An apparatus configured to be used in a drilling system conducting flow of drilling fluid, the flow of the drilling fluid having gas, liquid, and/or solids and being at a drilling pressure level used in drilling a wellbore, the apparatus comprising: a Coriolis flow meter for measuring the flow of the drilling fluid and having an inlet side and an outlet side, the meter comprising at least one flow tube adapted to vibrate and to conduct the flow of the drilling fluid from the inlet side to the outlet side, the at least one flow tube being adapted to withstand a pressure limit less than the drilling pressure level of the flow of the drilling fluid and being exposed to the flow at a first pressure level above the pressure limit of the at least one flow tube; a vessel enclosing the at least one flow tube in a chamber and holding an internal fluid separate from the drilling fluid at a second pressure level in the chamber about the at least one flow tube; and characterized in that the apparatus further comprises: a controller (152, 118) configured to monitor variation in the first pressure level and to regulate the second pressure level of the internal fluid relative to the first pressure level to control a pressure differential across the at least one flow tube so that the at least one flow tube under the controlled pressure differential conducts the flow at the first pressure level above the pressure limit of the at least one flow tube, the controller (152, 118) being configured to control the excitation signals to set the at least one flow tube into vibration so to account for at least one parameter related to the vibration of the at least one flow tube in the internal fluid at the second pressure level. a Coriolis flow meter for measuring the flow of the drilling fluid and having an inlet side and an outlet side, the meter comprising at least one flow tube adapted to vibrate and to conduct the flow of the drilling fluid from the inlet side to the outlet side, the at least one flow tube being adapted to withstand a pressure limit less than the drilling pressure level of the flow of the drilling fluid and being exposed to the flow at a first pressure level above the pressure limit of the at least one flow tube; a vessel enclosing the at least one flow tube in a chamber and holding an internal fluid separate from the drilling fluid at a second pressure level in the chamber about the at least one flow tube; and characterized in that the apparatus further comprises: a controller (152, 118) configured to monitor variation in the first pressure level and to regulate the second pressure level of the internal fluid relative to the first pressure level to control a pressure differential across the at least one flow tube so that the at least one flow tube under the controlled pressure differential conducts the flow at the first pressure level above the pressure limit of the at least one flow tube, the controller (152, 118) being configured to control the excitation signals to set the at least one flow tube into vibration so to account for at least one parameter related to the vibration of the at least one flow tube in the internal fluid at the second pressure level.