MECH 3300 Assignment # 1

5. A frictionless, incompressible steady flow field is given by
= 2 −
in arbitrary units. Let the density be ρ 0 = constant and neglect gravity. Find an
expression for the pressure gradient in the x direction.
6. Consider a steady, 2D, incompressible flow of a newtonian fluid in which the velocity
field is known: u = -2xy, v = y 2 -x 2 , w = 0.
a) Does this flow satisfy conservation of mass;
b) Find the pressure field, p(x,y) if the pressure at the point (x = 0, y = 0) is
equal to p a .
7. From the Navier-Stokes equations for incompressible flow in polar coordinates, find
the most general case of purely circulating motion v θ (r), v r = v z = 0, for flow with no
slip between two fixed concentric cylinders as in the figure.
2