def speed_of_sound(V, dP_dV, Cp, Cv, MW=None):
    r'''Calculate a real fluid's speed of sound. The required derivatives should 
    be calculated with an equation of state, and `Cp` and `Cv` are both the
    real fluid versions. Expression is given in [1]_ and [2]_; a unit conversion
    is further performed to obtain a result in m/s. If MW is not provided the 
    result is returned in units of m*kg^0.5/s/mol^0.5.

    .. math::
        w = \left[-V^2 \left(\frac{\partial P}{\partial V}\right)_T \frac{C_p}
        {C_v}\right]^{1/2}
        
    Parameters
    ----------
    V : float
        Molar volume of fluid, [m^3/mol]
    dP_dV : float
        Derivative of `P` with respect to `V`, [Pa*mol/m^3]
    Cp : float
        Real fluid heat capacity at constant pressure, [J/mol/K]
    Cv : float
        Real fluid heat capacity at constant volume, [J/mol/K]
    MW : float, optional
        Molecular weight, [g/mol]

    Returns
    -------
    w : float
        Speed of sound for a real gas, [m/s or m*kg^0.5/s/mol^0.5 or MW missing]
        
    Notes
    -----
    An alternate expression based on molar density is as follows:
    
    .. math::
       w = \left[\left(\frac{\partial P}{\partial \rho}\right)_T \frac{C_p}
       {C_v}\right]^{1/2}

    The form with the unit conversion performed inside it is as follows:
    
    .. math::
        w = \left[-V^2 \frac{1000}{MW}\left(\frac{\partial P}{\partial V}
        \right)_T \frac{C_p}{C_v}\right]^{1/2}
    
    Examples
    --------
    Example from [2]_:
    
    >>> speed_of_sound(V=0.00229754, dP_dV=-3.5459e+08, Cp=153.235, Cv=132.435, MW=67.152)
    179.5868138460819

    References
    ----------
    .. [1] Gmehling, Jurgen, Barbel Kolbe, Michael Kleiber, and Jurgen Rarey.
       Chemical Thermodynamics for Process Simulation. 1st edition. Weinheim: 
       Wiley-VCH, 2012.
    .. [2] Pratt, R. M. "Thermodynamic Properties Involving Derivatives: Using 
       the Peng-Robinson Equation of State." Chemical Engineering Education 35,
       no. 2 (March 1, 2001): 112-115. 
    '''
    if not MW:
        return (-V**2*dP_dV*Cp/Cv)**0.5
    else:
        return (-V**2*1000./MW*dP_dV*Cp/Cv)**0.5
def speed_of_sound(V, dP_dV, Cp, Cv, MW=None):
    r'''Calculate a real fluid's speed of sound. The required derivatives should 
    be calculated with an equation of state, and `Cp` and `Cv` are both the
    real fluid versions. Expression is given in [1]_ and [2]_; a unit conversion
    is further performed to obtain a result in m/s. If MW is not provided the 
    result is returned in units of m*kg^0.5/s/mol^0.5.

    .. math::
        w = \left[-V^2 \left(\frac{\partial P}{\partial V}\right)_T \frac{C_p}
        {C_v}\right]^{1/2}
        
    Parameters
    ----------
    V : float
        Molar volume of fluid, [m^3/mol]
    dP_dV : float
        Derivative of `P` with respect to `V`, [Pa*mol/m^3]
    Cp : float
        Real fluid heat capacity at constant pressure, [J/mol/K]
    Cv : float
        Real fluid heat capacity at constant volume, [J/mol/K]
    MW : float, optional
        Molecular weight, [g/mol]

    Returns
    -------
    w : float
        Speed of sound for a real gas, [m/s or m*kg^0.5/s/mol^0.5 or MW missing]
        
    Notes
    -----
    An alternate expression based on molar density is as follows:
    
    .. math::
       w = \left[\left(\frac{\partial P}{\partial \rho}\right)_T \frac{C_p}
       {C_v}\right]^{1/2}

    The form with the unit conversion performed inside it is as follows:
    
    .. math::
        w = \left[-V^2 \frac{1000}{MW}\left(\frac{\partial P}{\partial V}
        \right)_T \frac{C_p}{C_v}\right]^{1/2}
    
    Examples
    --------
    Example from [2]_:
    
    >>> speed_of_sound(V=0.00229754, dP_dV=-3.5459e+08, Cp=153.235, Cv=132.435, MW=67.152)
    179.5868138460819

    References
    ----------
    .. [1] Gmehling, Jurgen, Barbel Kolbe, Michael Kleiber, and Jurgen Rarey.
       Chemical Thermodynamics for Process Simulation. 1st edition. Weinheim: 
       Wiley-VCH, 2012.
    .. [2] Pratt, R. M. "Thermodynamic Properties Involving Derivatives: Using 
       the Peng-Robinson Equation of State." Chemical Engineering Education 35,
       no. 2 (March 1, 2001): 112-115. 
    '''
    if not MW:
        return (-V**2*dP_dV*Cp/Cv)**0.5
    else:
        return (-V**2*1000./MW*dP_dV*Cp/Cv)**0.5
def speed_of_sound ( V , dP_dV , Cp , Cv , MW = None ) : if not MW : return ( - V ** 2 * dP_dV * Cp / Cv ) ** 0.5 else : return ( - V ** 2 * 1000. / MW * dP_dV * Cp / Cv ) ** 0.5
r'''Calculate a real fluid's speed of sound. The required derivatives should 
    be calculated with an equation of state, and `Cp` and `Cv` are both the
    real fluid versions. Expression is given in [1]_ and [2]_; a unit conversion
    is further performed to obtain a result in m/s. If MW is not provided the 
    result is returned in units of m*kg^0.5/s/mol^0.5.

    .. math::
        w = \left[-V^2 \left(\frac{\partial P}{\partial V}\right)_T \frac{C_p}
        {C_v}\right]^{1/2}
        
    Parameters
    ----------
    V : float
        Molar volume of fluid, [m^3/mol]
    dP_dV : float
        Derivative of `P` with respect to `V`, [Pa*mol/m^3]
    Cp : float
        Real fluid heat capacity at constant pressure, [J/mol/K]
    Cv : float
        Real fluid heat capacity at constant volume, [J/mol/K]
    MW : float, optional
        Molecular weight, [g/mol]

    Returns
    -------
    w : float
        Speed of sound for a real gas, [m/s or m*kg^0.5/s/mol^0.5 or MW missing]
        
    Notes
    -----
    An alternate expression based on molar density is as follows:
    
    .. math::
       w = \left[\left(\frac{\partial P}{\partial \rho}\right)_T \frac{C_p}
       {C_v}\right]^{1/2}

    The form with the unit conversion performed inside it is as follows:
    
    .. math::
        w = \left[-V^2 \frac{1000}{MW}\left(\frac{\partial P}{\partial V}
        \right)_T \frac{C_p}{C_v}\right]^{1/2}
    
    Examples
    --------
    Example from [2]_:
    
    >>> speed_of_sound(V=0.00229754, dP_dV=-3.5459e+08, Cp=153.235, Cv=132.435, MW=67.152)
    179.5868138460819

    References
    ----------
    .. [1] Gmehling, Jurgen, Barbel Kolbe, Michael Kleiber, and Jurgen Rarey.
       Chemical Thermodynamics for Process Simulation. 1st edition. Weinheim: 
       Wiley-VCH, 2012.
    .. [2] Pratt, R. M. "Thermodynamic Properties Involving Derivatives: Using 
       the Peng-Robinson Equation of State." Chemical Engineering Education 35,
       no. 2 (March 1, 2001): 112-115.
r Calculate a real fluid s speed of sound . The required derivatives should be calculated with an equation of state and Cp and Cv are both the real fluid versions . Expression is given in [ 1 ] _ and [ 2 ] _ ; a unit conversion is further performed to obtain a result in m / s . If MW is not provided the result is returned in units of m * kg^0 . 5 / s / mol^0 . 5 .