Hydraulic diameter

(Difference between revisions)
 Revision as of 13:51, 24 March 2006 (view source)Jola (Talk | contribs)← Older edit Latest revision as of 09:58, 17 December 2008 (view source)Peter (Talk | contribs) m (Reverted edits by NorolRelor (Talk) to last version by Jola) (9 intermediate revisions not shown) 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== + + ===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: For a circular pipe or hole the hydraulic diamater is: Line 13: Line 27: 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 33: :$d_h = 4 \; \frac{a b}{2 a + 2 b} = 2 \; \frac{a b}{a + b}$ :$d_h = 4 \; \frac{a b}{2 a + 2 b} = 2 \; \frac{a b}{a + b}$ - ==Coaxial circular tube== + ===Coaxial circular tube=== - For a coaxial circular tube with an inner diameter of $d_i$ and an outer diameter of $d_o$ 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: :$d_h = 4 \; \frac{\frac{\pi d_o^2}{4} - \frac{\pi d_i^2}{4}}{\pi d_o + \pi d_i} = d_o - d_i$ :$d_h = 4 \; \frac{\frac{\pi d_o^2}{4} - \frac{\pi d_i^2}{4}}{\pi d_o + \pi d_i} = d_o - d_i$

Latest revision as of 09:58, 17 December 2008

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:

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