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Friction losses typically increase with an increasing wetted perimeter, resulting in a decrease in head. [1] In a practical experiment, one is able to measure the wetted perimeter with a tape measure weighted down to the river bed to get a more accurate measurement. When a channel is much wider than it is deep, the wetted perimeter approximates ...
The one-dimensional (1-D) Saint-Venant equations were derived by Adhémar Jean Claude Barré de Saint-Venant, and are commonly used to model transient open-channel flow and surface runoff. They can be viewed as a contraction of the two-dimensional (2-D) shallow-water equations, which are also known as the two-dimensional Saint-Venant equations.
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]
Units of n are often omitted, however n is not dimensionless, having dimension of T/L 1/3 and units of s/m 1/3. R h is the hydraulic radius (L; ft, m); S is the stream slope or hydraulic gradient, the linear hydraulic head loss loss (dimension of L/L, units of m/m or ft/ft); it is the same as the channel bed slope when the water depth is ...
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.
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In more recent years, computer programs have been used to find and calculate more precise approximations of the perimeter of an ellipse. In an online video about the perimeter of an ellipse, recreational mathematician and YouTuber Matt Parker, using a computer program, calculated numerous approximations for the perimeter of an ellipse. [10]
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