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The term wetted perimeter is common in civil engineering, environmental engineering, hydrology, geomorphology, and heat transfer applications; it is associated with the hydraulic diameter or hydraulic radius. Engineers commonly cite the cross sectional area of a river. The wetted perimeter can be defined mathematically as
is the hydraulic radius [length], which is the cross-sectional area of flow divided by the wetted perimeter, [1] [8] for a wide channel this is approximately equal to the water depth; S 0 {\displaystyle S_{0}} is the hydraulic gradient, which for uniform normal depth of flow is the slope of the channel bottom [unitless; length/length];
P is the wetted perimeter of the cross-section. More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius R H, which is defined as the cross-sectional area of the channel divided by the wetted perimeter. Here, the wetted perimeter includes all surfaces acted upon by shear stress from the fluid. [3]
The variations of Q/Q (full) and V/V (full) with H/D ratio is shown in figure(b).From the equation 5, maximum value of Q/Q (full) is found to be equal to 1.08 at H/D =0.94 which implies that maximum rate of discharge through a conduit is observed for a conduit partly full.
P is the wetted perimeter (L). For channels of a given width, the hydraulic radius is greater for deeper channels. In wide rectangular channels, the hydraulic radius is approximated by the flow depth. The hydraulic radius is not half the hydraulic diameter as the name may suggest, but one quarter in the case of a full pipe. It is a function of ...
where is the wetted perimeter (+), is the plate width, is the plate thickness, and is the contact angle between the liquid phase and the plate. In practice the contact angle is rarely measured; instead, either literature values are used or complete wetting ( θ = 0 {\displaystyle \theta =0} ) is assumed.
[5] Where F is the sediment flux, S is the slope of the source area, and a is the source area. The right-hand side of this relation determines channel stability or instability
where x is the space coordinate along the channel axis, t denotes time, A(x,t) is the cross-sectional area of the flow at location x, u(x,t) is the flow velocity, ζ(x,t) is the free surface elevation and τ(x,t) is the wall shear stress along the wetted perimeter P(x,t) of the cross section at x.