Question

Magnet wire is to be coated with varnish for insulation by drawing it through a circular die of 1.0 mm diameter. The wire diameter is 0.9 mm and it is centered in the die. The varnish (μ 5 20 centipoise) completely fills the space between the wire and the die for a length of 50 mm. The wire is drawn through the die at a speed of 50 m/s. Determine the force required to pull the wire.

I worked through the majority of it by why is d--> (D-d) and why is Area piDL and not 2piR or (piD^2/4). Please include an explanation as to why each step is happening, don't just solve.

Answer 1

In the given question a magnet wire is filled with varnish between wire and a die. The wire a pulled with some velocity which results in development of boundary layer between two surfaces.

The shear stress developed is maximum at the die surface and the Force required to pull the wire is calculated using The Area Under Shear which is Surafce are of the Die(πDL) not Cross Sectional Area (πD^2/4).

The shear stress is calculated using Newton's Law of Viscosity, i.e.

Shear stress acting on a fluid layer is directly proportional to the rate of deformation (velocity gradient).

The solution is as follows:-

Now the Area under shear is the Surface area of the Die i.e.

A = πDL

Where D = Diameter of the Die and L = Length of the Die

The Force required to pull the wire = 81.6814 Newtons.