Skip to content

polykin.transport.flow¤

vt_Stokes ¤

vt_Stokes(
    D: float, rhop: float, rho: float, mu: float
) -> float

Calculate the terminal velocity of an isolated sphere using Stokes' law.

In laminar flow (\(Re \lesssim 0.1\)), the terminal velocity of an isolated particle is given by:

\[ v_t = \frac{D^2 g (\rho_p - \rho)}{18 \mu} \]

where \(D\) is the particle diameter, \(g\) is the acceleration due to gravity, \(\rho_p\) is the particle density, \(\rho\) is the fluid density, and \(\mu\) is the fluid viscosity.

PARAMETER DESCRIPTION
D

Particle diameter (m).

TYPE: float

rhop

Particle density (kg/m³).

TYPE: float

rho

Fluid density (kg/m³).

TYPE: float

mu

Fluid viscosity (Pa·s).

TYPE: float

RETURNS DESCRIPTION
float

Terminal velocity (m/s).

See also
  • vt_sphere: generic method for laminar and turbulent flow.

Examples:

Calculate the terminal velocity of a 500 nm PVC particle in water.

>>> from polykin.transport.flow import vt_Stokes
>>> vt = vt_Stokes(500e-9, 1.4e3, 1e3, 1e-3)
>>> print(f"vt = {vt:.1e} m/s")
vt = 5.4e-08 m/s
Source code in src/polykin/transport/flow.py
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
def vt_Stokes(D: float,
              rhop: float,
              rho: float,
              mu: float
              ) -> float:
    r"""Calculate the terminal velocity of an isolated sphere using Stokes' law.

    In laminar flow ($Re \lesssim 0.1$), the terminal velocity of an
    isolated particle is given by:

    $$ v_t = \frac{D^2 g (\rho_p - \rho)}{18 \mu} $$

    where $D$ is the particle diameter, $g$ is the acceleration due to gravity,
    $\rho_p$ is the particle density, $\rho$ is the fluid density, and $\mu$ is
    the fluid viscosity.

    Parameters
    ----------
    D : float
        Particle diameter (m).
    rhop : float
        Particle density (kg/m³).
    rho : float
        Fluid density (kg/m³).
    mu : float
        Fluid viscosity (Pa·s).

    Returns
    -------
    float
        Terminal velocity (m/s).

    See also
    --------
    * [`vt_sphere`](vt_sphere.md): generic method for laminar and turbulent flow.

    Examples
    --------
    Calculate the terminal velocity of a 500 nm PVC particle in water.
    >>> from polykin.transport.flow import vt_Stokes
    >>> vt = vt_Stokes(500e-9, 1.4e3, 1e3, 1e-3)
    >>> print(f"vt = {vt:.1e} m/s")
    vt = 5.4e-08 m/s
    """
    vt = D**2*g*(rhop - rho)/(18*mu)

    Re = rho*vt*D/mu
    check_range_warn(Re, 0., 0.1, 'Re')

    return vt