Fluid Mechanics Assignment 1. A horizontal circular pipe of outer radius R 1 , is placed concentrically inside another circular pipe of inner radius R 2 . Considering fully developed laminar flow in the annular space between pipes show that the maximum velocity occurs at a radius R 0 given by R 0 = [ R 2 2 − R 1 2 2ln ( R 2 R 1 ) ] 1/2 2. Consider the laminar boundary layer on a flat plate with uniform suction velocity V 0 as shown in Fig. Far down the plate (large x), a fully developed situation may be shown to exist in which the velocity distribution does not vary with x. Find the velocity distribution in this region, as well as the wall shear. The governing equations are ∂u ∂x + ∂v ∂y =0 and u ∂u ∂x +v ∂u ∂y = −1 ρ dp dx +ϑ ∂ 2 u ∂y 2 The boundary conditions are at y = 0, u = 0, v = V 0 and u(∞) = U
Fluid Mechanics Assignment1. A horizontal circular pipe of outer
radius R1, is placed concentrically inside another circular pipe of
inner radius R2. Considering fully developed laminar flow in the
annular space between pipes show that the maximum velocity occurs
at a radius R0 given by
2. Consider the laminar boundary layer on a flat plate with
uniform suction velocity V0 as shown in Fig.
Far down the plate (large x), a fully developed situation may be
shown to exist in which the velocity distribution does not vary
with x. Find the velocity distribution in this region, as well as
the wall shear. The governing equations are
and The boundary conditions are at y = 0, u = 0, v = V0 and u()
= U
