in fluid mechanics and heat transfer* Name Definition Ratio of Significance Gravitational force Archimedes number P, - P) Viscous force L. AR = Length L. Length Aspect ratio or Width Diameter hl. Internal thermal resistance Biot number Surface thermal resistance Gravitational force Bond number Bo = Surface tension farce P- P, Pressure - Vapor pressure Cavitation number Ca (sometimes o)- Inertial pressure 2(P - РЭ Sometimes 87, Wall friction force Darcy friction factor Inertial force Fo Drag force Drag coefficient devA Dynamic force Kinetic energy Eckert number Enthalpy AP sometimes AP Pressure difference Euler number Eu = Dynamic preнsre 2r. G= Wall friction force Fanning frietion factor Incrtial force Physical time at Fo (sometimes t) - Fourier number Thermal diffusion time Inertial force Froude number Sometimes Gravitational force Gr = ATIL' Висуancy force Grashof number Viscous force G,(T - T) Ja = Sensible energy Jakob number Latent energy Mean free path length Characteristic length Knudsen number Kn = Thermal diffusion Lewis number Le = pe,Da Das Species diffusion F. Lift force Lift coefficient Dynamic force (continued) Name Definition Ratio of Significance Flow speed Speed of sound Mach number Ma (sometimes M) Convection heat transfer Nusselt number Nu= Conduction heat transfer pL.Vc, LV Bulk heat transfer Peclet number Conduction heat transfer Power Power number N.- pD'a Rotational inertia Viscous diffusion Prandtl number Thermal diffusion Static pressure difference Pressure coefficient Dynamic pressure RPIATEc, Висуancy force Viscous force Rayleigh numbeer ku pVL VI. Inertial force Reynelds number Re = Viscous force Висуаnсy foree Richardson number Ri = Inertial force Viscous diffusion Schmidt number Se DAn Species diffusion VI. Overall mass diffusion Sherwood number Species diffusion Enthalpy Internal energy Specifie heat ratio k (sometimes y) = Convection heat transfer Stanton number St = pr,V Thermal capacity Stk (sometimes St) = 18ul. Particle relaxation time Characteristic flow time Stokes number Characteristic flow time St (scmetimes Sor Sr) =4 Strouhal number Period of oscillation pVI. Inertial force Weber number We Surface tension force *Ais a characteristic ares, Disa caracteristic diameter, fisa characteristic froquency (Hz, Lisa characteristic length, risa characteristic time, Tisa characteristic (absotute) temperature, Visa daracteristic velocity, Wis a characteristic with Weecharacteristie nower ais a charatoristie anenter welovity drsd Other arametor end uidemneeties in
Oftentimes it is desirable to work with an established dimensionless parameter, but the characteristic scales available do not match those used to define the parameter. In such cases, we create the needed characteristic scales based on dimensional reasoning (usually by inspection). Suppose for example that we have a characteristic velocity scale V, characteristic area A, fluid density ? , and fluid viscosity ? , and we wish to define a Reynolds number. We create a length scale L = √A, and define Re = ρV√A/? In similar fashion, define the desired established dimensionless parameter for each case: (a) Define a Froude number, given V ·′ = volume flow rate per unit depth, length scale L, and gravitational constant g. (b) Define a Reynolds number, given V ·′ = volume flow rate per unit depth and kinematic viscosity ? .(c) Define a Richardson number (see Table, given V ·′ = volume flow rate per unit depth, length scale L, characteristic density difference Δ? , characteristic density ? , and gravitational constant g
![in fluid mechanics and heat transfer*
Name
Definition
Ratio of Significance
Gravitational force
Archimedes number
P, - P)
Viscous force
L.
AR =
Length
L.
Length
Aspect ratio
or
Width
Diameter
hl.
Internal thermal resistance
Biot number
Surface thermal resistance
Gravitational force
Bond number
Bo =
Surface tension farce
P- P,
Pressure - Vapor pressure
Cavitation number
Ca (sometimes o)-
Inertial pressure
2(P - РЭ
Sometimes
87,
Wall friction force
Darcy friction factor
Inertial force
Fo
Drag force
Drag coefficient
devA
Dynamic force
Kinetic energy
Eckert number
Enthalpy
AP
sometimes
AP
Pressure difference
Euler number
Eu =
Dynamic preнsre
2r.
G=
Wall friction force
Fanning frietion factor
Incrtial force
Physical time
at
Fo (sometimes t) -
Fourier number
Thermal diffusion time
Inertial force
Froude number
Sometimes
Gravitational force
Gr = ATIL'
Висуancy force
Grashof number
Viscous force
G,(T - T)
Ja =
Sensible energy
Jakob number
Latent energy
Mean free path length
Characteristic length
Knudsen number
Kn =
Thermal diffusion
Lewis number
Le =
pe,Da Das
Species diffusion
F.
Lift force
Lift coefficient
Dynamic force
(continued)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9cafe71-3f77-4c22-bfcd-b7265c087648%2F7764f1e1-8a9b-4d76-adc2-9489b251903c%2Feqs5k5g.png&w=3840&q=75)
![Name
Definition
Ratio of Significance
Flow speed
Speed of sound
Mach number
Ma (sometimes M)
Convection heat transfer
Nusselt number
Nu=
Conduction heat transfer
pL.Vc, LV
Bulk heat transfer
Peclet number
Conduction heat transfer
Power
Power number
N.-
pD'a
Rotational inertia
Viscous diffusion
Prandtl number
Thermal diffusion
Static pressure difference
Pressure coefficient
Dynamic pressure
RPIATEc,
Висуancy force
Viscous force
Rayleigh numbeer
ku
pVL VI.
Inertial force
Reynelds number
Re =
Viscous force
Висуаnсy foree
Richardson number
Ri =
Inertial force
Viscous diffusion
Schmidt number
Se
DAn
Species diffusion
VI.
Overall mass diffusion
Sherwood number
Species diffusion
Enthalpy
Internal energy
Specifie heat ratio
k (sometimes y) =
Convection heat transfer
Stanton number
St =
pr,V
Thermal capacity
Stk (sometimes St) =
18ul.
Particle relaxation time
Characteristic flow time
Stokes number
Characteristic flow time
St (scmetimes Sor Sr) =4
Strouhal number
Period of oscillation
pVI.
Inertial force
Weber number
We
Surface tension force
*Ais a characteristic ares, Disa caracteristic diameter, fisa characteristic froquency (Hz, Lisa characteristic length,
risa characteristic time, Tisa characteristic (absotute) temperature, Visa daracteristic velocity, Wis a characteristic
with Weecharacteristie nower ais a charatoristie anenter welovity drsd Other arametor end uidemneeties in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9cafe71-3f77-4c22-bfcd-b7265c087648%2F7764f1e1-8a9b-4d76-adc2-9489b251903c%2Faie9e5.png&w=3840&q=75)
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