USBR Water Measurement Manual - Chapter 2 - Basic Concepts Related to Flowing Water and Measurement, Section 11. Hydraulic Mean Depth and Hydraulic Radius

CHAPTER 2 - BASIC CONCEPTS RELATED TO FLOWING WATER AND MEASUREMENT

11. Hydraulic Mean Depth and Hydraulic Radius

Figure 2-4 shows an irregular flow cross section with different methods for defining depth of flow. In terms of frictional head losses, the perimeter is important. Hydraulic radius, R_h, is defined as the area of the flow section divided by the wetted perimeter, P_w, which is shown on figure 2-4 and is written as:

(2-23)

Thus, wetted perimeter times the hydraulic radius is equal to the area of irregular section flow as shown on figures 2-4a and 2-4c.

Figure 2-4 -- Definitions of hydraulic radius and hydraulic mean depth (area is the same for all three cases).

For use in Froude number and energy relationships in open channel flow hydraulics, mean depth, h_m, is defined as the depth which, when multiplied by the top water surface width, T, is equal to the irregular section area, A, shown on figures 2-4a and 2-4b, of the flow section and is commonly used for critical flow relationships. The equation for hydraulic mean depth, h_m, is:

(2-24)

In rectangular channels, hydraulic radius, R_h, does not equal depth, but approaches depth as the channel becomes very wide. However, the hydraulic mean depth, h_m, is the same as the depth of the rectangular flow section.