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{{anchor|How it works}}Theory and practice: corrected typesetting of trig functions
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The '''hydraulic diameter''', ''D<sub>H</sub>'', is a commonly used term when handling [[Fluid dynamics|flow]] in noncircular tubes and channels. Using this term one can calculate many things in the same way as for a round tube. It is defined as
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:<math> D_H = \frac {4A}{P} </math>


where ''A'' is the [[Cross section (geometry)|cross sectional]] [[area]] and ''P'' is the [[wetted perimeter]] of the cross-section.
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For a round tube, this checks as:
 
:<math> D_H = D </math>
 
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.
 
For an [[Annulus (mathematics)|annulus]] the hydraulic diameter is
 
:<math> D_H = \frac{4 \cdot 0.25 \pi (D_o^2 - D_i^2)} {\pi (D_o + D_i)} = D_o - D_i </math>
 
and for a rectangular duct, if completely filled with fluid:
 
:<math> D_H = \frac {4 L W} {2 (L + W)} = \frac{2LW}{L+W}</math>
 
And for a rectangular duct, if partly filled with fluid:
 
:<math> D_H = \frac {4 L W} {(L + 2W)}</math>
 
For the special case of a square duct, where ''L''=''W'', then ''D<sub>H</sub>'' = ''L''.  For the other limiting case of a very wide duct, i.e. a slot of width ''W'' where ''W'' ≫ ''L''', then ''D<sub>H</sub>'' = 2''L''.
 
For a fully filled duct or pipe whose cross section is a [[regular polygon]], the hydraulic diameter is equivalent to the diameter of a circle [[inscribed]] within the [[wetted perimeter]]. 
 
Hydraulic diameter is mainly used for calculations involving [[turbulent flow]]. [[secondary flow|Secondary flows]] can be observed in non-circular ducts as a result of turbulent [[shear stress]] in the turbulent flow. When the flow is [[Laminar flow|laminar]], secondary flows do not occur.
 
Hydraulic diameter is also used in calculation of heat transfer in internal flow problems.
 
==See also==
* [[Equivalent spherical diameter]]
* [[Hydraulic radius]]
* [[Darcy friction factor]]
 
[[Category:Fluid dynamics]]
[[Category:Heat transfer]]
[[Category:Hydrology| ]]
[[Category:Hydraulic engineering]]

Revision as of 22:23, 28 February 2014

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