The velocity field in a flow system is given by $v=2i+\left(x+y\right)j+\left(xyz\right)k$. The acceleration of the fluid at (1, 1, 2) is

Velocity field $\left(v\right)=2i+\left(x+y\right)j+\left(xyz\right)k$

$Acceleration\left(a_n\right)=\left(\frac{\delta v}{\delta t}\right)+\left(u\frac{\delta v}{\delta x}+v\frac{\delta v}{\delta y}+w\frac{\left(\delta v\right)}{\delta z}\right)$

Where $\left(\frac{\delta v}{\delta t}\right)\Rightarrow Localaccelaration$

$\left(u\frac{\delta v}{\delta x}+v\frac{\delta v}{\delta y}+w\frac{\left(\delta v\right)}{\delta z}\right)\Rightarrow Convectiveaccelaration$

Here, $u=2,v=x+y,w=xyz,t=0,$ n is direction

$a_x=0+2\times \frac{\partial }{\partial x}\left(2\right)+\left(x+y\right)\times \frac{\partial \left(2\right)}{\partial y}+\left(xyz\right)\times \frac{\partial \left(2\right)}{\partial z}$ 

a_x = 0

$a_y=0+2\times \frac{\partial \left(x+y\right)}{\partial x}+\left(x+y\right)\times \frac{\partial \left(x+y\right)}{\partial y}+\left(xyz\right)\times \frac{\partial \left(x+y\right)}{\partial z}$ 

a_y = 2 + x + y

$a_z=0+2\times \frac{\partial \left(xyz\right)}{\partial x}+\left(x+y\right)\times \frac{\partial \left(xyz\right)}{\partial y}+xyz\times \frac{\partial \left(xyz\right)}{\partial z}$ 

= 0 + 2yz + (x + y) × (xz) + xyz × xy

a_z = 2yz + (x + y) × (xz) + x²y²z

Acceleration = a_xi + a_yj + a_zk

$a=0+\left(2+x+y\right)j+\left(2yz+\left(x+y\right)xz+x^2{y}^{2}z\right)k$

$a_{\left(1,1,2\right)}=0+\left(2+1+1\right)j+\left(2\times 1\times 2+\left(1+1\right)\times 1\times 2+1^2\times 1^2\times 2\right)k$