Non-Circular Ducts and Hydraulic Diameter

The analysis of fully-developed flow (laminar/turbulent) in a non-circular duct is more complicated algebraically. The concept of hydraulic diameter is a reasonable method by which one can correlate the laminar/turbulent fully-developed pipe flow solutions to obtain approximate solutions of non-circular ducts. As derived from momentum equation in previous section, the head loss for a pipe and the wall shear stress is related as,

(5.6.1)

The analogous form of same equation for a non-circular duct is written as,

(5.6.2)

where, is the average shear stress integrated around the perimeter of the non-circular duct so that the ratio of cross-sectional area and the perimeter takes the form of length scale similar to the pipe radius . So, the hydraulic radius of a non-circular duct is defined as,

(5.6.3)

If the cross-section is circular, the hydraulic diameter can be obtained from Eq. (5.6.3) as, . So, the corresponding parameters such as friction factor and head loss for non-circular ducts (NCD) are then written as,

(5.6.4)

It is to be noted that the wetted perimeter includes all the surfaces acted upon by the shear stress. While finding the laminar/turbulent solutions of non-circular ducts, one must replace the radius/diameter of pipe flow solutions with the length scale term of hydraulic radius/diameter.