6. A long wire of length L to be coated moves at a velocity Vo through a long cylindrical die

filled with an incompressible fluid (density p and kinematic viscosity μ). Using cylindrical

co-ordinates (r-z) and assuming that pressure is uniform (i.e. dp/dz = 0 and dp/dr = 0).

Assume that the flow is steady, laminar and fully developed (neglect any end effects). Clearly

show all steps, starting from the Navier-Stokes equations, simplifying them, specify proper

boundary conditions.

4

(a) Find velocity v₂ as a function of radius inside the die. Use continuity, and momentum

equations and clearly show which terms vanish (and why).

(b) Also find the force F required to pull the wire in terms of the given known parameters

such as Vo, L, p, R₁, R₂ etc.

R₂

R₁

Incompressible fluid