The most important essential feature of any flow cytometric instrument is a stable fluid stream which presents the cells one at a time to a sensing volume where the measurements are made. To obtain consistency of measurement each cell has to be presented to the same volume within the sensor and in order to understand how this is achieved we must consider some basic concepts of fluid dynamics.

Bernoulli and Euler

Bernoulli was a Swiss mathematician who experimented with various aspects of fluid flow dynamics. He constructed a number of pieces of glass apparatus through which he pumped water. One particular apparatus consisted of a tube with a central constriction and he added three manometers along the tube. One was placed at the constriction and the other two were placed one upstream and one downstream in relation to the constriction. This is depicted in figure 2.1. It is perhaps a little surprising at first sight to find that the hydrostatic pressure is reduced in the manometer placed at the constriction and that the pressures are approximately equal in the upstream and downstream manometers. As the velocity must increase in the constricted portion of the tube Bernoulli (1738) concluded that velocity and pressure in fluid flow must be inversely related and he derived the equation to describe this phenomenon.

This is a beautiful simultaneous demonstration of two fundamental laws of physics, the law of conservation of energy and the second law of motion (Newton, 1687). The velocity is greater in the constriction, thus water must be accelerated which, from Newton's second law, requires a force.