5.1. Proving the Hydraulic Radius Relation

Try these first

1. 1.

   What is the hydraulic radius in a canal with an area of 50 m² and a wetted perimeter of 10 m?

   Hint

   Use the formula R_h = A / P.

2. 2.

   State what Manning's equation estimates in hydraulic engineering.

   Hint

   Think about what variables are combined in Manning's equation.

3. 3.

   What does R_h represent in fluid mechanics?

   • Hydraulic Radius
   • Flow Rate
   • Wetted Area

   Hint

   It's the area divided by the wetted perimeter.

4. 4.

   True or False: The wetted perimeter decreases as the hydraulic radius increases.

   • True
   • False

   Hint

   Consider how area and perimeter are related with hydraulic radius.

5. 5.

   Given a rectangular channel with dimensions 5 m by 2 m, calculate the flow discharge required for different depths using Manning's equation and the hydraulic radius.

   Hint

   Adjust depth in your calculations for different discharge outputs.

6. 6.

   Evaluate the effects of changing the roughness coefficient in Manning's equation on flow rates through a trapezoidal channel.

   Hint

   Consider both high and low n values in your calculations.