Method and apparatus for pumping drilling fluid (mud) containing drill cuttings, comprising a centrifugal pump with screw pump accelerator. The screw pump creating positive pressure for centrifugal pump inlet to increase performance. The screw pump mud level fluctuations are compensated by the vertical screw pumping unit. Adjusting the elevation of pump will adjust the quantity of mud pumping, which is not possible with ether one pump alone. Air is allowed to mix with the mud in the centrifugal pump to create air bubbles to decrease density of the mixture and decrease the head pressure.