Question

A velocity field is given as
$\overrightarrow{V}$ $=2y\hat{i}+3x\hat{j}$
where x and y are in metres.
The acceleration of a fluid particle at (x, y) = (1, 1) in the x direction is

• A. 0
• B. $5.00m/s^2$
• C. $6.00m/s^2$
• D. $8.48m/s^2$

Answer 1

The correct option is C $6.00m/s^2$

Given
$\overrightarrow{V}$ $=2y\hat{i}+3x\hat{j}$

i.e. $u=2yandv=3x$

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

$\Rightarrow$ $a_x=0+(2y\times 0)+(3x\times 2)$

$\Rightarrow$ $a_x=6x$

Now at (1, 1)

$a_x=6x=6\times 1=6m/s^2$