Consider steady, incompressible, laminar flow of a newtonian fluid in an infinitely long round pipe annulus of inner radius ri and outer radius ro ignore the effects of gravity. a constant negative pressure gradient _p/_x is applied in the x-direction, (∂p/∂x)=(p1-p2)/(x2-x1) where x1 and x2 are two arbitrary locations along the x-axis, and p1 and p2 are the pressures at those two locations. the pressure gradient may be caused by a pump and/or gravity. note that we adopt a modified cylindricaloordinate system here with x instead of z for the axial component, namely, ( r, θ ,x) and (ur, uθ ,ux) derive an expression for the velocity field in the annular space in the pipe.