Radius hydraulic

Show what the hydraulic radius of a right circular cylinder is, relative to its diameter. 

The procedures described so far have all required a pore model to be assumed at the outset, usually the cylinder, adopted on the grounds of simplicity rather than correspondence with actuality. Brunauer, Mikhail and Bodor have attempted to eliminate the over-dejjendence on a model by basing their analysis on the hydraulic radius r rather than the Kelvin radius r . The hydraulic radius is defined as the ratio of the cross-sectional area of a tube to its perimeter, so that for a capillary of uniform cross-section r is equal to the ratio of the volume of an element of core to... 

Now the left-hand side of Equation (3.54) is equal to the hydraulic radius r of the group of cores (cf. Equation (3.49)) and the right-hand side by the Kelvin equation (cf. Equation (3.20)) is equal to rjl. Consequently,... 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

The hydraulic radius is the cross-sec tional area divided by the wetted perimeter, where the wetted perimeter does not include the free. sur-... 

Darcy s law is considered valid for creeping flow where the Reynolds number is less than one. The Reynolds number in open conduit flow is the ratio of inertial to viscous forces and is defined in terms of a characteristic length perpendicular to flow for the system. Using four times the hydraulic radius to replace the length perpendicular to flow and conecting the velocity with porosity yields a Reynolds number in the form ... 

Lyachshenko number, dimensionless left hand side, dimensionless particle mass, kg pressure, N/m or force, N mass feed rate, kg/s or volumetric flowrate in mVhr drag or resistance force, N physical properties correction factor for slurries Reynolds number, dimensionless right hand side hydraulic radius, m... 

Equivalent diameter and hydraulic radius for non-circular flow ducts or pipes... 

For the narrow shapes with width small relative to length, the hydraulic radius is approximately [3] ... 

Free air, cubic feet per minute 60°F and 14.7 psia Individual gas constant = MR/M = 1544/M Reynolds number, see Figure 2-3 Hydraulic radius, ft... 

For a single particle, Dp can be taken as 2 (hydraulic radius), and the Sauter mean diameter for hindered particles. 

Use velocity of aerated mass same as for cleair liquid. Rh = hydraulic radius of the aerated mass for cross-flow, ft cross section... 

The volumetric equivalent diameter, d,. in., is again calculated on the basis of 4X the hydraulic radius see Figure 10-56. 

Dj = outside diameter of inner tube, ft Dj = inside diameter of outer pipe, ft r[, = hydraulic radius, ft = (radius of a pipe equivalent to the annulus cross-section)... 

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

A1V=wetted sewer pipe surface area divided by the water volume, i.e., R-1, where R is the hydraulic radius... 

R = hydraulic radius, i.e., the cross-sectional area of the water volume divided by the wetted perimeter (m)... 

When designing sewer networks, particularly gravity sewers, reaeration is the major process that should be focused on to reduce sulfide formation and the formation of organic odorous substances (cf. Section 4.4). A number of hydraulic and systems characteristics can be managed to increase the reaeration rate and avoid or reduce sulfide-related problems. The hydraulic mean depth, the hydraulic radius, the wastewater flow velocity and the slope of the sewer pipe are, in this respect, important factors that are dealt with in Section 4.4. It should be stressed that it is not necessarily the objective to avoid sulfide formation (in the sewer biofilm), but the sulfide that occurs in the bulk water phase should be at a low concentration level. Therefore, the DO concentration in the bulk water phase should not be lower than about 0.2-0.5 g02 m-3, sufficiently high to oxidize sulfide before a considerable amount is emitted to the sewer atmosphere. 

R hydraulic radius (m) s slope (m m-1) ii mean flow velocity (m s-1)... 

Figure 6. Separation factor-particle diameter tehavior as a function of packing diameter for the pore-partitioning model. Parameters are the same as in Figure 3 with the exception of the interstitial capillary radius which was computed from the hed hydraulic radius (Equation 11 (7.) with void fraction = 0.358).

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