Answer to Question #111776 in Physics for John Guz

Question

A needle with an internal diameter of 0.38 mm and length 4.1 cm is used to deliver an intravenous fluid of density 1050 kg m−3 and viscosity 12×10−4 Pa s into a vein.

If the pressure difference across the needle is 8.0 kPa then how many hours will it take to empty 1 litre of IV fluid through the needle? (to 2 s.f)

(1 litre = 1×10−3 m3)

Answer 1

$$\frac{\Delta V}{\Delta t}=\frac{\pi d^4\Delta p}{128\eta l}$$

$$\frac{0.001}{\Delta t}=\frac{\pi (0.00038)^4(8000)}{128(12\cdot10^{-4}) (0.041)}$$

$$t=12000\ s=3.3\ h$$