Abstract: The transducer has a case which is formed by a support frame for supporting a fluid-conducting flow tube and by a case cap for encasing at least one bent segment of the flow tube which vibrates during operation of the transducer. The case cap comprises a channel-shaped first cap segment with a circular-arc-shaped first segment edge of predeterminable radius R and with an essentially identically shaped second segment edge. The first cap segment has a circular-arc-shaped cross section with a radius r less than the radius R of the first segment edge. The case cap further comprises an essentially plane second cap segment, which is connected via a circular-arc-shaped first segment edge with the first segment edge of the first cap segment, and a third cap segment, which is essentially mirror-symmetric with respect to the second cap segment and which is connected via a circular-arc-shaped first segment edge with the second segment edge of the first cap segment.

Abstract: This mass flow sensor, which can be mounted by means of end parts, in particular flanges, in a conduit of a given diameter through which flows a fluid to be measured, has two parallel, circular-arc-segment-shaped measuring tubes which are fixed at their ends in respective flanges. The measuring tubes have the same inner diameter D and the same wall thickness w. The circular-arc segment has a height h, an arc radius R, and a chord length L. The inner diameter D is chosen as a function of the maximum permissible pressure loss in the measuring tubes, and the wall thickness w as a function of the maximum permissible pressure of the fluid. The stress .sigma..sub.T resulting from a maximum permissible temperature change .delta.T of the fluid is chosen to be less than the .sigma..sub.0.2 -value of the material of the measuring tubes. Under these conditions and for a given arc radius R, the segment height h is chosen as small as possible to become h.sub.min.