Question

An intravenous (IV) system is supplying saline solution to a patient at the rate of  0.120 cm 3 /sec  through a needle of radius  0.150 mm and length  2.50 cm. What pressure  is needed at the entrance of the needle to cause this flow, assuming the viscosity of the saline solution is  0.001 Pa · sec? The gauge pressure of the blood in the patient’s vein is         8.00 mm Hg.

Answer 1

Rate of flow, $V = 0.12\; cm^3 = 0.12 \times 10^{-6}\; m^3$

radius, r =0.15 mm $=0.15 \times 10^{-3}\; m$

length, L =2.5 cm $= 2.5 \times 10^{-2} \;m$

viscosity $= 8.9 \times 10^{-4}\; Pa s$

gauge pressure = 8 mm of Hg

The pressure is given by

$V=\frac{\pi pr^4}{8 η L}\\ 0.12 \times 10^{-6}= \frac{3.14 \times p \times (0.15 \times 10^{-3})^4}{8 \times 8.9 \times 10^{-4} \times 2.5 \times 10^{-2}} \\ p = 13437.1 \;Pa$

Pressure required

P= p + 8 mm of Hg

$= 13437.1 + 0.008 \times 13.6 \times 1000 \times 9.8 = 14503.34 \;Pa$

Answer: 14503.34 Pa