Dimensionless numbers

Functions are provided for the following dimensionless numbers:

  • Archimedes number (Ar)

  • Biot number (Bi)

  • Peclet number (Pe)

  • Prandtl number (Pr)

  • Pyrolysis number I (Py I)

  • Pyrolysis number II (Py II)

  • Reynolds number (Re)

  • Schmidt number (Sc)

  • Sherwood number (Sh)

  • Flow regime

Source code

chemics.archimedes(dp, rhog, rhos, mu)[source]

Calculate the dimensionless Archimedes number.

\[Ar = \frac{d_p^3 \rho_g (\rho_s - \rho_g) g}{\mu^2}\]
Parameters:

  • dp (float) – Particle diameter in meters

  • rhog (float) – Gas density in kg/m3

  • rhos (float) – Solid density in kg/m3

  • mu (float) – Dynamic viscosity in kg/(m⋅s)

Returns:

ar (float) – Archimedes number

Example

>>> cm.archimedes(0.001, 910, 2500, 0.001307)
8309.1452...

References

Daizo Kunii and Octave Levenspiel. Fluidization Engineering. Butterworth-Heinemann, 2nd edition, 1991.

chemics.biot(h, d, k)[source]

Calculate the dimensionless Biot number.

\[Bi = \frac{h\, d}{k}\]
Parameters:

  • h (float) – Convective heat transfer coefficient in W/(m2⋅K)

  • d (float) – Characteristic length or dimension in meters

  • k (float) – Thermal conductivity in W/(m⋅K)

Returns:

bi (float) – Biot number

Example

>>> cm.biot(4.63, 0.001, 3.84)
0.0012057...

References

Daizo Kunii and Octave Levenspiel. Fluidization Engineering. Butterworth-Heinemann, 2nd edition, 1991.

chemics.peclet(ui, L, Dax)[source]

Calculate the dimensionless Peclet number for mass transfer.

The Peclet number is defined as the ratio between the bulk mass transport (convection) and the molecular diffusion.

\[Pe = \frac{u_i L}{D_{ax}}\]
Parameters:

  • ui (float) – Interstitial velocity in m/s

  • L (float) – Length or characteristic dimension in meters

  • Dax (float) – Axial dispersion coefficient in m2/s

Returns:

pe (float) – Peclet number

Example

>>> cm.peclet(3.0e-3, 0.25, 4.7e-4)
1.5957...

References

J.D. Seader, E.J. Henley, D.K. Roper. Separation Process Principles. John Wiley & Sons, Inc., 3rd edition, 2011.

chemics.prandtl(cp=None, mu=None, k=None, nu=None, alpha=None)[source]

Calculate the dimensionless Prandtl number for a fluid or gas.

\[Pr = \frac{c_p \mu}{k} = \frac{\nu}{\alpha}\]
Parameters:

  • cp (float) – Specific heat in J/(kg⋅K)

  • mu (float) – Dynamic viscosity in kg/(m⋅s)

  • k (float) – Thermal conductivity in W/(m⋅K)

  • nu (float, optional) – Kinematic viscosity in m2/s

  • alpha (float, optional) – Thermal diffusivity in m2/s

Returns:

pr (float) – Prandtl number

Examples

>>> cm.prandtl(cp=4188, mu=0.001307, k=0.5674)
9.647...

>>> cm.prandtl(nu=1.5064e-5, alpha=2.1002e-5)
0.71726...
Raises:

ValueError – Must provide (cp, mu, k) or (nu, alpha)

References

Daizo Kunii and Octave Levenspiel. Fluidization Engineering. Butterworth-Heinemann, 2nd edition, 1991.

chemics.pyrolysis_one(k, kr, rho, cp, r)[source]

Calculate the pyrolysis number Py I for a biomass particle.

\[Py^I = \frac{k}{\rho\,C_p\,R^2\,K}\]
Parameters:

  • k (float) – Thermal conductivity of the biomass particle in W/(m⋅K)

  • kr (float) – Rate constant in 1/s

  • rho (float) – Density of the biomass particle in kg/m3

  • cp (float) – Heat capacity of the biomass particle in J/(kg⋅K)

  • r (float) – Radius or characteristic length of the biomass particle in meters

Returns:

pyro_one (float) – Pyrolysis number Py I

Example

>>> cm.pyrolysis_one(k=0.12, kr=1.38556, rho=540, cp=3092.871049, r=0.0001847)
1.52...

References

D.L. Pyle and C.A. Zaror. Heat Transfer and Kinetics in the Low Temperature Pyrolysis of Solids. Chemical Engineering Science, vol. 39, no. 1, pg. 147-158, 1984.

chemics.pyrolysis_two(h, kr, rho, cp, r)[source]

Calculate the pyrolysis number Py II for a biomass particle.

\[Py^{II} = \frac{h}{\rho\,C_p\,R\,K}\]
Parameters:

  • h (float) – Convective heat transfer coefficient in W/m2K

  • kr (float) – Rate constant in 1/s

  • rho (float) – Density of the biomass particle in kg/m3

  • cp (float) – Heat capacity of the biomass particle in J/(kg⋅K)

  • r (float) – Radius or characteristic length of the biomass particle in meters

Returns:

pyro_two (float) – Pyrolysis number Py II

Example

>>> cm.pyrolysis_two(h=862.6129, kr=1.38556, rho=540, cp=3092.871049, r=0.0001847)
2.018...

References

D.L. Pyle and C.A. Zaror. Heat Transfer and Kinetics in the Low Temperature Pyrolysis of Solids. Chemical Engineering Science, vol. 39, no. 1, pg. 147-158, 1984.

chemics.reynolds(u, d, rho=None, mu=None, nu=None)[source]

Calculate the dimensionless Reynolds number for a fluid or gas flow.

\[Re = \frac{\rho\, u\, d}{\mu} = \frac{u\, d}{\nu}\]
Parameters:

  • u (float) – Flow speed in m/s

  • d (float) – Characteristic length or dimension in meters

  • rho (float, optional) – Density of the fluid or gas in kg/m3

  • mu (float, optional) – Dynamic viscosity of the fluid or gas in kg/(m⋅s)

  • nu (float, optional) – Kinematic viscosity of the fluid or gas in m2/s

Returns:

re (float) – Reynolds number

Examples

>>> cm.reynolds(2.6, 0.025, rho=910, mu=0.38)
155.65789...

>>> cm.reynolds(0.25, 0.102, nu=1.4e-6)
18214.2857...
Raises:

ValueError – Must provide (u, d, rho, mu) or (u, d, nu)

References

Daizo Kunii and Octave Levenspiel. Fluidization Engineering. Butterworth-Heinemann, 2nd edition, 1991.

chemics.schmidt(mu, rho, Dm)[source]

Calculate the dimensionless Schmidt number.

The Schmidt number represents the ratio between momentum diffusivity (kinematic viscosity) and mass diffusivity.

\[Sc = \frac{\mu}{\rho D_m}\]
Parameters:

  • mu (float) – Viscosity of the fluid flowing through the packed bed in Pa⋅s

  • rho (float) – Density of the fluid flowing through the packed bed in kg/m3

  • Dm (float) – Molecular diffusion coefficient in m2/s

Returns:

sc (float) – Schmidt number

Example

>>> cm.schmidt(8.90e-4, 997.07, 2.299e-9)
388.26...

References

J.D. Seader, E.J. Henley, D.K. Roper. Separation Process Principles. John Wiley & Sons, Inc., 3rd edition, 2011.

chemics.sherwood(k, d, Dm)[source]

Calculate the dimensionless Sherwood number.

The Sherwood number represents the ratio between the convective mass transfer and the rate of diffusive mass transport.

\[Sh = \frac{k d}{D_m}\]
Parameters:

  • k (float) – Convective mass transfer coefficient in m/s

  • d (float) – Particle diameter or characteristic length in meters

  • Dm (float) – Molecular diffusion coefficient in m2/s

Returns:

sh (float) – Sherwood number

Example

>>> cm.sherwood(2.3e-4, 5.0e-6, 4.0e-9)
0.2875...

References

J.D. Seader, E.J. Henley, D.K. Roper. Separation Process Principles. John Wiley & Sons, Inc., 3rd edition, 2011.

chemics.flow_regime(Re=None, u=None, d=None, rho=None, mu=None, nu=None)[source]

Flow regime.

Determine flow regime (laminar, transitional or turbulent) considering the Reynolds number boundaries for the case of a straight, non-smooth pipe.

Laminar regime …….. Re < 2100
Transitional regime … 2100 <= Re <= 4000
Laminar regime …….. Re > 4000
Parameters:

  • Re (float, optional) – Reynolds number

  • u (float, optional) – Flow speed in m/s

  • d (float, optional) – Characteristic length or dimension in meters

  • rho (float, optional) – Density of the fluid or gas in kg/m3

  • mu (float, optional) – Dynamic viscosity of the fluid or gas in kg/(m⋅s)

  • nu (float, optional) – Kinematic viscosity of the fluid or gas in m2/s

Returns:

regime (string) – Flow regime. One of laminar, transitional or turbulent.

Examples

>>> cm.flow_regime(u=2.6, d=0.025, rho=910, mu=0.38)
'laminar'

>>> cm.flow_regime(Re=3250)
'transitional'

>>> cm.flow_regime(u=0.25, d=0.102, nu=1.4e-6)
'turbulent'
Raises:

ValueError – Must provide Re or (u, d, rho, mu) or (u, d, nu)

References

R.H. Perry, D.W. Green. Perry’s Chemical Engineers’ Handbook. McGraw-Hill, 8th edition, 2008.