# Turbulent Flow

## Properties of turbulent flow

Rough with much eddy current formation

Generated by sudden changes in direction or acute reduction in diameter

90% of turbulent flow in the airways occurs in the nose and trachea

Gas advances along tube at the same velocity at the center as at the periphery

Driving pressure to produce given gas flow proportional to the **square of volumetric flow rate**

Double flow by fourfold increase in pressure

## Reynold's Number (N_{R})

A way of combining the factors to detemine a number that can be used to indicate the presence of turbulent flow. It can be in as a varilable expression as:

velocity of gas flow

density of gas

radius of the tube

viscosity of the gas

[Velocity – the measure of linear distance traveled by the fluid per unit of time (cm/sec) which differs from flowrate which is volume/time]

NOTE: Egan's uses h for the symbol for viscosity and give the equation as which mathematically works the same.

Reynold's Number thus is:

(1) Determined mathematically from velocity of flow, radius of tube, density and viscosity of gas

(2) A unitless number

(3) Indicates that turbulent flow occurs when N_{R} > 2000 (assuming tube is smooth and regular - can occur at a lower number if surface of the tube is rough or irregular)

(4) Reynold's number increases if there is an

(a) Increase in linear velocity of gas, density of gas, or radius of tube

(b) Reduction in viscosity of gas

The above chart indicates that with increasing velocity the Reynold's number also increases - breathing in quickly creates more turbulent flow throughout the tracheobronchial tree and significantly increases the work of breathing. Getting a patient to take a slow breath could help reduce the effort and anxiety of breathing.

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