# Chapter 4: Flow and Velocity

The physics of flow underlies the behavior of all fluids. Liquids, such as plasma and crystalloid solutions, and gases, such as oxygen and sevoflurane, are all considered to be fluids. Flow (*F*) is defined as the *quantity* (*Q*, mass or volume) of a given fluid that passes by a certain point within a unit of time (*t*), most commonly expressed in liters per second. This relationship can be expressed by the equation *F = Q/t*. Fluid flow requires a pressure gradient (Δ*P*) between two points such that flow is directly proportional to the pressure differential. Higher pressure differences will drive greater flow rates. The pressure gradient establishes the direction of flow.

Flow is different than velocity. Velocity is defined as the *distance* a given fluid moves within a unit of time, most commonly expressed in centimeters per second. The flow of a fluid within a tube is related to velocity by the relationship *F = V ⋅ r*^{2}, where *V* is the mean velocity and *r* is the radius of the tube.

There are two types of flow patterns:

**Laminar**—Fluids assuming laminar flow contain molecules that move in numerous thin layers or concentric tubes that are known as streamlines. There are no fluctuations. Successive particles within each sheet will pass the same point at the same steady velocity. Although laminar fluid particles move in a straight line, each streamline has a different velocity. Molecules in the center of the flow have the highest velocity, whereas those at the periphery of the tube are almost motionless. Fluids flow in a laminar pattern when they have low flow rates through smooth tubes with large cross-sectional areas, such as at the lung periphery. Laminar flow is directly proportional to the pressure gradient (*F*∝*P*). In this linear relationship, according to Ohm’s law, resistance (*R*) serves as a constant such that*F*= Δ*P*/*R*.**Turbulent**—Turbulent fluid flow contains molecules that move in irregular directions due to eddy currents. The disordered nature of turbulent flow increases resistance to flow. Turbulent flow typically occurs when fluid particles move at higher rates but with fluctuations. Unlike laminar flow, turbulent fluids have a nonlinear relationship between flow and pressure. The flow rate is proportional to the square root of the pressure gradient (*F*∝ √*P*). To increase turbulent flow twofold, the pressure gradient requires a fourfold increase. This is why laminar flow patterns are preferable to turbulent ones. Turbulent fluids are less efficient; they require higher energy to generate the greater pressure differential necessary to achieve an identical flow rate as laminar fluids. For example, if the airflow in the upper airways becomes more turbulent due to an obstruction, the patient will require greater work of breathing to maintain ...