Assignment 6.3 – Due 6/20/2016 1. ρ

Assignment 6.3 – Due 6/20/2016
1. Fluid having density ρ and viscosity µ fills the space between the two cylinders. If the outer cylinder
is fixed, and the inner one rotates with an angular speed ω, apply the cylindrical form of the Navier–
Stokes to determine the velocity profile assuming the flow is laminar, under steady state and
axisymmetric. Notice that since the flow is laminar the radial and axial components of the velocity
are zero.
2. Consider a two–dimensional, steady–state, incompressible, laminar, viscous flow between two
stationary infinite parallel inclined plates separated a distance a, as shown. The fluid flows in the
direction from A to B due to a pressure gradient, ∂p/∂x, sufficiently large to overcome the body forces
acting in the opposite direction to the motion of the fluid. Using the Navier–Stokes equations,
determine an expression for the velocity of the flow, in terms of ∂p/∂x, g, µ, ρ, α, a, and coordinate
system. Assuming the fluid is water and α = 30o, what should the pressure gradient be to maintain the
flow if the average velocity in the flow is .2 m/s?