Key equations and laws Flashcards
Combine the Beer and Lambert law into one definition
◦ The measured absorbance for a single compound is directly proportional to the concentration fo the compound and the length of the light path through the sample
beer’s law
‣ Beers law deals the the concentration measurement - absorption or attenutation of light is proportional to concentration of the substance
Lamberts law
‣ Lamberts law deals with identification fo the pulsatile signal - ababsorption or attentuation is proportional to the distance the light has ti travel
Oxygen saturation equations (not fractional saturations)
Draw the equation for calculating HCO3 concentration
Joule thomson efffect
A gas changes temperature when it moves from higher pressure to lower pressure, and for most gasses they cool e.g. bike tire pumped = hot
Viscocity
Fluids resistance to flow
Newtonian fluid
Constant viscocity regardless of flow rate
Non newtonian fluid
Viscocity changes with flow rate
Surface tension
The result of attraction between moleciles across the surface of a liquid - as the molecules on the surface have reduced molecules to interact with compared to those deeper they form stronger bonds leaving the surface with the smallest possibel surface area for a given volume
Wall tension
Vessel wall that is an elasticated solid and the attraction between molecules across the surface of the solid (similar ot surface tension)
Laplace’s law
The larger the radius of the vessel the greater the wall tension required to withstand a given internal fluid pressure
What is Laplace’s equation for a spherical bubble
What is Laplace’s law for a cylinder
Work equation
Force applied x distance moved
Amount of energy applied to a system
ie. holding a shopping bag is not work because there is no distance moved
Energy definition
Capacity to do work
Measured in joules - the energy required to exert a force of one newton through a distance of one metre
Power equation
Work done/ time taken
Units watt (1 J/sec)
The rate at which work is done or the rate of transfer of energy
What is pressure by definiition?
Force divided by area
Define compliance
The change of volume with respect to pressure and a measure of the ease of expansion
Units metres/newton
Compliance equation
Change in volume / change in pressure
What is elastance
The opposite, or reciprocal of compliance
Chnage in pressure/change in volume
How to calculate the energy required to move a volume througha tube?
E = pressure x volume
How are power and flow related? (laminar)
If the pressure difference remains constant when E = P x V then
power = pressure x the rate of change of volume (or flow rate)
therefore since pressure is directly related to flow in laminar conditions
Power directly related to flow squared for laminar flow
In turbulent flow how is this related to pressure?
Power is directly proportional to flow ^ 3
Explain pressure as a concept then define it
Gas in a box contains millions of molecules zipping around in all directions bouncing off one antoher and off the walls, the combined effect of these collisions with the walls of the box create pressure
Pressure = force per unit of area
Define flow
the movement of gas through a tube or system
Volume / time
What is the conservation of flow?
Flow remains constant although if cross sectional area changes the velocity will also change to account for flow being conserved therefore
Q = A1 x V1 = A2 x V2
What is laminar flow
Orderly movement of a fluid that complies with a model in which parallel layers have different velocities relative to one another
What is the velocity profile within a blood vessel
Parabolic - fastest at the middle, decreasingly fast either side
Flow occurs when…
There is a difference in pressure between two points
What effect does resistance have on flow?
If resistance is increased a greater driving pressure is needed to maintain a fixed flow rate, BUT it will not prevent flow
Describe the relationship between flow and resistance
Flow = change in pressure or driving pressure / flow resistance of the tube
What is Ohms law
Current = potential difference or voltage/ resistance
Flow has what relationship to pressure
Directly proportional
What is resistance defined by
Hagen Poiseuelle law
What are the assumptions of the hagen Poiseuille equation
liquid is incompressible
Viscosity is stable
Flow is laminar
Hagen poiseuelle equation
What equation is this
Hagen Poiseulle equation
What is the equation for low solved for the Hagen POisuelle equation
Define turbulent flow
Movement of a fluid in which small scale currrents in the fluid move in irregular patterns while the overall flow is one directoin
What is Reynolds number?
A number used to predict whether turbulent or laminar flow would occur in a given system. It has no units
Reynaulds number equation
Reynaulds number equation
What is the unit for density
kg/m cubed
What is the unit for viscocity
newton x seconds/ metres cubed
What are the cutoffs for the Reynolds number
<2000 predominantly laminar
>4000 turbulen flow predominant
2000-4000 transitional with eddies and vortices
What effect does viscocity have on laminar flow?
Increasing viscocity reduces the reynolds number proportionally and therefore makes flow more laminar
What effect does density have on laminar flow
the more dense something is the hgiher the reynolds number and the more turbulent the flow will be
What is the COanda effect
fluid or gas stream will hug the convex contour when directed at a tangent to the surface
Explain the coanda effect
As has already been seen with the Venturi effect, when the water leaves the tap at speed, the flowing fluid entrains fluid (in this case air) into the stream of flow. When there is an obstruction, such as the spoon’s surface, this entrainment is dramatically reduced on the spoon side. There is a drop in pressure on the spoon side of the jet and this causes a deflection in the flow towards the spoon.
Define an ideal gas
An ideal gas has 3 conditions
- the molecules are assumed to be so far apart there is no attraction between them
- volume of the molecules themselves is negligible
- moleculears in random motion obeying newtons laws of motion
Avogadros law
equal volumes of gasses at the same temperature and pressure contain the same number of molecules
What is a mole
one mole is 6.02 x 10 ^ 23 atoms/molecules such that it represents a standard amount - it is derived from 12g of carbon
What is molar mass
the mass of 6.02 x 10 ^23 partiicles of the substance measured in g / mol
Daltons law
for a gas the total pressure is simply all the partial pressures added up
Pt = P1 + P2 + P3
How would you calculate the partial pressure of oxygen change between dry air at standard H20 pressures, and alveolar gas pressures?
Boyles law
the volume of gas is inversely proportional to its pressure at a fixed temperature
Describe the relationship between pressure and volume in gasses and draw a diagram to represent the same
What is Charle’s law
at a given pressure the temperature is directly proportional to the volume of the gas - linera relationship
Guy-Lussac’s law
the pressure of a gas is directly proportional to its temperature within a fixed volume
Draw a curve representing Guy Lussacs law
Benedict Roth spirometer - collecting gas passing through an airway opening. It is an expandable compartment consistent of a moveable statically counterbalanced rigid chamber or bell, a stationary base and a dynamic seal between them. The bell can move up and down freely so pressure inside it is close to atmospheric, the seal is often water but dry seals have been used. Changes in internal volume are proportional to displacement
What is the combined gas law
What is the univertsal gas equation
Define diffusion
Passive movemen tof a substance from an area of high concentration to that of lower concentration
Ficks law of diffusion
Add the diffusion constant to Fick’s law of diffusion
What factors lead to a faster rate of diffusion
Large surface area
Large concentration gradient
Small thickness ot diffuse through
High solubility in medium diffusing thorugh
Low molecular weight or density
Grahams law of diffusion
rate at which gasses diffuse are inversely proportional to the square root of their densities
Why is Grahams law of diffusion based on density? How can it be rearranged for molecular mass?
When does solubility of a gas matter to diffusion rate?
When diffusion is moving from a gas through a membrane into a liquid the rate of diffusion is proportional to soliubility of the gas
What two factors does the diffusion constant involve
What is osmotic pressure
the pressure required to stop the flow from one side of a semi permeable membrane to another
Henry’s law
at a cosntant temperature the amount of gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium wiht that liquid
Define partition coefficient
the ratio of conentrations of a substance in two phases of a mixture of two immiscible solvents
Blood gas coefficient- what does this mean and reflect?
The ratio fo the concentration of an anaesthetic agent in blood to that in the same volume of gas in contact with that blood at equilibrium
This reflects the solubility of the gas in blood
Oil/gas coefficeint - what does it reflect and why does it matter
the ratio of the concentration of an anaeshtetic agent in oil (adipose) to that in the same volume of gas in contact with that oil at equilibrium
this reflects the solubility of the gas in adipose/brain tissues in comparison to blood - it will reflect how easily it crosses the BBB. If the oil:blood coefficient is >1 (or blood:oil <1) then the concentration or amount of gas dissolved in adipose tissue will be higher than that in blood
What characteristics are ideal in an inhaled agent?
Low solubility in blood
If highly soluble it transfers quickly from the lungs, but has a lower partial pressure in blood once dissolved therefore staying in solution rather than passing to brian tissue therefore taking longer to work, longer to exit the body.
Raoults law
the fall in vapour pressure of a solvent is proportional to the molar concentration of the solute
Mathematics of the Beer-Lambert law
Define current
the flow of an electric charge - this can be electrons or flow of charged particles e.g. ions
Wire resistance is proportional to?
Increases with length
Decreases with cross sectoinal area increases
Conduct better at lower temperatures
What is voltage
an informal term for electrical potential difference - this is the amount of energy required to move a unit of charge between two points.
1 volt is if 1 coulomb were to move through a potential differenceof 1 volt it would require 1 joule of energy ; or the electrical potential required to move 1 ampere through 1 ohm resistor
Ohms law
the potential difference between two points is the product of the resitance and the current flowing
Draw the Ohm;s law pyramid
Kirchoffs first law
current in = current out
Or the sum of all currents going in and out is zero
Kirchoffs second law
closed loop netowrk the total voltage around the loop is equal tot he sum of all voltage drops within the same loop - this is also equal to zero (as the battery produces the voltage gain)
What is power in electircal terms
the rate of electrical energy usage/transferrance per second measured in watts - 1 watt is 1 joule transfered per second
Power in electrical terms =
Voltage x current
voltage squared / resistance
Current squared x resistance
Resistance in series calculation
the total resistance is greater than the largest reisstors
Resistors in parallel equation
the total resisstance is smaller than the smallest resistor
Impedence
the resistance to thef low of an alternating current - instead of resistance using in DC
Calculations for power remain the same
What is capacitance
a measure of the charge a device can hold measured in Farads
The cpacitance = charge stored in coulombs/ potential difference in volts
Energy stored = 1/2 capacitance x voltage squared
The charge Q in a capacitor is given by what equation
Q = C x Vc
C is caacitance
Vc is appplied voltage
How do you calculate distance in the pulse echo principle
2d = v x t
What is the equation for natural frequency
What is the Windkessel effect and how does it apply to arterial lines?
◦ The reflected wave in the upper aorta is more prominent however they merge as you progress down the vascular tree, amplification increases as the vascular tree becomes less compliant and more and more reflection waves accumulate —> windkessel effect as the stored energy
In the simple flow model of dye calculation of cardiac output what equation is used to calculate the rate of dye removal from a tank?
rate of dye removal = liquid flow x dye concentration
In the simple flow model of dye dilution cardiac output calculation what is flow rate equal to
amount of dye added / area under the graph
What is cardiac output equal to in the circulatory flow model diagram dye dilution technique
Amount of dye injected / area under graph
Describe the Fick principle in words where oxygen is the substrate
- Total uptake of oxygen by the body is equal to the product of the cardiac output and the arterial-venous oygen content difference
FICK EQUATION
- CO = VO2/ Ca - Cv
◦ Blood flow to an organ = rate of uptake or excretion of a substance / arterio-venous concentration difference
How is VO2 measured in the direct Fick method
- VO2 measurement
◦ patients breaths through a spirometer containing a known volume of 100% oxygen and a CO2 absorbed, after a minute the volume of O2 remaining in the spirometer allows the calculation of O2 uptake
What is the Stewart Hamilton equation
How is the Fick principle used indirectly?
- Measured of cardiac outptu using the Fick equation but substituting estimated values for the some of the measured variables
- Estimations
◦ Uses age/weight and sex based nomogram to estimate VO2 - especially inaccurate if morbidly obese, paralysed, thyrotoxicosis, burns, sepsis, hypothermia where metabolically not normal patients. Additionally pulmonary O2 consumption can be dramatically increased in pnumonia overestimating cardiac output
◦ Mixed venous blood assumed on the basis of normal vlues or estimated from CVC samplws; or from end tidal
◦ Arterial oxygen content can be estimated from pulse oximetry
What is the equation for cardiac output when an indicator dye is used?
What is the equationf or cardiac output when temperature change is used?
How is stroke volume derived from pulse contour analysis? How is it calibrated? What is the calibration factor?
What is the doppler equation for measuring velocity? How does velocity relate to flow?
◦ V = F (d)c / 2 F(O) cos (theta)
‣ V = velocity of blood in descending aorta
‣ F(d)c = change in frequency of the reflected ultrasound x speed of ultrasound in tissue
‣ F(O) = transmitted ultrasound freqeuncy
◦ Blood flow is then determined by velocity x cross sectional area of the descending aorta (thoracic) estimated from patients height and weight
What is the equation for SVR
BSA calculation
What is cardiac index? How is it calculated? What are its normal values?
Cardiac output / BSA
COmparison between cardiac output of patients of a different size
Normal 2.5 - 4 L/min/metre squared
Define stroke volume
the volume of blood pumped out fo the L of the heart during each systolic contraction
How is stroke volume determined using cardiac measurement devices
cardiac output / HR –> i.e. average SV over 1 minute
SVI define? Normal values
CI / HR x 1000
Indexed for body size
33 - 47 mL/metre squared / beat