Water Leakage through a Small Opening

This paper presents a numerical simulation of a pressurized water leakage through a small opening into an ambient water reservoir. A modified Euler number indicating the relative importance between the forces due to pressure difference and the viscous effect was found good enough to characterize a problem of this nature. The effect of the gap aspect (H/L) ratio was investigated too. Only when the gap aspect ratio is close to unity, the gap flow is found existent in a bi-stable mode. In contrast, the uni-stable mode is possible with the right combination of modified Euler number and gap aspect ratio. More surprisingly, there exists a threshold aspect ratio approximately unity based on this work. Below the threshold aspect ratio, the maximum velocity is only a function of the modified Euler number. However, beyond the threshold aspect ratio, the maximum velocity increases with the gap aspect ratio and the modified Euler number.