FORMULASHEET
Generalformulas:
Newton’s2ndlawofmotion.
Kineticenergy.
Gravitationalenergy.
Angularvelocityofcircularmotion,whereTistheperiodofthemotion.
:
𝜔= 1
𝑝𝑉 = 𝑛𝑅𝑇
8
𝜌 = '+∗;
9
.
TheconversionofgoingfromCelsiustoKelvin.Itisimportanttonotethatnegative
temperaturesdonotexistontheKelvinscale,whiletheydofortheCelsiusscale,so
whencalculatingwithabsolutetemperatures,useKelvin.Inrelativecalculationswhere
youtakeatemperaturedifference,itdoesn’tmattersinceKelvinandCelsiusarethe
samescale,excepttheyareshifted.
Theradiusofacircle,whereristheradius(halfthediameter)ofthecircle.
Theareaofacircle.
Thevolumeofasphere.
)0
Idealgaslaw.RistheGasconstant
Densityinmassperunitvolume.
Specificheat:Heatneededtoheatanobjectby1degreeCelsius.Unitsare
𝐹 = 𝑚 ∗ 𝑎 (
𝐸' = ) 𝑚𝑣 ) 𝐸+ = 𝑚 ∗ 𝑔 ∗ ℎ
=
𝐶=
8>1
𝑇; = 𝑇°C + 273,15 𝑠 = 2𝜋𝑟
𝐴 = 𝜋𝑟 ) L
𝑉 = M 𝜋𝑟 M Constants
𝑁 = 6.022 ∗ 10)M 𝑅 = 8.315
:
8ST∗;
.
Thenumberofmoleculesinamole,calledAvogadro’sConstant.
Thegasconstant
Quantities&Units
Mass
Time
Volume
Velocity
Density
Force
Temperature
Pressure
Flow
Diffusioncoefficient
ordiameter
Internalenergy
Heat
Work
Totalenergy
Area
Heattransfer
coefficient
Thermalconductivity
Specificheat
Dragcoefficient
Thermaldiffusivity
Viscosity
Fourier’snumber
Masstransfer
coefficient
𝑚
𝑡
𝑉
𝑣
𝜌
𝐹
𝑇
𝑝𝑜𝑟𝑃
𝜙
𝐷
kg
s
m3
m/s
kg.m-3
N
K
Pa
kg.m-2s-1
𝑈
𝑄
𝑊
𝐸
𝐴
ℎ
Nm
J
m2
𝜆
𝐶^ 𝐶_ 𝑎
𝜂
𝐹𝑜
𝑘
WEEK1:
Thegeneralbalanceequation.
𝑑
= 𝑖𝑛 − 𝑜𝑢𝑡 + 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛
𝑑𝑡
WEEK2:
Totalenergybalance
FirstlawofThermodynamics,whereΔ𝑊isthenetwork
doneonthesystem. Thethermalenergybalanceinasteadystatewithout
energychange.
Themechanicalenergybalance.
Bernoulli’sequation:Neglectsallfrictionandheat
production.ℎisheight.
Bernoulli’sPrinciple:Theenergyperunitvolumebeforeis
thesameastheenergyperunitvolumeafter.
𝑑𝐸
𝑝 1
= 𝜙8,gh ∗ 𝑈 + + 𝑣 ) + 𝑔ℎ
𝑑𝑡
𝜌 2
Δ𝑈 = Δ𝑄 + Δ𝑊
0 = 𝜙8
)
)
𝑣gh
− 𝑣Sij
𝑝gh − 𝑝Sij
+ 𝑔 ℎgh − ℎSij +
+ 𝜙p − 𝜙8 𝐸no 2
𝜌
𝑝 𝑣)
+
+ 𝑔ℎ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝜌 2
1
1
𝑃( + 𝜌𝑣() + 𝜌𝑔ℎ( = 𝑃) + 𝜌𝑣)) + 𝜌𝑔ℎ) 2
2
WEEK3:
gh
𝑝 1 )
+ 𝑣 + 𝑔ℎ
𝜌 2
0 = 𝜙8 𝑢gh − 𝑢Sij + 𝜙l + 𝜙8 𝑒no Reynoldsnumber,where𝜌n isthedensityofthefluid,𝑣o istherelativevelocity,Disthediameterand𝜇isthe
viscosityofthefluid
Thedragforce.𝐶_ isthedragcoefficient,Aisthefrontal
area,vistherelativevelocity.
Stokes’law:Thedragforceonaspherewithalow
Reynoldsnumber(𝑅𝑒 < 1).
− 𝜙8,Sij ∗ 𝑈 +
𝑅𝑒 =
𝜌n 𝑣o 𝐷
𝜇
1
𝐹_ = 𝐶_ 𝐴 ∗ 𝜌n 𝑣o) 2
𝐹_ = 3𝜋𝐷𝜇𝑣o Sij
WEEK4:
Fourier’slaw,thetransferofheat.𝜆isthematerial
conductivity,Δ𝑥isthethickness,Aisthearea,Δ𝑇isthe
differenceintemperature.
Fick’slawofdiffusion,analogoustoFourier’slaw.𝐷isthe
uv
diffusioncoefficient,Aistheareaand w isthechangein
ut
concentrationoverx.
𝜙l = 𝜆𝐴 ∗
>1
>t
uxy
𝜙8 = −𝐷 ∗ 𝐴 ∗
ut
WEEK5:
Newton’slawofcooling.ℎistheheattransfercoefficient.
Nusseltnumber.Usedtomakehdimensionless.
𝜙l = ℎ ∙ 𝐴 ∙ Δ𝑇
𝑁𝑢 =
{∙|
}
Masstransfercoefficient,where𝑆ℎistheSherwood
{
number,analogoustoNusseltnumber.Δ𝑥isthesizeofthe 𝑘 = 𝑆ℎ ∙ >t
object,alsocalledDsometimes.
WEEK6:
Thermaldiffusivity.𝜆isthermalconductivity,𝜌ismaterial
density,𝐶^ isspecificheat.
𝑎=
𝜆
𝜌 ∙ 𝐶^
Penetrationdepth.Onlyvalidwhilepenetrationtheorystill
_
holds,for 𝜋𝑎𝑡 < ,whereDisthesizeofthesheetbeing 𝑥^ = 𝜋𝑎𝑡
)
penetratedbyheat.
𝑎𝑡
Fouriernumber.
𝐹𝑜 =
Nusseltnumberforpenetrationtheory.
WEEK7:
Nonewformulasthisweek!J
𝑁𝑢 =
𝐷)
𝜋
𝐹𝑜
GRAPHS:
FORASPHERE