So for an experiment, we injected a small volume of fluid into a capillary (76 micrometer diameter) through a pressure difference and I'm trying to calculate exactly how much was injected.
diameter of capillary = 76e-6 m
height one end was raised above the other = 5.334 cm = 0.05334 m
density of the fluid = .997 g/mL
viscosity of the fluid = 1 g/(m*s) = 0.001 kg/(m*s)
elapsed time during injection = 31 s
capillary length = 78 cm = 0.78 m
The formulas we are given are:
pressure = (density) * (gravitational constant) * (change in height)
volume injected = (pressure * pi * d^4 * t)/(128 * viscosity * capillary length) <-- Poiseuille's Law
The Attempt at a Solution
Based on my calculations, I'm getting:
P = (997 kg/m^3)*(9.81 m/s^2)*(0.05334 m) = 521.7 Pa
V = (521.7 Pa)(pi)(76e-6 m)(31s)/(128 * .001 kg/(m*s) * .780 m) = 37.676 m^3
Clearly, we didn't inject anywhere close to that much into a tiny capillary, so where am I going wrong?
Thanks in advance!