Flow through a wire-coating die (see figure below) is similar to the flow situation shown in Problem 2B.7 except that the fluid coats the wire with a thickness that depends on the die dimensions and wire speed, V. Use the velocity field calculated for a power-law fluid in Homework set 3 and do the following:

a. Obtain an expression for the coating thickness, d, using a volume balance.

b. Obtain an expression for determining the die radius, R, required to produce a coating thickness of 3.3x10 ^-3 m on a metal wire of diameter of 6.55x10 ^-3 m. Take m = 7602 Pa s ⁿ and n = 0.44. Identify the type of equation and explain how you would solve it.

c. Does the thickness depend on the wire speed, V?

2KR 2R L 50 || = 2. ? V