Hydraulic diameter
Encyclopedia
The hydraulic diameter, DH, is a commonly used term when handling flow
in noncircular tubes and channels. Using this term one can calculate many things in the same way as for a round
tube.
Definition:
where A is the cross sectional
area
and P is the wetted perimeter
of the cross-section.
For a round tube, this checks as:
The Manning formula
contains a quantity called the hydraulic radius. Despite what the name may suggest, the hydraulic diameter is not twice the hydraulic radius, but four times.
For an annulus
the hydraulic diameter is
and for a rectangular duct, if completely filled with fluid:
And for a rectangular duct, if partly filled with fluid:
For the special case of a square duct, where L=W, then DH = L. For the other limiting case of a very wide duct, i.e. a slot of width W where L ≫ W, then DH = 2W.
For a fully filled duct or pipe whose cross section is a regular polygon
, the hydraulic diameter is equivalent to the diameter of a circle inscribed within the wetted perimeter
.
Hydraulic diameter is mainly used for calculations involving turbulent flow. Secondary flows
can be observed in non-circular ducts as a result of turbulent shear stress
in the turbulent flow. These secondary flows force the fluid into the "corners" of the pipe.
When the flow is laminar, secondary flows do not occur, and therefore the entire cross section of the pipe is not filled. This will result in errors in calculations.
Hydraulic diameter is also used in calculation of heat transfer in internal flow problems.
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
in noncircular tubes and channels. Using this term one can calculate many things in the same way as for a round
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
tube.
Definition:
where A is the cross sectional
Cross section (geometry)
In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...
area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...
and P is the wetted perimeter
Wetted perimeter
The wetted perimeter is the perimeter of the cross sectional area that is "wet." The term wetted perimeter is common in Civil Engineering, Environmental Engineering and heat transfer applications; it is associated with the hydraulic diameter...
of the cross-section.
For a round tube, this checks as:
The Manning formula
Manning formula
The Manning formula, known also as the Gauckler–Manning formula, or Gauckler–Manning–Strickler formula in Europe, is an empirical formula for open channel flow, or free-surface flow driven by gravity...
contains a quantity called the hydraulic radius. Despite what the name may suggest, the hydraulic diameter is not twice the hydraulic radius, but four times.
For an annulus
Annulus (mathematics)
In mathematics, an annulus is a ring-shaped geometric figure, or more generally, a term used to name a ring-shaped object. Or, it is the area between two concentric circles...
the hydraulic diameter is
and for a rectangular duct, if completely filled with fluid:
And for a rectangular duct, if partly filled with fluid:
For the special case of a square duct, where L=W, then DH = L. For the other limiting case of a very wide duct, i.e. a slot of width W where L ≫ W, then DH = 2W.
For a fully filled duct or pipe whose cross section is a regular polygon
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
, the hydraulic diameter is equivalent to the diameter of a circle inscribed within the wetted perimeter
Wetted perimeter
The wetted perimeter is the perimeter of the cross sectional area that is "wet." The term wetted perimeter is common in Civil Engineering, Environmental Engineering and heat transfer applications; it is associated with the hydraulic diameter...
.
Hydraulic diameter is mainly used for calculations involving turbulent flow. Secondary flows
Secondary flow
In fluid dynamics, a secondary flow is a relatively minor flow superimposed on the primary flow, where the primary flow usually matches very closely the flow pattern predicted using simple analytical techniques and assuming the fluid is inviscid...
can be observed in non-circular ducts as a result of turbulent shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
in the turbulent flow. These secondary flows force the fluid into the "corners" of the pipe.
When the flow is laminar, secondary flows do not occur, and therefore the entire cross section of the pipe is not filled. This will result in errors in calculations.
Hydraulic diameter is also used in calculation of heat transfer in internal flow problems.