Find the acceleration of a fluid particle in the x direction at (x,y) = (3,1) for a velocity field, which is given by\vec{V} = 3y\hat{i}+4x\hat{j}. x and y are in meters.
Find the acceleration of a fluid particle in the x direction at (x,y) = (3,1) for a velocity field, which is given by\vec{V} = 3y\hat{i}+4x\hat{j}. x and y are in meters.
Velocity field is \vec{V}=3y\hat{i}+4x\hat{j}
Here, \vec{V}=u\hat{i}+v\hat{j}
Acceleration of the fluid particle in the x-direction is given asa_{x}=u\frac{\partial u}{\partial x}+v\frac{\partial u }{\partial y}\Rightarrow a_{x}=3y\frac{\partial }{\partial x}\left ( 3y \right )+4x\frac{\partial }{\partial y}\left ( 3y \right )=\left ( 3y\times 0 \right )+\left ( 4x\times 3 \right )=12xAt point (x,y)=(3,1), acceleration of the fluid particle =12x= 12\times 3= 36\,m/s^{2}