Which equation is used for open-pipe flow?

The correct choice for open-pipe flow is the Manning's Equation. This equation is specifically designed for analyzing flow in open channels, such as rivers or ditches, where the flow is not under pressure and the liquid surface is open to the atmosphere.

Manning's Equation relates the flow rate to the hydraulic radius and slope of the channel, incorporating a roughness coefficient that accounts for the material of the channel bed and walls. This makes it particularly suitable for determining the velocity and flow rate in natural and artificial open channels.

In contrast, other equations serve different purposes. The Hazen-Williams Equation is used for calculating water flow in pressurized pipe systems, specifically for determining the head loss due to friction. Bernoulli's Equation can be applied to fluid flow in both closed and open systems but is primarily used for pressure-driven flow analysis rather than open channels. The Continuity Equation describes the conservation of mass in a fluid flow system but does not provide a direct way to analyze flow specifics in open-pipe scenarios like Manning's Equation does.