wall and casing in the casing is a drill string 14 which comprises a series of joints of drill pipe which are supported in the rotary table not shown and are terminated at the bottom end by an appropriate bit 24 for drilling into the rock the drill steam or drill pipe indicated generally by the numeral 14 has a fixture called a swivel 22 at its top end so that drilling mud from a mud standpipe 20 can flow through an appropriate flexible pipe 21 to the swivel while the pipe turns and the swivel remains stationary mud flows from the standpipe through the flexible section 21 through the swivel 22 and down the drill pipe 14 and through the bit 24 into the annular space 46 between the drill pipe 14 and the borehole wall 12 or the casing 13 as the drilling mud flows down through the drill pipe as shown by arrows 41 and up the annular 46 in accordance with arrows 40 it overflows into a conduit 39 in accordance with arrow 43 and empties into a mud pit or mud tank 18 having a mud surface 42 a mud pump indicated schematically by the rectangle 16 is of conventional construction it withdraws mud from the mud tank 18 through conduit 44 to increase its pressure and discharge it in accordance with arrow 38 through the mud standpipe 20 at a selected pressure it then flows down through the drill pipe 14 and so forth while the mud flows at the same mass flow rate through these three sections of conduits they have been numbered 38 41 and 40 the actual velocity of flow will be a function of conduit size and so on the flow velocity of the mud through the drill.