Unsteady characteristics of a slot whose opening changes by small amounts in a stepwise manner are presented. As the results of theoretical analysis based on the free surface theory, it was clarified that a stepwise change caused by changes in the opening adds to both its free surface position and velocity potential, and these changes propagate downstream with an initial steady-state velocity at the vena contracta.
These results are applied as the boundary conditions for the numerical calculation of the discharge coefficient, and it is shown that the coefficient settles down at the steady-state value after a short time when there is a small stepwise change in the opening.

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