Question

Derive an expression for the flow rate of a power-law fluid in a

cylindrical channel; i.e. where: z = m | z/ |^(−1)
(z/)

Answer 1

The flow rate of a power-law fluid in a cylindrical channel can be derived using Poiseuille's law, which depends on the pressure difference, radius, length, and viscosity of the fluid.

Step-by-step explanation:

The flow rate of a power-law fluid in a cylindrical channel can be derived using Poiseuille's law, which applies to the laminar flow of an incompressible fluid. The flow rate (Q) is directly proportional to the pressure difference (P₂ - P₁) and the fourth power of the radius (r⁴), and inversely proportional to the length of the tube (L) and the viscosity of the fluid (η). Mathematically, the expression for the flow rate of a power-law fluid in a cylindrical channel is:

Q = (π / 8) * (P₂ - P₁) * r⁴ / (L * η)

For example, if you want to determine the flow rate of a power-law fluid in a cylindrical channel, you need to know the pressure difference, the radius of the channel, the length of the channel, and the viscosity of the fluid.