Theoretical investigation of discharge and pressure distribution of a pipe with a continuous longitudinal slot

Abstract

This study provides detailed information on the pressure distribution inside a pipe with a continuous longitudinal slot, theoretically investigating the parameter dependency of the pressure distribution on the design parameters of the pipe: Reynolds number at the inlet, aspect ratio of the pipe, slot width, and pressure loss coefficient of the slot. The flow through a pipe with a continuous longitudinal slot is theoretically modeled in one dimension. The model follows the mass and energy conservation laws and considers the pressure loss at the slot. The results show that depending on the aspect ratio of the pipe and the Reynolds number at the inlet, the pressure distribution inside the pipe is categorized into three regimes: monotonically increasing, monotonically decreasing, and downward concave profiles. A parametric study indicates that a monotonically decreasing profile appears for a high aspect ratio pipe. A lower aspect ratio pipe, on the other hand, has a monotonically increasing pressure profile. The present paper also reports the effects of the slot width and pressure loss coefficients on the pressure distribution, indicating that the regime of the pressure distribution is mathematically predictable using the function of the design parameters.