**Hydraulic engineering is a subfield of civil engineering that centers around the transport and management of water resources. **Hydraulic engineers design things like channels, canals, dams and levees. They must consider many factors before beginning a project, including the collection, storage, flow, measurement and use of the water, in order to ensure its control, safety and cleanliness.

In a canal, its **flow rate** can be defined as the amount of water that is passing through a specific cross-section of the canal every second. The flow rate is important to monitor and manage. A flow rate that is too high can cause flooding and damage to the canal itself, while a flow rate that is too low can result in unsanitary conditions.

**2.1** Marcos is working on a canal that has been designed to transport water across a field. He locates and measures the below cross-section of the canal in order to determine its flow rate. What is the cross-sectional area of the canal? Express your answer as a decimal to the nearest hundredth.

**2.2** A **velocimeter **is a tool that uses laser beams to estimate the speed of water. Marcos stands on the edge of the canal with the velocimeter and points it at the water just in front of his feet. He finds that the water is moving at 1.5 ft/s. If flow rate is equal to the cross-sectional area of the canal multiplied by the speed of the water, what is the flow rate of the canal in cubic feet per second (cfs)? Express your answer to the nearest whole number.

**2.3 **Nadine, Marcos’s colleague, uses the velocimeter to take a second measurement, this time pointing it towards the center of the canal. Nadine’s reading indicates that the speed of the water is 2 ft/s. Because she and Marcos got different measurements, Nadine suggests using a better method for estimating flow rate called **Manning’s Equation**. Manning’s Equation for this canal can be simplified as:

Flow rate = 1.571 × *A* × *R* ^{2/3}

where *A* is the cross-sectional area of the canal and *R* is the **hydraulic radius**, a ratio that indicates how efficiently the water is flowing. If the hydraulic radius for this canal is 2.29 ft, what is the estimated flow rate of the canal using Manning’s Equation? Express your answer as a decimal to the nearest tenth.

*Huge thanks to Criss Ward for his invaluable help with the EWeek 2024 Hydraulic Engineering problem set! *

*Criss is a transportation engineer working for Kimley-Horn in Portland, OR. He attended the University of Idaho, where he received his bachelor’s and master’s degrees in civil engineering. Currently, Criss is working on the Everett Link Extension project in Seattle, which involves designing 16 miles of new light rail infrastructure. If you’d like to ask Criss any questions about civil engineering or college, feel free to email him at [email protected].*