ANS:A - Hagen-Poiseulle's equation

The capillary tube method of viscosity measurement is based on Hagen-Poiseuille's equation. Here's why:

• Hagen-Poiseuille's Equation: This equation describes the laminar flow of an incompressible fluid through a cylindrical pipe (or tube), such as a capillary tube. It relates the flow rate of the fluid to the pressure gradient along the length of the tube, the viscosity of the fluid, and the dimensions of the tube. The equation is given by: Q=πr4(P1−P2)8ηLQ = \frac{\pi r^4 (P_1 - P_2)}{8 \eta L}Q=8ηLπr4(P1​−P2​)​ Where:
  • QQQ is the volumetric flow rate,
  • rrr is the radius of the tube,
  • P1−P2P_1 - P_2P1​−P2​ is the pressure difference driving the flow,
  • η\etaη is the viscosity of the fluid,
  • LLL is the length of the tube.

• A known pressure difference is applied across the capillary tube.
• The flow rate of the fluid through the tube is measured.
• By measuring the flow rate and knowing the dimensions of the tube, the viscosity η\etaη of the fluid can be calculated using Hagen-Poiseuille's equation.