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Flow in Non-circular Ducts

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For turbulent flow in a duct of non-circular cross-section, the *hydraulic mean diameter* may be used in place of the pipe diameter and the formulae for circular pipes can then be applied without introducing a large error. This method of approach is entirely empirical.

The hydraulic mean diameter D_{H }is defined as four times the *hydraulic mean radius* r_{H}. Hydraulic mean radius is defined as the flow cross-sectional area divided by the wetted perimeter: some examples are given. For circular pipe:

D_{H} = 4(p/4)D^{2} / (pD) = D

For an annulus of outer dia D_{o} and inner dia D_{i} :

D_{H} = 4 ( (pD_{o}^{2} /4) - (pD_{i}^{2} /4) ) / ( p(D_{o} + D_{i}) ) = (D_{o}^{2} - D_{i}^{2}) / (D_{o} + D_{i}) = D_{o} - D_{i}

For a duct of rectangular cross-section D_{a} by D_{b} :

D_{H} = 4 D_{a}D_{b} / ( 2(D_{a} + D_{b}) = 2D_{a}D_{b} / (D_{a} + D_{b})

For a duct of square cross-section of size D_{a} :

D_{H} = 4 D_{a}^{2} / (4D_{a}) = D_{a}

For laminar flow this method is not applicable, and exact expressions relating the pressure drop to the velocity can be obtained for ducts of certain shapes only.

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Last Modified on: 14-Sep-2014

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