It has been appreciated for some time that bypassing the upper airway with a tube will increase the resistance to airflow. As a result, the work of breathing will be increased since a greater pressure will be necessary to generate a particular airflow. To understand better those factors which determine the resistance to flow through tubes, some knowledge of fluid mechanic principles is required. The easiest system of tubes to study is that of flow in long, straight tubes for which much experimental and theoretic work has been done.
Flow of a gas (or fluid) in a straight smooth tube is opposed by two kinds of friction. One is the friction between the walls of the tube itself and the gas, and the other is the internal friction caused between gas molecules as they slide over each other. This latter component is called viscosity. These two frictional components create resistance, and, as with electric resistance, resistance is defined as the ratio of the change in pressure required to produce a certain flow rate. As gas flows through a tube of fixed diameter (D) and length (L), the pressure required to create a certain flow increases linearly with increasing flow when the flow rates are low. At higher flow rates, the effect on pressure is curvilinear. In between the low and the high flow rates, there is a transition zone where the change in pressure with flow is variable (Fig 1). add comment
At low flow rates, flow in a tube is termed laminar because the molecules of fluid are streaming past each other in parallel albeit at different speeds. As fluid enters the tube, the molecules near the wall adhere to the wall due to friction and are not moving. Because of fluid viscosity (|x), the velocity of the subsequent layers of fluid are retarded but to a lesser and lesser extent as one proceeds away from the wall. Thus, fluid linear velocity, as measured in ft/s or cm/s, increases with distance from the wall. Maximum velocity is achieved in the center of the tube (Fig 2).
Equations describing the profile of fluid velocities across a tube have been developed. They describe a parabolic velocity profile (Fig 2). However, this velocity profile is achieved when the laminar flow is fully developed, which means that the flow has existed long enough for steady-state conditions to be achieved. The boundary layer, which is that region adjacent to the wall of the tube extending to the region where most of the bulk flow of fluid occurs (the center of the tube), increases in size until it reaches to the center of the tube. Thus, for tubes, the thickness of the boundary layer is equal to the radius of the tube (or nearly so). The establishment of a fully developed flow regimen, for which the boundary layer growth is complete (ie, boundary layer thickness is equal to tube radius for laminar flow), is achieved only at some distance from the point at which fluid enters the tube. This distance, from the entry point to the establishment of the fully developed flow regimen, is called the entrance length (Le) (Fig 2).
Figure 1. Schematic diagram showing the relationship between flow and pressure required to generate the flow in a straight smooth tube.
Figure 2. Schematic diagram showing the growth of the boundary layer in the development of a fully developed laminar velocity profile as fluid enters a long, straight tube. The thickness of the boundary layer at the pipe entrance is equal to 0 and at the point of fully developed flow is approximately equal to the pipe radius (r). The length of pipe required, from the point of fluid entry, to the achievement of the fully developed profile is called the entrance length (Le).
Tags: artificial airways, breathing, endotracheal tube