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Hydraulic diameter

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The hydraulic diameter, d_h, is commonly used when dealing with non-circular pipes, holes or ducts.

The definition of the hydraulic diamater is:

d_h \equiv 4 \; \frac{\mbox{cross-sectional-area of duct}}{\mbox{wetted perimeter of duct}}


Use of hydraulic diameter

=Estimating the turbulent length-scale

For fully-developed flow in non-circular ducts the turbulent length-scale can be estimated as 0.07 d_h. This is as usefull estimation for setting the turbulence boundary conditions for inlets that have fully developed flow.

Hydraulic diameters for different duct-geometries

Using the definition above the hydraulic diamater can easily be computed for any type of duct-geometry. Below follows a few examples.

Circular pipe

For a circular pipe or hole the hydraulic diamater is:

d_h = 4 \; \frac{\frac{\pi d^2}{4}}{\pi d} = d

Where d is the real diameter of the pipe. Hence, for circular pipes the hydraulic diameter is the same as the real diameter of the pipe.

Rectangular tube

For a rectangular tube or hole with the width a and the height b the hydraulic diamter is:

d_h = 4 \; \frac{a b}{2 a + 2 b} = 2 \; \frac{a b}{a + b}

Coaxial circular tube

For a coaxial circular tube with an inner diameter d_i and an outer diameter d_o the hydraulic diameter is:

d_h = 4 \; \frac{\frac{\pi d_o^2}{4} - \frac{\pi d_i^2}{4}}{\pi d_o + \pi d_i} = d_o - d_i
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