Paper 3 · Kinematics and Dynamics
Poiseuille's law for fluid flux Φ through a pipe is , where ρ is density, η is viscosity (units Pa s), is a pressure difference, R is the pipe's internal radius and L is its length. Determine the base SI units of Φ.
Model answer
kg/s
Also accepted: kg s^-1, kilograms per second, kg s-1
Explanation: Substituting base units: [ρ]=kg m^-3, [η]=kg m^-1 s^-1, [P]=kg m^-1 s^-2, [R^4]=m^4, [L]=m. Combining these as the formula requires gives (kg m^-3)/(kg m^-1 s^-1) × (kg m^-1 s^-2) × m^4/m = kg s^-1, so fluid flux has base units of kg s^-1 (a mass flow rate).
Derived from ZIMSEC Physics Paper 3, June 2004, Q1