Question

Saline solution is delivered into a patient’s vein through a needle. The saline solution has a viscosity of 0.37 × 10-3 N s m-2, a
density of 1060 kg m-3, and is delivered through a 7 cm long needle with an internal diameter of 0.24 mm directly into the patient’s
vein in which the blood pressure is 130 mmHg. The saline solution must be delivered at a flow rate of 0.04 × 10-6 m3s-1. How
high must the saline solution be suspended in order to achieve this
flow rate? (Ignore variations between systolic and diastolic blood
pressure when doing this question. Also assume that the viscosity
of the saline solution is low enough that it does not affect the flow
of the solution through the IV tube, only the needle itself.)

Answer 1

pressure drop p in the needle is given by

.............................(1)

where friction coefficient, L is length of needle, D is diameter of needle, is density of saline and v is velocity of saline flow in the needle.

Friction coefficient = 64/ Re , where Re is Reynold's number , Re = ( v D ) /

we get velocity v of saline in the needle as, v = Q/ A , where Q is the volumetric flow rate of saline and A is area of cross section of needle, A = D² /4

using all these substitutions, eqn.(1) is written as,

............(2)

To sustain the saline flow through blood, we need

( ) + p = 130 mm mercury pressure = 130 10^-313593 9.8 = 17317 Pa ...........(3)

where h is vertical height of saline column above needle

Using eqn.(2) and eqn.(3), we get the required height h as,

h = ( 17317 - 12721 ) / ( g ) = 4596 /( 1060 9.8) = 0.44 m