A typical wire coating die is schematically shown in the figure. The incompressible viscous fluid cannot be squeezed out of the die along its length, and an isothermal flow is assumed. The rheological properties of the fluid are described by the power$-$law model, and elastic effects $($such as die swelling$)$ are negligible. There is no significant gravitational effect along the length of the die, and there is no significant pressure drop. Derive the expression for the velocity profile that includes integration constants.