Fluid mechanics: Flow and Poiseuille's law in operation

Poiseuille’s Law is a description of the pressure of a fluid as it travels through a cylindrical pipe. Combined with Ohm’s law describing flow as a function of pressure and resistance, clinicians can determine the amount of fluid delivery in many different aspects of medicine, including arterial blood flow, IV administration, and airway resistance. This is readily apparent in conditions like asthma, where resistance is caused by the decrease in airway diameter due to inflammation.

In applying Poiseuille’s law to an airway, variables that are inversely related to flow such such as length of the airway and viscosity of the fluid can be ignored, as these are constant. Therefore, the airflow into the lungs then is directly dependent on the air pressure as well as the radius of the airway. In addition, because flow is related exponentially (r4) to the radius of the airway, even modest decreases in airway radius can result in respiratory distress due to lack of oxygen availability.

In an operating room, Poiseuille’s law is extremely important. For procedures requiring general anesthesia, a patient’s airway must be kept open for proper exchange of oxygen and carbon dioxide. This can be achieved via an endotracheal tube. If an improperly sized tube is provided, a patient may not receive enough oxygen and enter respiratory distress. Similarly, if a patient is rapidly losing blood, blood transfusions must be done to prevent the patient from bleeding out. If the IV needle used for transfusion is not an appropriate size, complications can occur, including simply not returning enough blood if the flow is too little, and inducing fluid overload if the flow is too high.

Attribution: http://www.gosh.nhs.uk/health-professionals/clinical-guidelines/flush-volumes-for-central-venous-access-devices-cvads/ Berry, K., Bravery, K., & Ho, A. (2014). Central venuous access devices (CVADs): flush volumes. Great Ormond Street Hospital for Children. London, UK.