Pressure, Flow & Measurement Dr James F Peerless November 2013

Objectives Pressure Flow Measurement of Volume and Flow

Pressure

“The force applied per unit area” P = f. a P = f. a

Pressure SI unit: pascal (Pa) (Nm -2 ) Other units – 1 bar = 100 kPa – 7.5 mmHg = 1 kPa – 10.2 cmH 2 O = 1 kPa – 1 atm = kPa

SI Units of Pressure Pressure = force / area Force= mass x acceleration = kg.m.s -1 (where 1 N = force required to give a mass of 1 kg an acceleration of 1 second per second) Area = m 2 Therefore: Pressure= kg.m.s -1 / m 2 = kg.m -1.s -1

Different Types of Pressure Partial pressure, Total pressure – Dalton’s Law The pressure exerted by an individual gas in a gas mixture is the same as if it was alone This is partial pressure of a gas – Total pressure is therefore the sum of partial pressures of a gas mixture

Absolute, Gauge Pressure Gauge Pressure – Pressure measurements above/below atmospheric pressure – Empty cyclinder = 0 kPa Absolute Pressure – Is zeroed against a vacuum, so; – = Gauge Pressure + Atmospheric Pressure – Empty cylinder = 101 kPa

Base SI Units Temperature: K Time: s Length: m Current: A Amount of Substance: mol Luminous Intensity: cd Mass: kg “Try To Look CALM”

Measuring Pressure Manometers Aneroid gauges Barometers Electrical transducers: Wheatstone bridge

Manometers Fluid-filled column Open to atmosphere – Read gauge pressure (not absolute) Measurers of low pressures Inaccuracies: – Surface tension H 2 0 – over-read Hg – under-read – No clinical significance but loved by MCQs!

Barometers Closed to atmosphere – Measure absolute pressure – Zeroed against a vacuum Not used in medicine

Aneroid Gauges Greek: “no water” E.g. Bourdon gauge High pressure measurements – e.g. cylinders Elliptical bourdon tube

Pressure Transducers

Flow

What is flow? “The amount of fluid passing a given point per unit time” F = Q/t = Q̇

Laminar Flow Fluid moves in a steady manner No eddies or turbulence Typically seen in smooth tubes at low rates Flow greatest at centre (x 2x̄) Pressure difference must exist for flow to occur Q̇ ∝ ΔP Viscosity is main component of laminar flow

Laminar Flow

Calculating Laminar Flow

Turbulent Flow Characterised by swirls and eddies Can occur at constrictions Velocity varies across the tube Flow proportional to square root of p Density is important factor of determinant of turbulent flow

Turbulent Flow

Predicting Flow Reynolds Number LAMINAR < 2000 < TURBULENT Can determine Critical Velocity

Bernoulli Effect Fall in pressure at a constriction in a tube There is a fall in potential energy (assoc. with pressure) Subsequent gain in kinetic energy (assoc. with flow) – no loss or gain of energy

Venturi Principle

Coanda Effect Tendency of a jet of fluid to attach itself to a curved surface due to areas of low pressure Fluid will preferentially flow down a limb of a Y-junction rather than being equally distributed. E.g. – ventilators – coronary vessels – bronchioles

Measurement of Volume and Flow

Measuring Volume & Flow Volume Benedict Roth Spirometer Dry Gas Meter Vitalograph Wright’s Respirometer Electronic Volume Monitor Flow Rotameters Wright’s Peak Flow Meter Fleisch Pneumotachograph Pitot Tubes Electronic Mass Flowmeter

Volume Benedict-Roth Spirometer

Dry Gas Meter Volume

Vitalograph Volume

Wright’s Respirometer Volume

Flow

Wright’s Peak Flow Meter Variable orifice, constant pressure

Flow

Pitot Tube

Flow Electronic Flowmeter

Reference Cross M, Plunkett E. Physics, Pharmacology and Physiology for Anaesthetists; Cambridge University Press, Cambridge. Davis P, Kenny G. Basic Physics and Measurement in Anaesthesia: 5 th Edition; Butterworth Heinemann, Edinburgh. Wijayasiri L, McCombe K, Patel A. The Primary FRCA Structured Oral Examination Study Guide 1; Radcliffe Publishing, Oxford.