The rate of filtration through a Gooch crucible increases due to its design, which features a fine porcelain or glass filter that allows for efficient passage of liquids while retaining solid particles. The high surface area of the porous material facilitates quicker flow, and the gravitational pull encourages faster drainage. Additionally, applying a vacuum can further enhance the rate of filtration by reducing pressure above the liquid, thereby increasing the driving force for the liquid to pass through the filter.