polykin.transport.flow

DP_tube

DP_tube(
    Q: float,
    D: float,
    L: float,
    rho: float,
    mu: float,
    er: float = 0.0,
) -> float

Calculate the pressure drop due to friction for flow through a circular pipe.

This method acts as a convenience wrapper for DP_Darcy_Weisbach. It determines the flow regime and estimates the Darcy friction factor using the appropriate equation. For laminar flow, it applies \(f_D=64/Re\). For turbulent flow, it uses fD_Haaland. Finally, the method calls DP_Darcy_Weisbach with the correct parameters.

Tip

In laminar flow, \(\Delta P \propto Q/D^4\), while in turbulent flow, \(\Delta P \propto Q^2/D^5\).

PARAMETER	DESCRIPTION
Q	Volume flowrate (m³/s). TYPE: float
D	Diameter (m). TYPE: float
L	Length (m). TYPE: float
rho	Density (kg/m³). TYPE: float
mu	Viscosity (Pa·s). TYPE: float
er	Relative pipe roughness, \(\epsilon/D\). Only required for turbulent flow. TYPE: float DEFAULT: 0.0

RETURNS	DESCRIPTION
float	Pressure drop (Pa).

Examples:

Calculate the pressure drop for water flowing at 3 m³/h through 500 m of PVC pipe with an internal diameter of 25 mm.

>>> from polykin.transport import DP_tube
>>> Q = 3.0/3600 # m³/s
>>> rho = 1e3    # kg/m³
>>> mu = 1e-3    # Pa·s
>>> L = 5e2      # m
>>> D = 25e-3    # m
>>> er = 0.0015e-3/D # from pipe table
>>> DP = DP_tube(Q, D, L, rho, mu, er)
>>> print(f"DP = {DP:.1e} Pa")
DP = 6.2e+05 Pa

Source code in src/polykin/transport/flow.py

def DP_tube(Q: float,
            D: float,
            L: float,
            rho: float,
            mu: float,
            er: float = 0.0
            ) -> float:
    r"""Calculate the pressure drop due to friction for flow through a circular
    pipe.

    This method acts as a convenience wrapper for
    [`DP_Darcy_Weisbach`](DP_Darcy_Weisbach.md). It determines the flow regime
    and estimates the Darcy friction factor using the appropriate equation. For
    laminar flow, it applies $f_D=64/Re$. For turbulent flow, it uses
    [`fD_Haaland`](fD_Haaland.md). Finally, the method calls
    [`DP_Darcy_Weisbach`](DP_Darcy_Weisbach.md) with the correct parameters. 

    !!! tip

        In laminar flow, $\Delta P \propto Q/D^4$, while in turbulent flow, 
        $\Delta P \propto Q^2/D^5$.

    Parameters
    ----------
    Q : float
        Volume flowrate (m³/s).
    D : float
        Diameter (m).
    L : float
        Length (m).
    rho : float
        Density (kg/m³).
    mu : float
        Viscosity (Pa·s).
    er : float
        Relative pipe roughness, $\epsilon/D$. Only required for turbulent flow.

    Returns
    -------
    float
        Pressure drop (Pa).

    Examples
    --------
    Calculate the pressure drop for water flowing at 3 m³/h through 500 m of
    PVC pipe with an internal diameter of 25 mm.
    >>> from polykin.transport import DP_tube
    >>> Q = 3.0/3600 # m³/s
    >>> rho = 1e3    # kg/m³
    >>> mu = 1e-3    # Pa·s
    >>> L = 5e2      # m
    >>> D = 25e-3    # m
    >>> er = 0.0015e-3/D # from pipe table
    >>> DP = DP_tube(Q, D, L, rho, mu, er)
    >>> print(f"DP = {DP:.1e} Pa")
    DP = 6.2e+05 Pa
    """

    v = 4*Q/(pi*D**2)
    Re = rho*v*D/mu
    if Re < 2.3e3:
        fD = 64/Re
    else:
        fD = fD_Haaland(Re, er)

    return DP_Darcy_Weisbach(v, D, L, rho, fD)