Question $10$: The Navier$-$Stokes Equations for a Newtonian fluid is given by:

$\frac{D{u}_i}{Dt}=-\frac{\text{d}\text{e}\text{l}\text{p}}{del{x}_i}+\frac{\text{d}\text{e}\text{l}}{del{x}_i}(\frac{del{u}_k}{del{x}_k})+\frac{\text{d}\text{e}\text{l}}{del{x}_j}[(\frac{del{u}_i}{del{x}_j}+\frac{del{u}_j}{del{x}_i})]+f_i$

Explain what each term means in this tensor form of the equation.

Starting from the above equation, show how would the equation look like in tensor format for an

incompressible fluid with constant viscosity? Explain your steps clearly.

Starting from the above equation, show how would the Euler Equation look like in tensor format?

Explain your steps clearly.