Key equations and laws Flashcards
(128 cards)
1
Q
Combine the Beer and Lambert law into one definition
A
◦ 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
2
Q
beer’s law
A
‣ Beers law deals the the concentration measurement - absorption or attenutation of light is proportional to concentration of the substance
3
Q
Lamberts law
A
‣ Lamberts law deals with identification fo the pulsatile signal - ababsorption or attentuation is proportional to the distance the light has ti travel
4
Q
Oxygen saturation equations (not fractional saturations)
A
5
Q
Draw the equation for calculating HCO3 concentration
A
6
Q
Joule thomson efffect
A
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
7
Q
Viscocity
A
Fluids resistance to flow
8
Q
Newtonian fluid
A
Constant viscocity regardless of flow rate
9
Q
Non newtonian fluid
A
Viscocity changes with flow rate
10
Q
Surface tension
A
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
11
Q
Wall tension
A
Vessel wall that is an elasticated solid and the attraction between molecules across the surface of the solid (similar ot surface tension)
12
Q
Laplace’s law
A
The larger the radius of the vessel the greater the wall tension required to withstand a given internal fluid pressure
13
Q
What is Laplace’s equation for a spherical bubble
A
14
Q
What is Laplace’s law for a cylinder
A
15
Q
Work equation
A
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
16
Q
Energy definition
A
Capacity to do work
Measured in joules - the energy required to exert a force of one newton through a distance of one metre
17
Q
Power equation
A
Work done/ time taken
Units watt (1 J/sec)
The rate at which work is done or the rate of transfer of energy
18
Q
What is pressure by definiition?
A
Force divided by area
19
Q
Define compliance
A
The change of volume with respect to pressure and a measure of the ease of expansion
Units metres/newton
20
Q
Compliance equation
A
Change in volume / change in pressure
21
Q
What is elastance
A
The opposite, or reciprocal of compliance
Chnage in pressure/change in volume
22
Q
How to calculate the energy required to move a volume througha tube?
A
E = pressure x volume
23
Q
How are power and flow related? (laminar)
A
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
24
Q
In turbulent flow how is this related to pressure?
A
Power is directly proportional to flow ^ 3
25
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
26
Define flow
the movement of gas through a tube or system
Volume / time
27
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
28
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
29
What is the velocity profile within a blood vessel
Parabolic - fastest at the middle, decreasingly fast either side
30
Flow occurs when...
There is a difference in pressure between two points
31
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
32
Describe the relationship between flow and resistance
Flow = change in pressure or driving pressure / flow resistance of the tube
33
What is Ohms law
Current = potential difference or voltage/ resistance
34
Flow has what relationship to pressure
Directly proportional
35
What is resistance defined by
Hagen Poiseuelle law
36
What are the assumptions of the hagen Poiseuille equation
liquid is incompressible
Viscosity is stable
Flow is laminar
37
Hagen poiseuelle equation
38
What equation is this
Hagen Poiseulle equation
39
What is the equation for low solved for the Hagen POisuelle equation
40
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
41
What is Reynolds number?
A number used to predict whether turbulent or laminar flow would occur in a given system. It has no units
42
Reynaulds number equation
43
Reynaulds number equation
44
What is the unit for density
kg/m cubed
45
What is the unit for viscocity
newton x seconds/ metres cubed
46
What are the cutoffs for the Reynolds number
<2000 predominantly laminar
>4000 turbulen flow predominant
2000-4000 transitional with eddies and vortices
47
What effect does viscocity have on laminar flow?
Increasing viscocity reduces the reynolds number proportionally and therefore makes flow more laminar
48
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
49
What is the COanda effect
fluid or gas stream will hug the convex contour when directed at a tangent to the surface
50
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.
51
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
52
Avogadros law
equal volumes of gasses at the same temperature and pressure contain the same number of molecules
53
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
54
What is molar mass
the mass of 6.02 x 10 ^23 partiicles of the substance measured in g / mol
55
Daltons law
for a gas the total pressure is simply all the partial pressures added up
Pt = P1 + P2 + P3
56
How would you calculate the partial pressure of oxygen change between dry air at standard H20 pressures, and alveolar gas pressures?
57
Boyles law
the volume of gas is inversely proportional to its pressure at a fixed temperature
58
Describe the relationship between pressure and volume in gasses and draw a diagram to represent the same
59
What is Charle's law
at a given pressure the temperature is directly proportional to the volume of the gas - linera relationship
60
Guy-Lussac's law
the pressure of a gas is directly proportional to its temperature within a fixed volume
61
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
62
What is the combined gas law
63
What is the univertsal gas equation
64
Define diffusion
Passive movemen tof a substance from an area of high concentration to that of lower concentration
65
Ficks law of diffusion
66
Add the diffusion constant to Fick's law of diffusion
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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
68
Grahams law of diffusion
rate at which gasses diffuse are inversely proportional to the square root of their densities
69
Why is Grahams law of diffusion based on density? How can it be rearranged for molecular mass?
70
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
71
What two factors does the diffusion constant involve
72
What is osmotic pressure
the pressure required to stop the flow from one side of a semi permeable membrane to another
73
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
74
Define partition coefficient
the ratio of conentrations of a substance in two phases of a mixture of two immiscible solvents
75
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
76
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
77
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.
78
Raoults law
the fall in vapour pressure of a solvent is proportional to the molar concentration of the solute
79
Mathematics of the Beer-Lambert law
80
Define current
the flow of an electric charge - this can be electrons or flow of charged particles e.g. ions
81
Wire resistance is proportional to?
Increases with length
Decreases with cross sectoinal area increases
Conduct better at lower temperatures
82
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
83
Ohms law
the potential difference between two points is the product of the resitance and the current flowing
84
Draw the Ohm;s law pyramid
85
Kirchoffs first law
current in = current out
Or the sum of all currents going in and out is zero
86
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)
87
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
88
Power in electrical terms =
Voltage x current
voltage squared / resistance
Current squared x resistance
89
Resistance in series calculation
the total resistance is greater than the largest reisstors
90
Resistors in parallel equation
the total resisstance is smaller than the smallest resistor
91
Impedence
the resistance to thef low of an alternating current - instead of resistance using in DC
Calculations for power remain the same
92
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
93
The charge Q in a capacitor is given by what equation
Q = C x Vc
C is caacitance
Vc is appplied voltage
94
How do you calculate distance in the pulse echo principle
2d = v x t
95
What is the equation for natural frequency
96
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
97
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
98
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
99
What is cardiac output equal to in the circulatory flow model diagram dye dilution technique
Amount of dye injected / area under graph
100
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
101
FICK EQUATION
* CO = VO2/ Ca - Cv
◦ Blood flow to an organ = rate of uptake or excretion of a substance / arterio-venous concentration difference
102
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
103
What is a typical VO2 normal value
250ml/min
104
What is a typical CaO2 value in the direct Fick equation
0.2mL O2 per mL of blood
105
What is a typical CvO2 in the Fick equation
0.15mL of O2 per mL of venous blood
106
What is the Stewart Hamilton equation
107
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
108
What different methods of indicator dilution are there? What underlying prinicple is there?
Stewart Hamilton equation underlies
Methods
* Thermodilution by PAC or PICCO
* Lithium dilution
* Conductivity dilution using saline
* Indicator dye dilution
109
What is the equation for cardiac output when an indicator dye is used?
110
What is the equationf or cardiac output when temperature change is used?
111
How is stroke volume derived from pulse contour analysis? How is it calibrated? What is the calibration factor?
112
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
113
What is the equation for SVR
114
What is a normal BSA for males and females
These are indexed to BSA- The normal average adult BSA is 1.9 m2 for males and 1.6 m2 for females. Thus, a normal adult male with a cardiac output of 5.0 L/min would score a cardiac index (CI) of 2.6 L/min/m2.
115
BSA calculation
116
When does BSA measurement break down
* Morbidly obese - BSA higher than actual required output, so required index may be below expected
* Children - BSA and metabolic rate do not correlate as well, so even with normal index can be insufficent
117
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
118
Define stroke volume
the volume of blood pumped out fo the L of the heart during each systolic contraction
119
How is stroke volume determined using cardiac measurement devices
cardiac output / HR --> i.e. average SV over 1 minute
120
Normal stroke volume values
60 -100mL/beat
121
SVI define? Normal values
CI / HR x 1000
Indexed for body size
33 - 47 mL/metre squared / beat
122
SVR calculation and normal values
80 x (MAP - CVP) / cardiac output
Normal 800 - 1200 dynes-sec/cm ^ -5
123
SVRI - Define?
SVR indxed to body size
80 x (MAP - CVP) / CI
Normal vlue 1970 - 2390 dynes-sec/cm^-5 x metres squared
124
Pulmonary vascular resistance calculation
80 x (MPAP - PAWP) / cardiac output
Normal value <250 dynes - sec / cm^ -5
125
Hagen Poiseuille law
126
Turbulent flow is proportional to? and inversely proportional to?
127
Reynolds number
128
What affects flow
