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The wetted perimeter can be defined mathematically as = = where l i is the length of each surface in contact with the aqueous body. In open channel flow, the wetted perimeter is defined as the surface of the channel bottom and sides in direct contact with the aqueous body.
This means the greater the hydraulic radius, the larger volume of water the channel can carry. Based on the 'constant shear stress at the boundary' assumption, [6] hydraulic radius is defined as the ratio of the channel's cross-sectional area of the flow to its wetted perimeter (the portion of the cross-section's perimeter that is "wet"):
P is the wetted perimeter of the cross-section. More intuitively, the hydraulic diameter can be understood as a function of the hydraulic radius R H, which is defined as the cross-sectional area of the channel divided by the wetted perimeter. Here, the wetted perimeter includes all surfaces acted upon by shear stress from the fluid. [3]
This is the cross-sectional area of the channel divided by the wetted perimeter. For a semi-circular channel, it is a quarter of the diameter (in case of full pipe flow). For a rectangular channel, the hydraulic radius is the cross-sectional area divided by the wetted perimeter.
For free surfaces (such as in open-channel flow), the wetted perimeter includes only the walls in contact with the fluid. [ 3 ] Similarly, in the combustion chamber of a rocket engine , the characteristic length L ∗ {\displaystyle L^{*}} is defined as the chamber volume divided by the throat area. [ 4 ]
The area-equivalent radius of a 2D object is the radius of a circle with the same area as the object Cross sectional area of a trapezoidal open channel, red highlights the wetted perimeter, where water is in contact with the channel. The hydraulic diameter is the equivalent circular configuration with the same circumference as the wetted perimeter.
This can only occur in a smooth channel that does not experience any changes in flow, channel geometry, roughness or channel slope. During uniform flow, the flow depth is known as normal depth (yn). This depth is analogous to the terminal velocity of an object in free fall, where gravity and frictional forces are in balance (Moglen, 2013). [ 3 ]
In fluid mechanics and hydraulics, open-channel flow is a type of liquid flow within a conduit with a free surface, known as a channel. [1] [2] ...