FLOW MEASUREMENT

Principles of Flow

Pressure in fluids can be thought of as a form of potential energy, as described earlier. Kinetic energy in fluids is expressed in terms of flow, the bulk movement of fluid with a given direction and speed. We must carefully distinguish between fluid flow and fluid velocity, which are often confused. Flow () refers to the volume of fluid passing a particular location per unit of time; its SI units are meter cubed per second, but it is more commonly measured in milliliters per second or liters per minute. Fluid velocity (U) is simply the speed of the fluid at a particular point in space, measured in meters per second. By analogy, imagine a multilane freeway: the speed (velocity) of individual cars may vary depending on the lane; the flow is the number of cars passing a point per minute. The potential energy of pressure can be converted into the kinetic energy of flow; for example, the hydrostatic pressure generated by gravity acting on a vertical column of liquid can be transformed into flow by opening a valve at the bottom of the column. Pressure and flow can also change independently. With the human

TABLE 30-2 -- Comparison of hydrodynamic and electrical energy commonly encountered

Water	Electricity	Energy
Squirt gun	Static electric spark	High pressure, low flow, low energy
Garden hose	House current	Moderate pressure, moderate flow, moderate energy
	Car battery	Low pressure, moderate flow, moderate energy
River flood		Low pressure, huge flow, huge energy
Fire hose	High-tension wires	High pressure, high flow
	Lightning	High pressure, high flow

circulatory system used as an example, a healthy young trauma patient can have relatively high blood pressure but low blood flow (hypovolemic shock) with high systemic resistance. On the other hand, a septic patient can have very low blood pressure accompanied by high blood flow (high-output septic shock). The total mechanical energy of a moving fluid is the sum of the kinetic (flow) energy and the potential (pressure) energy ( Table 30-2 ).

A pressure gradient exerts a force on the fluid, and the fluid tends to accelerate in the direction of decreasing pressure. Pressure gradient is only one of the forces that commonly act on fluids; other forces include gravity (discussed earlier) and viscous force or friction. If these other forces are negligible and the fluid is incompressible (i.e., a liquid with constant density), the equation of motion (F = ma) can be integrated to yield

P + ½ρU² = P₀ (5)

where P is pressure, ρ is fluid density, U is the magnitude of the fluid velocity, and P₀ is a constant called the stagnation pressure (see Appendix 5 ). This form of the Bernoulli equation tells us that as velocity increases in a frictionless flow, pressure decreases and vice versa. This concept resolves the common misconception that pressure always decreases in the direction of flow. For example, in the flow inside a tube (a pipe or a large vein) of gradually increasing diameter, fluid velocity (U) decreases in the downstream direction as the diameter and cross-sectional area of the tube increase. As U decreases, Equation 5 tells us that P actually increases in the direction of flow. This example again shows the relationship of potential and kinetic energy in fluids: as the kinetic energy of this tube flow decreases (U² falls) in the flow direction, the potential energy increases (P rises) by an equal amount. The total energy remains constant because we have assumed no friction.

Flow can be determined by knowing the average velocity of the fluid across the tube. In laminar flow, Figure 30-16A , the velocity profile is distributed such that the highest velocity is in the center and the fluid at the edges is virtually stationary. In turbulent flow, the velocity profile is "flattened" ( Fig. 30-16B ). Some monitors measure flow directly, but most measure flow indirectly, by either pressure or velocity measurements.

The Bernoulli equation applies to a specific subset of flow parameters as listed earlier. Many flows important to anesthesiologists do not follow the Bernoulli equation. Most commonly, the flow that we desire to measure is not laminar but turbulent. The transition from laminar

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Figure 30-16 Laminar and turbulent flow. In a smooth-walled tube at low flow rates (i.e., small pressure gradients), the flow rate is laminar; that is, flow moves smoothly in concentric circles, with the centermost area having the greatest flow velocity and the area nearest the wall of the tube being virtually stationary. As the flow rate (and pressure gradient) increases, the flow transitions from laminar to turbulent. Instead of a neatly ordered flow, the velocities are more randomly distributed, energy is dissipated as heat, and the energy needed for a given flow rate increases. Many factors govern this transition, including size of the tube, viscosity of the fluid, flow rate, and pressure gradient. These factors are combined in determination of the Reynolds number (see Appendix 5 ).