TURBULENT FLOW AND CLINICAL APPLICATIONS

⚱️The flow pattern of a river running over rapids is very different to the steadily flowing river (laminar flow). Here, the water’s path of travel becomes far less predictable than for laminar flow. This is an example of turbulent flow. An intermediate example is water flowing near the bank of a steadily flowing river, which often tends to meander, turning round in gentle circles. This is an example of eddies, the forerunner to full-blown turbulence.

⚱️As flow is, by definition, unpredictable, there is no single equation that defines the rate of turbulent flow as there is with laminar flow.

⚱️But, in well controlled circumstances the point at which flow changes from laminar to turbulent flow can be estimated using the Reynolds number, Re, which is named after Osborne Reynolds (1842–1912) of Manchester University, an engineering professor.

⚱️The Reynolds number allows us to predict whether turbulent or laminar flow would occur in a given system. The Reynolds number is a dimensionless quantity, i.e. it has no units. It is defined as the ratio of inertial and viscous forces. 

⚱️A Reynolds number <2000, where viscous forces predominate, predicts flow to be laminar. Between 2000 and 4000, both laminar and turbulent flow are anticipated. Above 4000, flow is likely to be completely turbulent because inertial forces are dominant. Critical flow is the point above which turbulent flow commences, which occurs at a Reynolds number of around 2000.

⚱️Viscosity is the important property for laminar flow

⚱️Density is the important property for turbulent flow

⚱️Reynold’s number of 2000 delineates laminar from turbulent flow (Tim and Pinnock: Re < 1000 is associated with laminar flow, while Re > 2000 results in turbulent flow)

⚱️A high Reynolds number means that the inertial forces dominate, and any eddies in the flow will be easily created and persist for a long time, creating turbulence. In a given airway with a known gas and flow velocity, the likelihood of turbulent flow can be predicted from Re.

⚱️APPLICATIONS: Both laminar and turbulent flow exist within the respiratory tract, usually in mixed patterns. Turbulent flow will increase the effective resistance of an airway compared with laminar flow. Turbulent flow occurs at the laryngeal opening, the trachea and the large bronchi (generations 1–5) during most of the respiratory cycle. It is usually audible and almost invariably present when high resistance to gas flow is encountered

⚱️APPLICATIONS: The principal sites of resistance to gas flow in the respiratory system are the nose and the major bronchi rather than the small airways. Since the cross-sectional area of the airway increases exponentially as branching occurs, the velocity of the airflow decreases markedly with progression through the airway generations, and laminar flow becomes predominant below the fifth generation of airway

LAMINAR FLOW

# When watching a steadily flowing river, the flow of water may be seen to be fastest in the middle, while near the banks of the river the water flows more slowly. 

# This behaviour is also observed in fluid travelling slowly along a wide straight cylindrical tube, where the fastest velocity occurring in the centre of the tube and the slowest at the edge where there is friction between the wall of the tube and the fluid. This is known as laminar flow.

# Viewed from the side as it is passing through a tube, the leading edge of a column of fluid undergoing laminar flow appears parabolic. The fluid flowing in the centre of this column moves at twice the average speed of the fluid column as a whole. The fluid flowing near the edge of the tube approaches zero velocity.

#  #Hagen (in 1839) and #Poiseuille, a surgeon (in 1840) discovered the laws governing laminar flow through a tube. If a pressure P is applied across the ends of a tube of length, l, and radius, r. Then the flow rate, Q, produced is proportional to:
*The pressure gradient (P/l) *The fourth power of the tube radius *The reciprocal of fluid viscosity . This is often combined as: (see the figure for the equation)

where Q is flow, ΔP is pressure gradient, r is radius, η is fluid viscosity and l is length

# Also note: Viscosity is the important property for laminar flow, whereas density is the important property for turbulent flow. Reynold’s number of 2000 delineates laminar from turbulent flow

Physics For Anesthesiologist ( #PFA ) : #IMPEDANCE

🖊Impedance is a term that is commonly used in the world of #electrophysiology and #BiomechanicalEngineering. 

🖊The chance of getting an electric shock is high when you have wet hands because the impedance of the skin is lower than when it is dry. 

🖊Thoracic impedance increases during inspiration.

🖊When applying electric current to the chest during #defibrillation, less energy may reach the heart during the inspiratory phase than during the expiratory phase because of this phenomenon, thereby decreasing the possible success of defibrillation. 

🖊So better to attempt defibrillation during the expiratory phase of mechanical ventilation.

🖊Where the #resistance of a circuit is dependent on the frequency of the current through it, the term impedance is used. 

 🖊The unit of impedance is therefore the same as that of resistance (the ohm), but the symbol Z is used to differentiate it from the symbol used for resistance (Ω).

🖊In case of a capacitor, as the frequency of the current increases, the current passes through the circuit more easily, i.e. the resistance of the capacitor falls with increasing current frequency. 

🖊In contrast, the resistance of an inductor rises as the frequency of the current increases.

#PhysicsForAnesthesiologist , #anesthesiologist , #anesthesia , #biomedical

Davis PD, Kenny GNC. Basic Physics and Measurement in Anaesthesia, 5th edn. Oxford: Butterworth–Heinemann, 2003; pp. 149–64 . Ewy GA, Hellman DA, McClung S, Taren D. Influence of ventilation phase on transthoracic impedance and defibrillation effectiveness. Crit Care Med 1980; 8: 164–6

MEASUREMENT OF CEREBRAL BLOOD FLOW

✔️Can be measured by Fick Principle

✔️This states that the uptake/ release of a substance e.g. O2 (Vo2) by an organ is the product of the blood flow (Q) through that organ and the arteriovenous difference in content (Cao2-Cvo2)

✔️This is applied using Kety-Schmidt technique where 10% Nitrous oxide is inhaled for 10-15 minutes, and the jugular venous concentration is measured and assumed to be the same as the brain concentration

✔️Once CBF is determined, additional values like CMRO2 and vascular resistance may be derived. 

✔️N2O offers significant advantages over other agents used for the measurement of CBF in that it is safe, stable, cheap, readily available and has a partition coefficient unaffected by varying levels of lipid and water and hence is unlikely to change with age or cerebral oedema.

✔️CBF calculated by this technique represents the mean blood flow from the area of the brain draining into the particular jugular venous bulb being sampled: i.e. the ipsilateral cerebral hemisphere. Therefore, the Kety–Schmidt method of CBF measurement is unable to discriminate between grey and white matter and is insensitive to regional changes in flow. 

Ref: Textbook of Neuroanaesthesia and Critical Care, Basil F Matta