- Problem Statement
- Unit normal to a surface

- Relevant Equations
- Unit normal to a surface

I have came across a problem where each point of a surface parallel to the x-y cartesian plane and having it's normal along the z axis is having velocity along the z direction ##v_z## and there exists a velocity gradient across the plane (e.g ##v_z(x,y)## ,

After time ##\delta t## it is written the normal to surface will be ##n'=\hat k-(\hat iv_{zx}+\hat j v_{zy})\delta t## where ##v_{ij}=\frac{\partial v_i}{\partial x_j}## and ##\vec r'=\vec r+\vec v \delta t##.

Can anyone please help me out how to proceed to prove this result....

After time ##\delta t## it is written the normal to surface will be ##n'=\hat k-(\hat iv_{zx}+\hat j v_{zy})\delta t## where ##v_{ij}=\frac{\partial v_i}{\partial x_j}## and ##\vec r'=\vec r+\vec v \delta t##.

Can anyone please help me out how to proceed to prove this result....