Laminar flowmeters have strong advantages as transfer standards for measuring low flow rates of gases. Ideally, the difference between the flowmeter's entrance and exit pressures, P@sub 1@ and P@sub 2@, is that associated with viscous, creeping flow. One can then approximate the volume flow rate by the value Q@sub 0@ = @pi@R@super 4@(P@sub 1@-P@sub 2@)/(8@eta@L). This is the Hagen-Poiseuille relation which describes an incompressible fluid of viscosity @eta@ flowing through a capillary of circular cross-section with length L and radius R. In practice, the actual flow rate Q is described by the discharge coefficient C@sub d@=Q/Q@sub 0@. Achieving an accuracy of 0.1% requires a series of corrections to C@sub d@, each associated with at least one dimensionless parameter. Identifying the form of these corrections allows one to define useful dimensionless parameters. Important deviations of C@sub d@ from unity occur because the gas is compressible. A steady mass flow rate causes the volume flow rate to depend on position along the capillary. This corrects C@sub d@ by a factor proportional to (P@sub 1@+P@sub 2@). Furthermore, the additional pressure drop associated with the expanding gas adds to C@sub d@ a term proportional to the Reynolds number Re. Recent analysis of capillary viscometers by van den Berg and coworkers showed that the nonparabolic flow associated with the expanding gas increased the size of this term. Their result is used here to describe the performance of a laminar flowmeter. Dimensionless parameters incorporated in this correction include Re, the pressure ratio P@sub 2@/P@sub 1@, and the aspect ratio R/L. Other significant dimensionless parameters include the Mach number, the ratio of the gas's slip length to the capillary's radius, the Dean number characterizing centrifugal effects in a coiled capillary, and the correction terms in the gas's virial equation of state.