Tidal Flow Rate Calculator

Understanding Tidal Flow in Coastal Embayments

As the tide rises and falls, water flows into and out of a coastal basin through its inlet. The tidal prism is the total volume of water exchanged during a single flood or ebb tide, and it is the product of the basin surface area and the tidal range: P = A × Δh. A large basin with a big tidal range holds a large prism, which drives strong flows through a narrow inlet. This calculator starts from the prism and derives the peak discharge, the peak velocity through the inlet, the fraction of the basin exchanged each tide, and the time required to flush the embayment.

For a tide that rises and falls sinusoidally, the discharge through the inlet also varies sinusoidally, reaching a peak at mid-flood and mid-ebb. Integrating that sinusoidal flow over half a tidal period gives the prism, which rearranges to the peak discharge Q_peak = π·P / T. Dividing by the inlet cross-section area yields the peak velocity V_peak = Q_peak / A_inlet — the speed at which water rushes through the inlet at the strongest point of the tide. This velocity is the key driver of scour, sediment transport, and navigability at the inlet.

Tidal Exchange and Flushing

The tidal exchange coefficient is the fraction of the basin volume that is replaced by new ocean water on each tide, computed as the ratio of the tidal prism to the total basin volume (A × h). A value of 0.4, for example, means 40% of the basin water is exchanged per tidal cycle. The flushing time is the average time it takes to replace the basin water, estimated with the tidal-prism method as the number of tidal cycles needed (basin volume divided by prism) multiplied by the tidal period. Shorter flushing times indicate better water quality and faster removal of pollutants, while long flushing times can lead to stagnation and poor water exchange.

Practical Applications

Tidal flow analysis is essential for designing and managing coastal inlets, harbors, and lagoons. Engineers use the peak velocity to check whether inlet currents are safe for navigation and to estimate scour around structures. The tidal prism and flushing time inform environmental studies of water quality, pollutant dispersion, and larval transport. The exchange coefficient helps assess how effectively a basin renews its water, which is critical for marinas, cooling-water intakes, and coastal restoration projects. This calculator provides the core tidal-prism quantities from a few basic basin measurements.