Shear flow outputs from a slot or cylindrical die

2 Shear flow outputs from a slot or cylindrical die 

The analysis proceeds in three stages. Details will be given for the rectangular slot, with the cylindrical slot result given in square brackets. 

Ap is the pressure drop between the section entrance and exit. Next, we consider the forces on the slab of liquid between y. For the steady flow, the forces are in equilibrium, so 

This linear variation of shear stress with position is a consequence of constant pressure gradient in channel. 

The constant rj is the shear viscosity. We introduce the value of the shear stress at the channel wall 

---