The volume flow rate through a long capillary tube is believed to depend on the…
PHYSICS · Single correct · A Level · Physics · Measurements and their errors · Measurements and their errors
Problem
The volume flow rate Q through a long capillary tube is believed to depend on the pressure difference ΔP, the radius r of the tube, the coefficient of viscosity η, and the length l of the tube. Using the relation Q∝(ΔP)arbηcld, dimensional analysis alone cannot give unique values of the exponents a,b,c,d. Which statement gives the correct reason?
(a) Because the pressure difference is not itself a fundamental quantity, its exponent cannot be fixed purely by dimensional reasoning.
(b) Dimensional analysis breaks down whenever the final relation contains numerical constants like π or 8, so it cannot yield the unique exponents in this case.
(c) There are four independent physical quantities but only three fundamental dimensions, so one exponent remains undetermined.
(d) Viscosity would introduce a fourth fundamental dimension (temperature), leaving too many dimensions for the three equations available.