I come up with using equation of continuity, but don't know how to proceed.

1. (60 pts) Refer to example 3.1-1 in your textbook as can also be found below. In this problem, we will ext the concepts discussed to compressible fluids. Show that zzz=0=(34+)(tln)z=0 Also discuss the significance of this equation. EXAMPLE 3.1-1 Show that for any kind of flow pattern, the normal stresses are zero at fluid-solid boundaries, Normal Stresses at for Newtonian fluids with constant density. This is an important result that we shall use Solid Surfaces for often. Incompressible SOLUTION Newtonian Fluids We visualize the flow of a fluid near some solid surface, which may or may not be flat. The flow may be quite general, with all three velocity components being functions of all three coordinates and time. At some point P on the surface we erect a Cartesian coordinate system with the origin at P. We now ask what the normal stress 22 is at P. According to Table B.1 or Eq. 1.2-6, zz=2(vz/z), because (v)=0 for incompressible fluids. Then at point P on the surface of the solid zzz=0=2zvzz=0=+2(xvx+yvy)z=0=0 First we replaced the derivative vz/z by using Eq. 3.1-3 with constant. However, on the solid surface at z=0, the velocity vx is zero by the no-slip condition (see $2.1 ), and therefore the derivative vx/x on the surface must be zero. The same is true of vy/y on the surface. Therefore zz is zero. It is also true that xx and yy are zero at the surface because of the vanishing of the derivatives at z=0. (Note: The vanishing of the normal stresses on solid surfaces =(v+(v))+(32k)(v), where k is dialational const. zz=2(zz)+(32k)(v) By egn. of continuity, t+(v)=0