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**1. Homework Statement**

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

**2. Homework Equations**

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

**3. 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!