docs: def Rizk(mp, dp, rhog, D):
      r'''Calculates saltation velocity of the gas for pneumatic conveying,
      according to [1]_ as described in [2]_ and many others.
  
      .. math::
          \mu=\left(\frac{1}{10^{1440d_p+1.96}}\right)\left(Fr_s\right)^{1100d_p+2.5}
  
          Fr_s = \frac{V_{salt}}{\sqrt{gD}}
  
          \mu = \frac{m_p}{\frac{\pi}{4}D^2V \rho_f}
  
      Parameters
      ----------
      mp : float
          Solid mass flow rate, [kg/s]
      dp : float
          Particle diameter, [m]
      rhog : float
          Gas density, [kg/m^3]
      D : float
          Diameter of pipe, [m]
  
      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 from [3]_.
  
      >>> Rizk(mp=0.25, dp=100E-6, rhog=1.2, D=.078)
      9.8833092829357
  
      References
      ----------
      .. [1] Rizk, F. "Pneumatic conveying at optimal operation conditions and a
         solution of Bath's equation." Proceedings of Pneumotransport 3,
         paper D4. BHRA Fluid Engineering, Cranfield, England (1973)
      .. [2] Klinzing, G. E., F. Rizk, R. Marcus, and L. S. Leung. Pneumatic
         Conveying of Solids: A Theoretical and Practical Approach.
         Springer, 2013.
      .. [3] Rhodes, Martin J. Introduction to Particle Technology. Wiley, 2013.
      '''
      alpha = 1440*dp + 1.96
      beta = 1100*dp + 2.5
      term1 = 1./10**alpha
      Frs_sorta = 1/(g*D)**0.5
      expression1 = term1*Frs_sorta**beta
      expression2 = mp/rhog/(pi/4*D**2)
      V = (expression2/expression1)**(1./(1 + beta))
      return V