When water is added at constant rate to a container the depth of the water will be a function of time. The rate at which the depth increases will be slow if the container is wide at the water surface and fast if the container is narrow at the water surface. The rate of increase of depth is inversely proportional to the cross sectional area of the container at the water surface. The rate at which the depth of water increases in the top diagram below is constant because the cross sectional area of the container is constant.
The rate at which the depth of water increases in the bottom diagram above deacreases as the depth of water increases because the cross sectional area of the container increases. Fluid filling functions for various containers are shown below.
