This paper introduces a novel analytical model for estimating the cache hit ratio as a function of time. The cache may not reach the steady-state hit ratio when the number of Web objects, object popularity, and/or caching resources themselves are subject to change. Hence, the only way to quantify the hit ratio experienced by Web users is to calculate the instantaneous hit ratio. The proposed analysis considers a single Web cache with infinite or finite capacity. For a cache with finite capacity, two replacement policies are considered: Least Recently Used (LRU) and First-In-First-Out (FIFO). Based on the insights from the proposed analytical model, we propose a new replacement policy, called Frequency-Based-FIFO (FB-FIFO). The results show that FB-FIFO outperforms both LRU and FIFO, assuming that the number of Web objects is fixed. Assuming that new popular objects are generated periodically, the results show that FB-FIFO adapts faster than LRU and FIFO to the changes in the popularity of the cached objects when the cache capacity is large relative to the number of newly generated objects.