For a two dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression $\frac{\delta (u^2)}{\delta x}+\frac{\delta (uv)}{\delta y}$ can be simplified to

Answer :

Solution :

$\frac{\delta (u^2)}{\delta x}+\frac{\delta (uv)}{\delta y}$

After differentiating we get,

$2u\frac{\delta u}{\delta x}+u\frac{\delta v}{\delta y}+v\frac{\delta u}{\delta y}$

$u\frac{\delta u}{\delta x}+u[\frac{\delta u}{\delta x}+\frac{\delta v}{\delta y}]+v\frac{\delta u}{\delta y}$

According to continuity equation for 2D incompressible flow $\frac{\delta u}{\delta x}+\frac{\delta v}{\delta y}=0$

∴ $u\frac{\delta u}{\delta x}+v\frac{\delta u}{\delta y}$