Hydraulic diameters

The constant depends on the hydraulic diameter of the static mixer. The mass-transfer coefficient expressed as a Sherwood number Sh = df /D is related to the pipe Reynolds number Re = D vp/p and Schmidt number Sc = p/pD by Sh = 0.0062Re Sc R. ... 

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. 

With the hydraulic diameter subsititued for D in/and Re, Eqs. (6-37) through (6-40) are good approximations. Note that V appearing in/and Re is the actual average velocity V = Q/A for noncircular pipes it is not ( /(7CD /4). The pressure drop should be calculated from the friction factor for uoucirciilar pipes. Eqiiations relating Q to AP and D for circular pipes may not he used for noncircular pipes with D replaced by because V Q/( KDh/4). 

Re using the equivalent diameters defined in the following. This situation is, by arbitrary definition, opposite to that for the hydraulic diameter used for turbulent flow. 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

Skin friction loss. Skin friction loss is the loss from the shear forces on the impeller wall caused by turbulent friction. This loss is determined by considering the flow as an equivalent circular cross section with a hydraulic diameter. The loss is then computed based on well-known pipe flow pressure loss equations. 

The characteristic length L denotes the pipe diameter or the hydraulic diameter djjyj = 4A/F A is the cross-sectional area and P is the wet periphery). If the cross-section is not circular, or in the case of a plane, the length is measured in the flow direction. 

To calculate the thermal plume, the cube can be presented as a cylinder with a diameter equivalent To the hydraulic diameter of the top of the cube ... 

D , is the hydraulic diameter of one cross-section between the plates, calculated from... 

The hydraulic diameter is four times the flow area divided by the duct perimeter. 

For rectangular and oval ducts, a corrected hydraulic diameter should be used. 

It should be pointed out that the hydraulic diameter method does not work well for laminar flow because the shape affects the flow resistance in a way that cannot be expressed as a function of the ratio of cross-sectional area to wetted perimeter (Green and Maloney 1997). However, some flame arrester manufacturers use this method for noncircnlar flame arrester passages. 

Table 5-2 shows the equations for calculating the hydraulic diameter for various flame arrester passageways. 

Equations for Calculation of Hydraulic Diameter for Various Flame Arresters... 

Eor noncircular apertures, the equivalent hydraulic diameter should be used. Eor crimped metal ribbon elements, the equivalent hydraulic diameter of a right isosceles triangle is 0.83 times the crimp height, and the thickness (width) should be at least 0.5 inches (EISE 1980). 

Hydraulic Diameter An eqnivalent diameter for noncircnlar apertnres which is eqnal to 4x apertnre area/apertnre perimeter. 

Hydraulic diameter, or equivalent diameter, in. Orifice diameter, or nozzle opening, in. 

Dh = hydraulic diameter, ft = 4 (flow area for the phase in question/wetted perimeter of the flow channel)... 

For other length-to-diameter ratio, refer to Ref. [27]. For cross sections other than circular or square, use the hydraulic diameter ... 

D = the hydraulic diameter, 2(flow area)/ wetted perimeter)... 

D = Inside diameter of pipe, ft DH = Hydraulic diameter, ft d = Inside diameter of pipe, in. = d de = Equivalent or reference pipe diameter, in. dn = Hydraulic diameter, or equivalent diameter, in. dQ = Orifice diameter, or nozzle opening, in. 

Al = Cross-secdonal area allocated to lighL phase, sq ft Ap = Area of particle projected on plane normal to direction of flow or motion, sq ft A, = Cross-sectional area at top of vessel occupied by continuous hydrocarbon phase, sq ft ACFS = Actual flow al conditions, cu ft/sec bi = Constant given in table c = Volume fraction solids C = Overall drag coefficient, dimensionless D = Diameter of vessel, ft Db = See Dp, min Dc = Cyclone diameter, ft Dc = Cyclone gas exit duct diameter, ft Dh = Hydraulic diameter, ft = 4 (flow area for phase in question/wetted perimeter) also, DH in decanter design represents diameter for heavy phase, ft... 

Barnett confirmed that dh does not fully describe the cross-sectional geometry for burn-out in an annulus, and he decided to introduce as an extra term—the wetted equivalent diameter, i.e., the hydraulic diameter dw = d0 — di. The final expressions found suitable for A, B, and C are... 

The connection that has been shown in Section VIII to exist between burn-out in a rod bundle and in an annulus leads to the question of whether or not a link may also exist between, for example, a round tube and an annulus. Now, a round tube has its cross section defined uniquely by one dimension—its diameter therefore if a link exists between a round tube and an annulus section, it must be by way of some suitably defined equivalent diameter. Two possibilities that immediately appear are the hydraulic diameter, dw = d0 — dt, and the heated equivalent diameter, dh = (da2 — rf,2)/ however, there are other possible definitions. To resolve the issue, Barnett (B4) devised a simple test, which is illustrated by Figs. 38 and 39. These show a plot of reliable burn-out data for annulus test sections using water at 1000 psia. Superimposed are the corresponding burn-out lines for round tubes of different diameters based on the correlation given in Section VIII. It is clearly evident that the hydraulic and the heated equivalent diameters are unsuitable, as the discrepancies are far larger than can be explained by any inaccuracies in the data or in the correlation used. 

The coefficient CD depends on the shape of the float and the Reynolds number (based on the velocity in the annulus and the mean hydraulic diameter of the annulus) for the... 

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