x y = +h y=-h y u(y) Fixed u(y) Fixed Fixed (a) (b) u max P4.28 For the velocity distribution of Prob. see below, i.e. u = 4y and v = 2x (incompressible flow) (a) check continuity. (b) Are the Navier-Stokes equations valid? (c) If so, determine p(x,y) if the pressure at the origin is po.

An incompressible velocity field is given by u=a(x°y²-y), v unknown, w=bxyz where a and b are constants. (a)What is the form of the velocity component for that the flow conserves mass? (b) Write Navier- Stokes's equation in 2-dimensional space with x-y coordinate system.

A velocity field is given by u = 5y2,  v = 3x,   w = 0. (a) Is this flow steady or unsteady? Is it two- or three- dimensional? (b) At (x,y,z) = (3,2,–3), compute the velocity vector. (c) At (x,y,z) = (3,2,–3), compute the local (i.e., unsteady part) of the acceleration vector. (d ) At (x,y,z) = (3,2,–3), compute the convective (or advective) part of the acceleration vector. (e) At (x,y,z) = (3,2,–3), compute the (total) acceleration vector.

For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0: (a) Is this flow one-, two-, or three-dimensional? (b) Is this flow steady? (c) Is this flow incompressible? (d) Find the x-component of the acceleration vector.