docs: def Matsumoto_1977(mp, rhop, dp, rhog, D, Vterminal=1):
      r'''Calculates saltation velocity of the gas for pneumatic conveying,
      according to [1]_ and reproduced in [2]_, [3]_, and [4]_.
  
      First equation is used if third equation yeilds d* higher than dp.
      Otherwise, use equation 2.
  
      .. math::
          \mu = 5560\left(\frac{d_p}{D}\right)^{1.43}\left(\frac{Fr_s}{10}\right)^4
  
          \mu = 0.373 \left(\frac{\rho_p}{\rho_f}\right)^{1.06}\left(\frac{Fr_p}
          {10}\right)^{-3.7}\left(\frac{Fr_s}{10}\right)^{3.61}
  
          \frac{d_p^*}{D} = 1.39\left(\frac{\rho_p}{\rho_f}\right)^{-0.74}
  
          Fr_s = \frac{V_{salt}}{\sqrt{gD}}
  
          Fr_p = \frac{V_{terminal}}{\sqrt{gd_p}}
  
          \mu = \frac{m_p}{\frac{\pi}{4}D^2V \rho_f}
  
      Parameters
      ----------
      mp : float
          Solid mass flow rate, [kg/s]
      rhop : float
          Particle density, [kg/m^3]
      dp : float
          Particle diameter, [m]
      rhog : float
          Gas density, [kg/m^3]
      D : float
          Diameter of pipe, [m]
      Vterminal : float
          Terminal velocity of particle settling in gas, [m/s]
  
      Returns
      -------
          V : float
              Saltation velocity of gas, [m/s]
  
      Notes
      -----
      Model is rearanged to be explicit in terms of saltation velocity
      internally.
  
      Examples
      --------
      Example is only a self-test.
  
      Course routine, terminal velocity input is from example in [2].
  
      >>> Matsumoto_1977(mp=1., rhop=1000., dp=1E-3, rhog=1.2, D=0.1, Vterminal=5.24)
      16.64284834446686
  
      References
      ----------
      .. [1] Matsumoto, Shigeru, Makoto Kikuta, and Siro Maeda. "Effect of
         Particle Size on the Minimum Transport Velocity for Horizontal Pneumatic
         Conveying of Solids." Journal of Chemical Engineering of Japan 10,
         no. 4 (1977): 273-79. doi:10.1252/jcej.10.273.
      .. [2] Klinzing, G. E., F. Rizk, R. Marcus, and L. S. Leung. Pneumatic
         Conveying of Solids: A Theoretical and Practical Approach.
         Springer, 2013.
      .. [3] Gomes, L. M., and A. L. Amarante Mesquita. "On the Prediction of
         Pickup and Saltation Velocities in Pneumatic Conveying." Brazilian
         Journal of Chemical Engineering 31, no. 1 (March 2014): 35-46.
         doi:10.1590/S0104-66322014000100005
      .. [4] Rabinovich, Evgeny, and Haim Kalman. "Threshold Velocities of
         Particle-Fluid Flows in Horizontal Pipes and Ducts: Literature Review."
         Reviews in Chemical Engineering 27, no. 5-6 (January 1, 2011).
         doi:10.1515/REVCE.2011.011.
      '''
      limit = 1.39*D*(rhop/rhog)**-0.74
      A = pi/4*D**2
      if limit < dp:
          # Corase routine
          Frp = Vterminal/(g*dp)**0.5
          Frs_sorta = 1./(g*D)**0.5
          expression1 = 0.373*(rhop/rhog)**1.06*(Frp/10.)**-3.7*(Frs_sorta/10.)**3.61
          expression2 = mp/rhog/A
          V = (expression2/expression1)**(1/4.61)
      else:
          Frs_sorta = 1./(g*D)**0.5
          expression1 = 5560*(dp/D)**1.43*(Frs_sorta/10.)**4
          expression2 = mp/rhog/A
          V = (expression2/expression1)**(0.2)
      return V