Answer to Question #183468 in Physics for Te Waiwhakaata Ratu

Question

You wish to deliver 95 ml of a viscous drug (η = 22×10⁻⁴ Pa s) through a needle of length 50 mm and with an internal radius of 0.36 mm.

If a pressure difference of 66 kPa is maintained across the needle as the drug is delivered then how long will it take to deliver the 95 ml of fluid? (to 2 s.f and in s)

(Note: 1 ml = 1×10⁻⁶ m³)

Answer 1

The flow of the fluid can be calculated according to Poiseuille law $Q = \frac{\pi R^4}{8 \eta l}\Delta p$.

Hence the time needed to deliver volume $V$ of the fluid is:

$t = \frac{V}{Q} = \frac{8 \eta l V}{\pi R^4 \Delta p} \approx 24.01 s$.