Abstract:Without considering the rotation, the differential equation of fluid leakage along the center opening at the bottom of a stationary cylindrical container is established, and the relationship between the height of the liquid surface from the bottom and the initial height and time of the liquid surface, as well as the relationship between the liquid surface deceleration, the liquid velocity and flow rate at the circular hole with time are obtained by using quasi steady approximation, unsteady step-by-step approximation, and unsteady accurate analytical solution. The results show that there is a proportional coefficient βⁿbetween the theoretical time corresponding to the reduced height of the liquid surface and the quasi steady flow solution in the unsteady flow solution obtained by the step-by-step approximation method, and the coefficient β is related to the ratio ε of the diameter of the cylindrical container to the diameter of the small hole. The experimental results using water, saturated brine and alcohol as media are well verified the good linear relationship t=k'Z' of liquid surface height Z' with time t. Because of the unsteady effect, the actual ratio coefficient k' is greater than the quasi steady calculated value k, and within the diameter ratio range of this paper, k'/k is about 1.5, which is weakly related to the type of liquid. Under the same ε, the k' and n are also consistent, but with ε changes, they are proportional to ε ²and ε ⁴respectively. Based on the experimental data, the numerical analytical expressions of, and, and the actual time corresponding to the reduced height of the liquid surface are obtained.