# 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> | ||

- | ==Circular pipe== | + | ==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 <math>0.07 \, d_h</math>. 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. | ||

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+ | ==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: | 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. | ||

- | ==Rectangular tube== | + | ===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> | ||

- | ==Coaxial circular tube== | + | ===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> |

## Latest revision as of 09:58, 17 December 2008

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

The definition of the hydraulic diamater is:

## Contents |

## 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 . 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:

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 and the height the hydraulic diamter is:

### Coaxial circular tube

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