Mixing-transport of solute entering at sinkholes or from within the limestone matrix in cavernous conduits is an important process for contaminant migration in karst aquifers. This process may be described with a one-dimensional advection-dispersion equation incorporating the fluxes of solute and water across the conduit wall. For the dilution-dispersion equation, which does not include solute flux across the wall but has the flux of water through the wall, the sufficient and necessary condition for neglecting conduit dispersion is showed by scale analysis to be L P &a, where a is the conduit radius, and L P is the spatial scale of the solute plume. A straightforward necessary and practically, though not strictly, sufficient condition is a=WT B %1, where W is the mean velocity of conduit flow, and T B is the time scale of the breakthrough curve. For the releasing-dispersion equation, which includes the fluxes of water and solute across the wall, L P &a is still a sufficient condition, but no longer a necessary one. The inequality a%WT B is neither a necessary condition nor a sufficient condition.

By using the FINE software developed by NUMECA Company, the hydraulic performance of the impeller of a centrifugal pump with spatial guide vanes was numerically simulated. The S-A turbulent model was used to numerically calculate the three-dimensional flow field in the centrifugal pump under three different conditions. The flow analysis shows that the pressure gradient on the vane surface gradually reduces with the increasing of the flow rate; the position of axial vortex between vanes has nothing to do with the flow rate; the tangential flow gradient in the flow passage decreases with the increasing of the flow rate. Compared with the test results, it is obvious that this numerical simulation can accurately predicate the complicated three-dimensional flow and the hydraulic performance of the pump.