Surface wetted perimeter

Thus, for a vapor of p,.-0.2 Ibn/Tt at an apparent velocity of l, 3 ft/s carrying an entrained liquid of density p,>45 Ibm/fl, with the interfacial tension 0.066 Ibm/s, the minimum size at which coalesced droplets will start to disengage is D >0.0I7 ft (5.000 Sim). The actual disengagement size may be smaller, due to the droplets smaller wetted perimeter (smaller surface-tension force) and droplet deformation (smaller projected area receiving the vapor momentum). 

The hydraulic radius is the cross-sectional area divided by the wetted perimeter, where the wetted perimeter does not include the free surface. Letting S = sin 0 = channel slope (elevation loss per unit length of channel, 0 = angle between channel and horizontal), Eq. (6-53) reduces to... 

The only wetted surface is that in contact with the wall. Hence, for a unit width of film, the wetted perimeter is unity and the hydraulic diameter is given by ... 

As with noncircular ducts the hydraulic mean diameter is employed in formulae that involve diameter. If a channel has a height of a and a width b, the flow area of the channel is ab. In the calculation of the wetted perimeter the free surface is not included so that the wetted perimeter is 2a - - b, and the hydraulic mean diameter... 

The hydrauhc diameter (Dh) is defined as four times the open area divided by the wetted perimeter which is eq uvalent to four times the open firontal area divided by the geometric surface area. 

The wetting perimeter renders the electric current, 7(r, y), at the metal contact surface, 2Trr2 ... 

In what follows we derive an empirical relation for the permeability, known as the Kozeny-Carman equation, which supposes the porous medium to be equivalent to a series of channels. The permeability is identified with the square of the characteristic diameter of the channels, which is taken to be a hydraulic diameter or equivalent diameter, d. This diameter is conventionally defined as four times the flow cross-sectional area divided by the wetted perimeter, and measures the ratio of volume to surface of the pore space. In terms of the porous medium characteristics. 

In Example 6,13 the wetted perimeter was the entire perimeter of the duct. Here we do not include the perimeter facing the air, because the air exerts little resistance to the flow, compared with the walls of the canal. You can verify this by watching the flow of leaves or bits of wood on any open stream or irrigation ditch those at the center move much faster than those at the edges. If the air restrained the flow as much as the solid walls, then the whole top surface of the flow would not move at all, just as the fluid right at the solid boundaries does not move. Therefore, the hydraulic radius is... 

Fig.6.1 Equilibrium of surface tension forces on wetting perimeter...

Wetted perimeter surface area of packing Volume of flow channels... 

Fluids flow in response to a pressure difference. Buoyancy forces, due to density differences related to differences in the temperature or salinity, can cause fluid flow. Buoyancy forces are considered in models of convective flow. Fluids also flow because of differences in the hydrostatic head between a source and discharge region. Hydrostatic head is the difference in elevation (Az, m), which produces a pressure difference because of gravitational acceleration P = pgAz). The Manning equation and Darcy s law are examples of equations that model flow driven by hydrostatic forces. The Manning equation predicts flow velocity (v, m/sec) in open chaimels (Chaudhry, 2008) as a function of the channel s cross-sectional area (A, m ), wetted perimeter P, m), and the slope of the water surface (j m/m). 

Surface water velocities are measured roughly by floats during field surveys. Flow velocities are computed on a uniform channel reach by Manning s formula (Equation 5.7) if the slope, channel section (area and wetted perimeter), and roughness coefficient ( ) are known. 

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