Hydraulic diameter concept

Obot NT (1988) Determination of incompressible flow friction in smooth circular and nondrcular passages. A generaUzed approach including validation of the century old hydraulic diameter concept. Trans ASME J Fluid Eng 110 431-440... 

The wall shear stress can be calculated on the basis of the fully developed pipe flow correlation (the hydraulic diameter concept). 

Cheremisinoff and Davis (1979) relaxed these two assumptions by using a correlation developed by Cohen and Hanratty (1968) for the interfacial shear stress, using von Karman s and Deissler s eddy viscosity expressions for solving the liquid-phase momentum equations while still using the hydraulic diameter concept for the gas phase. They assumed, however, that the velocity profile is a function only of the radius, r, or the normal distance from the wall, y, and that the shear stress is constant, t = tw. ... 

Now for a circular duct, i.e., a pipe with a uniform heat flux at the wall, the analysis discussed in the previous section gave Nup = 4.364. Therefore, for fully developed flow in a plane duct with a uniform heat flux at the wall, this would indicate using the hydraulic diameter concept, that ... 

This is very different from the actual value of 4.118 derived above showing that the use of the hydraulic diameter concept can sometimes give very erroneous results for the heat transfer rate. j... 

Use the Reynolds analogy to derive an expression for the Nusselt number for fully developed turbulent flow in an annulus in which the inner wall is heated to a uniform temperature and the outer wall is adiabatic. Assume that the friction factor can be derived by introducing the hydraulic diameter concept. 

Although the hydraulic-diameter concept frequently yields satisfactory relations for fluid friction and heat transfer in many practical problems, there are some notable exceptions where the method does not work. Some of the problems involved in heat transfer in noncircular channels have been summarized by Irvine [20] and Knudsen and Katz [9]. The interested reader should consult these discussions for additional information. 

However, just as for different geometric forms, we are frequently able to introduce the concept of hydraulic diameter behind which differences in the geometric forms are hidden, we may assume that there exists an effective chemical reaction time which is identical in formulas (13)—(15), so that in this case the form of formulas (16) and (17) will not depend on the reaction kinetics. The basis for such an assumption is the fact that in a... 

The concept of a channel with a hydraulic diameter equivalent to the complex interstitial network which exists in a powder bed leads to Eq. (18),... 

The present model development is based on a semi-heuristic model of flow through solid matrices using the concept of hydraulic diameter, which is also known as the Carman-Kozeny theory [7]. The theory assumes the porous medium to be equivalent to a series of parallel tortuous tubules. The characteristic diameter of the tubules is taken to be a hydraulic diameter or... 

The drawback of randomly packed microreactors is the high pressure drop. In multitubular micro fixed beds, each channel must be packed identically or supplementary flow resistances must be introduced to avoid flow maldistribution between the channels, which leads to a broad residence time distribution in the reactor system. Initial developments led to structured catalytic micro-beds based on fibrous materials [8-10]. This concept is based on a structured catalytic bed arranged with parallel filaments giving identical flow characteristics to multichannel microreactors. The channels formed by filaments have an equivalent hydraulic diameter in the range of a few microns ensuring laminar flow and short diffusion times in the radial direction [10]. 

The legitimacy of employing Blasius type models for the shear stresses in stratified flows was checked in several studies. Kowalski made direct measurements of the Reynolds shear stress in the gas for horizontal stratified flow in pipes and found that the gas-wall friction factors are well approximated by the Blasius equation provided that the hydraulic diameter is utilized [64]. For the liquid phase, Andritsos and Hanratty [28] found that the use of the Blasius equation to calculate introduces some error. However, improvements achieved by using a more complicated model for which is based on velocity profile and eddy viscosity concepts, were found to be of mild effect on the integral flow characteristics. 

This leads to the concept that there is an equivalent or hydraulic diameter for any cross section such that... 

The concept of the hydraulic diameter (D//) provides a quantitative means of ranking the flow resistance of the various runner configurations. The... 

The use of hydrauhc diameter in calculating pressure drop is a commonly used concept for simplifying geometry. The hydraulic diameter for an opening is calculated by multiplying the open surface area by 4, then dividing by the wetted periphery, e.g. for a cylindrical opening d = Mnd IAt)l(nd), and for a square duct d = / Ad). 

Because the thermal performances of the concepts analyzed were equalized, the disciiminating variable between concepts was the resulting hot leg iimer diameter. Hydraulically, the concept with the largest inner diameter will have the best performance. The internally insulated concept had the largest iimer diameter as a result of having only one insulating layer. A summary of the thermal and hydraulic performance of the analyzed concepts is presented in Table 3. 

S is the ratio of the surface area of the medium to its pore volume and stands for equivalent diameter of the pores. The hydraulic (mean) radius m is defined as the ratio of the average pore cross-sectional area to the average wet perimeter, in line with the concept of the equivalent loads (as explained in Section III). All the geometrical parameters from Eq. (19) can be estimated for particulars of the porous media. For example, in the case of aligned fibers, hydraulic radius and equivalent diameter can be expressed by ... 

Concept with the largest inner diameter will have the best hydraulic performance... 

---