Question

- write N-S equations for incompressible flows in cartesian coordinates in long form (in x,y,z coordinates) (1 point)

- also write continuity equation and N-S equations for incompressible flows in polar coordinates in long form (in r,θ,z) (since one of your friends ask you can find it easily in online resources or in books) (1 point)

- Write down N-S equations in x direction for Planar Couette- Pouseille flow and derive an equation for velocity variation using boundary layer conditions mentioned in the last lecture (1 point) (assuming incompressible, steady and fully developed flow)

BONUS: Assume an incompressible, steady, axissymmetric Pouseille flow in a cylindrical pipe (infinitesimally long in z direction). The flow is in z direction, and radial and tangetial velocity is zero. Derive and simplify the N-S equation in z direction to find out the velocity in z direction. (need to use the boundary conditions to solve for integration constants) (2 points)

Answer 1