Volumetric Flow Rate in a Viscous Fluid

A cylindrical tube with a radius of 0.02 m and a length of 1.5 m is filled with a viscous fluid. The fluid has a density of 950 kg/m³ and a dynamic viscosity of 1.2 Pa·s. When a pressure difference of 3000 Pa is applied across the ends of the tube, calculate the volumetric flow rate of the fluid using Poiseuille’s Law.

According to Poiseuille’s Law, the volumetric flow rate (Q) for a cylindrical tube can be expressed as:

Q = (π * r² * ΔP) / (8 * η * L)

where:

• r = radius of the tube
• ΔP = pressure difference
• η = dynamic viscosity of the fluid
• L = length of the tube