The recoil force on a leaking water tank

Abstract In this paper, we address the question of the recoil force resulting from leakage through a hole at the bottom of a water tank. Different theoretical arguments are presented, leading to three conflicting outcomes. To identify the correct result, an experiment is conducted, involving parallel measurements of the water level and the holding force of the water tank as a function of time during the leakage process. The recoil force is determined by calculating the difference between the weight derived from the water level and the holding force. The experimental results clearly indicate which theoretical prediction is correct. An analysis of the incorrect theoretical arguments provides insight into the nature of the water flow near the hole. By applying the principle of conservation of water flux, it is found that the acceleration zone forms a funnel shape, with a wide entry that becomes narrower as it approaches the hole. Additionally, the average area of the acceleration funnel is found to be twice the effective area of the hole at the bottom of the water tank. Suggestions for integrating this material into undergraduate physics courses and labs are also provided.