At a point where an irrigation canal having a rectangular...

At a point where an irrigation canal having a rectangular cross section is 18.5 $\mathrm{m}$ wide and 3.75 $\mathrm{m}$ deep, the water flows at 2.50 $\mathrm{cm} / \mathrm{s} .$ At a point downstream, but on the same level, the canal is 16.5 $\mathrm{m}$ wide, but the water flows at 11.0 $\mathrm{cm} / \mathrm{s} .$ How deep is the canal at this point?

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Key Concepts

Continuity Equation

The continuity equation is a mathematical representation of conservation of mass for fluid flow. It states that the product of cross-sectional area and velocity at one point in a channel must equal the product at any other point along the same streamline. This relationship is critical in determining how changes in channel geometry, such as width or depth alterations, affect the flow speed.

Cross-Sectional Area

For channels with a rectangular cross-section, the cross-sectional area can be calculated by multiplying the width by the depth. This area is a key factor in the continuity equation since it, along with the flow velocity, determines the volumetric flow rate of the fluid through the channel.

Conservation of Mass

This principle states that for any fluid flowing through a system, the total mass entering the system must equal the total mass leaving it, assuming there is no accumulation of mass within the system. In the context of fluid flow in channels, this ensures that the flow rate remains constant from one section of the channel to another, provided there are no sources or sinks along the way.

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