# Hydraulic diameter

(Difference between revisions)
 Revision as of 13:52, 24 March 2006 (view source)Jola (Talk | contribs)m← Older edit Revision as of 13:56, 24 March 2006 (view source)Jola (Talk | contribs) Newer edit → Line 5: Line 5: :$d_h \equiv 4 \; \frac{\mbox{cross-sectional-area of duct}}{\mbox{wetted perimeter of duct}}$ :$d_h \equiv 4 \; \frac{\mbox{cross-sectional-area of duct}}{\mbox{wetted perimeter of duct}}$ - ==Circular pipe== + ==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: For a circular pipe or hole the hydraulic diamater is: Line 13: Line 19: 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 $a$ and the height $b$ the hydraulic diamter is: For a rectangular tube or hole with the width $a$ and the height $b$ the hydraulic diamter is: Line 19: Line 25: :$d_h = 4 \; \frac{a b}{2 a + 2 b} = 2 \; \frac{a b}{a + b}$ :$d_h = 4 \; \frac{a b}{2 a + 2 b} = 2 \; \frac{a b}{a + b}$ - ==Coaxial circular tube== + ===Coaxial circular tube=== For a coaxial circular tube with an inner diameter $d_i$ and an outer diameter $d_o$ the hydraulic diameter is: For a coaxial circular tube with an inner diameter $d_i$ and an outer diameter $d_o$ the hydraulic diameter is: :$d_h = 4 \; \frac{\frac{\pi d_o^2}{4} - \frac{\pi d_i^2}{4}}{\pi d_o + \pi d_i} = d_o - d_i$ :$d_h = 4 \; \frac{\frac{\pi d_o^2}{4} - \frac{\pi d_i^2}{4}}{\pi d_o + \pi d_i} = d_o - d_i$

## 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:

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

## 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:

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