Curved Tubes
A profile of the upper respiratory tract shows that there are curves that any tube will need to negotiate as it courses between the nose or mouth and the trachea. As the tube is warmed by the body to body temperature, it will soften and have a reversal of curvature as it enters the trachea. The radius of curvature of the bend of an endotracheal tube is less when it is inserted nasally than when it is inserted orally. It is even smaller for a tracheostomy tube which has a 90° bend. As fluid rounds a bend in a tube, fluid going the fastest in the center is carried to the outside wall, and this sets up a secondary motion within the tube. This secondary motion requires energy so that there is further pressure drop incurred in rounding a bend. The result is that resistance is increased for a tube of the same diameter (D) if there is a bend in the tube. If the radius of curvature R is known, a dimensionless number called the Dean number (De) can be calculated. this

Formule 8

Pressure drop in curved tubes vs De have been measured, and as De increases, so does pressure drop. Pressure drop increases linearly with De for low values of De. A transition point does occur, however, at which pressure increases dramatically so that after a critical De, the pressure drop rises rapidly. This is analogous to the relationship between pressure and flow in straight tubes that was described earlier. An important consideration in the value of De is the ratio of D/R. The greater the radius of curvature of the tube relative to the tube diameter, the smaller the De. A straight tube would have an R of infinity. Thus, a slowly curving endotracheal tube of a certain length L and diameter D will have a lesser De (and thus a smaller resistive pressure drop) than a sharply curved tracheostomy tube of similar length and diameter with a small radius of curvature. Thus, for die latter, the pressure drop for a given flow will be greater.