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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 turbulence boundary conditions for inlets that have fully developed flow.

Computing Reynolds number

The hydraulic diamater is often used when computing the dimensionless Reynolds number for non-circular ducts.

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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