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For a fully wetted noncircular duct, hydraulic diameter defines a characteristic length from flow area and wetted perimeter.
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Formula
Dh in m; A in m2; wetted perimeter in m
| Symbol | Meaning | Unit |
|---|---|---|
| Hydraulic diameter | m | |
| Flow cross-sectional area | m2 | |
| Pbenetzt | Wetted perimeter, excluding a free surface | m |
D_h=\frac{4A}{P_\mathrm{benetzt}}Four times area divided by wetted perimeter equals the inside diameter for a circular pipe. It is a useful characteristic length for Reynolds number and friction models, not a literal pipe width. In partly filled ducts, determine wetted perimeter without the free surface. Applying circular-pipe friction correlations to unusual geometries remains model-dependent.
Four times area divided by wetted perimeter equals the inside diameter for a circular pipe. It is a useful characteristic length for Reynolds number and friction models, not a literal pipe width. In partly filled ducts, determine wetted perimeter without the free surface. Applying circular-pipe friction correlations to unusual geometries remains model-dependent.
For a fully wetted noncircular duct, hydraulic diameter defines a characteristic length from flow area and wetted perimeter.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Hydraulic diameter” and check its unit and magnitude.
A fully wetted rectangular duct with A=0.12 m2 and wetted perimeter 1.4 m has Dh≈0.343 m.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: Dh in m; A in m2; wetted perimeter in m.
Formula cluster
For a fully wetted noncircular duct, hydraulic diameter defines a characteristic length from flow area and wetted perimeter.
A fully wetted rectangular duct with A=0.12 m2 and wetted perimeter 1.4 m has Dh≈0.343 m.
Scale Reynolds-number and friction estimates for noncircular ducts.
Here is how to work through a typical Hydraulic diameter (Dh = 4A/Pbenetzt) task step by step:
Task
Work through the numerical example for “Hydraulic diameter” and check its unit and magnitude.
Solution path
A fully wetted rectangular duct with A=0.12 m2 and wetted perimeter 1.4 m has Dh≈0.343 m.
The definition 4A/P is chosen so a circular pipe returns its actual diameter: A=πD2/4 and P=πD, so 4A/P=D. This carries a familiar pipe length scale to noncircular ducts without claiming they have a literal circular diameter. Hydraulic diameter is a characteristic internal-flow length, not a replacement for every geometric dimension. Compute wetted perimeter from the fluid-contact boundary and omit a free surface. Its use in correlations depends on geometry and correlation assumptions. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
Wetted perimeter includes boundary actually touching the fluid. In a partly filled open channel, the free surface is excluded. A wrong perimeter changes Dh and then the Reynolds number or friction correlation. Sketch the fluid boundary and mark wetted and free sections before substituting. Hydraulic diameter is a characteristic internal-flow length, not a replacement for every geometric dimension. Compute wetted perimeter from the fluid-contact boundary and omit a free surface. Its use in correlations depends on geometry and correlation assumptions. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
Only for particular geometries does hydraulic diameter equal a width. For a rectangle of width a and height b, Dh=2ab/(a+b), generally neither a nor b. Use hydraulic diameter for Reynolds-number scaling, but retain actual dimensions for section area, fittings and heat transfer. Hydraulic diameter is a characteristic internal-flow length, not a replacement for every geometric dimension. Compute wetted perimeter from the fluid-contact boundary and omit a free surface. Its use in correlations depends on geometry and correlation assumptions. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
Write the quantity and unit from the variable list next to every value: Dh in m; A in m2; wetted perimeter in m. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A fully wetted rectangular duct with A=0.12 m2 and wetted perimeter 1.4 m has Dh≈0.343 m. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Hydraulic diameter is a characteristic internal-flow length, not a replacement for every geometric dimension. Compute wetted perimeter from the fluid-contact boundary and omit a free surface. Its use in correlations depends on geometry and correlation assumptions. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
The background states this starting condition: Four times area divided by wetted perimeter equals the inside diameter for a circular pipe. It is a. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Hydraulic diameter is a characteristic internal-flow length, not a replacement for every geometric dimension. Compute wetted perimeter from the fluid-contact boundary and omit a free surface. Its use in correlations depends on geometry and correlation assumptions. Finally check units, assumptions, measurement conditions and reference quantities against the problem before using the result.
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Curated exam set for "Hydraulic diameter":
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Which formula describes Hydraulic diameter?
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How do you rearrange Hydraulic diameter for Base equation for the target quantity?
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Which common mistake happens with Hydraulic diameter?
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