[Instantaneous pressure-flow relations in a continuous flow in a collapsible tube: impact on the evaluation of urethral resistance].

The urethra is a collapsed tube in the absence of micturition. Consequently, the evaluation of instantaneous urethral resistance by the pressure/flow relation (R = P/Q2) derived from Bernoulli's equation has been criticised for not taking into account the opening pressure or at least the fact that flow must maintain patency of the urethra during voiding. The objective of this study was to determine whether such a criticism is justified in terms of fluid mechanics. A study of the pressure/flow relation was performed in a soft tube, collapsed by various peritubular pressures, which subsequently opened in response to flow. Experiments demonstrated that the pressure/flow relation, the instantaneous resistance to flow and the pressure drop were identical when the tube reached the same calibre, despite different peritubular pressures. The same pressure therefore propels the flow and maintains the patency of the tube. Consequently, it would be unreasonable to expect to improve the evaluation of instantaneous urethral resistance by subtracting an opening pressure from the maximal bladder pressure. The formula R = P/Q2 is valid, experimentally, and complies with the principles of fluid mechanics. In theory and in practice, it constitutes a good method of evaluation of instantaneous resistance.