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Hydraulic diameter

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:<math>d_h \equiv 4 \; \frac{\mbox{cross-sectional-area of duct}}{\mbox{wetted perimeter of duct}}</math>
:<math>d_h \equiv 4 \; \frac{\mbox{cross-sectional-area of duct}}{\mbox{wetted perimeter of duct}}</math>
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==Circular pipe==
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==Use of hydraulic diameter==
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==Hydraulic diameters for different duct-geometries==
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Using the definition above the hydraulic diamater can easily be computed for any type of duct-geometry. Below follows a few examples.
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===Circular pipe===
For a circular pipe or hole the hydraulic diamater is:
For a circular pipe or hole the hydraulic diamater is:
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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.
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.
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==Rectangular tube==
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===Rectangular tube===
For a rectangular tube or hole with the width <math>a</math> and the height <math>b</math> the hydraulic diamter is:
For a rectangular tube or hole with the width <math>a</math> and the height <math>b</math> the hydraulic diamter is:
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:<math>d_h = 4 \; \frac{a b}{2 a + 2 b} = 2 \; \frac{a b}{a + b}</math>
:<math>d_h = 4 \; \frac{a b}{2 a + 2 b} = 2 \; \frac{a b}{a + b}</math>
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==Coaxial circular tube==
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===Coaxial circular tube===
For a coaxial circular tube with an inner diameter <math>d_i</math> and an outer diameter <math>d_o</math> the hydraulic diameter is:
For a coaxial circular tube with an inner diameter <math>d_i</math> and an outer diameter <math>d_o</math> the hydraulic diameter is:
:<math>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</math>
:<math>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</math>

Revision as of 13:56, 24 March 2006

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}}

Contents

Use of hydraulic diameter

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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