Hydraulic Diameter
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The hydraulic diameter, , is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. When the cross-section is uniform along the tube or channel length, it is defined as : D_\text = \frac, where : is the cross-sectional area of the flow, : is the wetted perimeter of the cross-section. More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius , 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. : R_\text = \frac, : D_\text = 4R_\text, Note that for the case of a circular pipe, : D_\text =\frac=2R The need for the hydraulic diameter arises due to the use of a single dimension in the case of a
dimensionless quantity Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...
such as the
Reynolds number In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ...
, which prefers a single variable for flow analysis rather than the set of variables as listed in the table below. The Manning formula contains a quantity called the hydraulic radius. Despite what the name may suggest, the hydraulic diameter is ''not'' twice the hydraulic radius, but four times larger. Hydraulic diameter is mainly used for calculations involving
turbulent flow In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by Chaos theory, chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disrupt ...
. Secondary flows can be observed in non-circular ducts as a result of turbulent shear stress in the turbulent flow. Hydraulic diameter is also used in calculation of heat transfer in internal-flow problems.


Non-uniform and non-circular cross-section channels

In the more general case, channels with non-uniform non-circular cross-sectional area, such as the Tesla valve, the hydraulic diameter is defined as: : D_\text = \frac, where : is the total wetted volume of the channel, : is the total wetted surface area. This definition is reduced to \frac for uniform non-circular cross-section channels, and 2R for circular pipes.


List of hydraulic diameters

For a fully filled duct or pipe whose cross-section is a convex
regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex ...
, the hydraulic diameter is equivalent to the diameter D of a circle inscribed within the wetted perimeter. This can be seen as follows: The N -sided regular polygon is a union of N triangles, each of height D/2 and base B = D \tan(\pi/N). Each such triangle contributes BD/4 to the total area and B to the total perimeter, giving : D_\text = 4\frac = D for the hydraulic diameter.


References

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See also

* Equivalent spherical diameter * Hydraulic radius * Darcy friction factor Fluid dynamics Heat transfer Hydrology Hydraulics Radii