Hydraulic mean diameter

For turbulent flow in a duct of non-circular cross-section, the hydraulic mean diameter may be used in place of the pipe diameter and the formulae for circular pipes may then be applied without introducing a large error. This approach is entirely empirical. 

The hydraulic mean diameter dm is defined as four times the cross-sectional area divided by the wetted perimeter. For a circular pipe, for example, the hydraulic mean diameter is ... 

The frictional loss for a fluid flowing parallel to the axes of the tubes may be calculated in the normal manner by considering the hydraulic mean diameter of the system, although this applies strictly to turbulent flow only. 

For flow in an open channel, only turbulent flow is considered because streamline flow occurs in practice only when the liquid is flowing as a thin layer, as discussed in the previous section. The transition from streamline to turbulent flow occurs over the range of Reynolds numbers, updm/p = 4000 — 11,000, where dm is the hydraulic mean diameter discussed earlier under Flow in non-circular ducts. 

The shear stress Ri at the pipe wall in the upper portion of the pipe may be calculated on the assumption that the liquid above the bed is flowing through a non-circular duct, bounded at the top by the wall of the pipe and at the bottom by the upper surface of the bed. The hydraulic mean diameter may then be used in the calculation of wall shear stress. However, this does not take account of the fact that the bottom boundary, the top surface of the bed, is not stationary, and will have a greater effective roughness than the pipe... 

An alternative approach has been suggested by Kern(28) who worked in terms of the hydraulic mean diameter de for flow parallel to the tubes ... 

For the heat transfer for fluids flowing in non-circular ducts, such as rectangular ventilating ducts, the equations developed for turbulent flow inside a circular pipe may be used if an equivalent diameter, such as the hydraulic mean diameter de discussed previously, is used in place of d. 

CARPENTER et alS35) suggest using the hydraulic mean diameter de = dj — d i) in the Sieder and Tate equation (9.66) and recommend the equation ... 

If vapour condenses on the outside of a vertical tube of diameter d , then the hydraulic mean diameter for the film is ... 

Calculate the hydraulic mean diameter of the annular space between a 40 mm and a 50 mm tube. 

In some texts the equivalent (hydraulic mean) diameter is defined differently for use in calculating the heat transfer coefficient in a conduit or channel, than for calculating the pressure drop. The perimeter through which the heat is being transferred is used in place of the total wetted perimeter. In practice, the use of de calculated either way will make... 

The correlations for flow in conduits can be used to estimate the heat transfer coefficient and pressure drop in the channels using the hydraulic mean diameter as the characteristic dimension. 

The heat transfer coefficient to the vessel wall can be estimated using the correlations for forced convection in conduits, such as equation 12.11. The fluid velocity and the path length can be calculated from the geometry of the jacket arrangement. The hydraulic mean diameter (equivalent diameter, de) of the channel or half-pipe should be used as the characteristic dimension in the Reynolds and Nusselt numbers see Section 12.8.1. 

Various correlations for mean droplet size generated by plain-jet, prefilming, and miscellaneous air-blast atomizers using air as atomization gas are listed in Tables 4.7, 4.8, 4.9, and 4.10, respectively. In these correlations, ALR is the mass flow rate ratio of air to liquid, ALR = mAlmL, Dp is the prefilmer diameter, Dh is the hydraulic mean diameter of air exit duct, vr is the kinematic viscosity ratio relative to water, a is the radial distance from cup lip, DL is the diameter of cup at lip, Up is the cup peripheral velocity, Ur is the air to liquid velocity ratio defined as U=UAIUp, Lw is the diameter of wetted periphery between air and liquid streams, Aa is the flow area of atomizing air stream, m is a power index, PA is the pressure of air, and B is a composite numerical factor. The important parameters influencing the mean droplet size include relative velocity between atomization air/gas and liquid, mass flow rate ratio of air to liquid, physical properties of liquid (viscosity, density, surface tension) and air (density), and atomizer geometry as described by nozzle diameter, prefilmer diameter, etc. 

Similar effects are obtained with non-cylindrical vessels although, in the absence of adequate data, it is best to use the correlations for cylinders, basing the vessel size on its hydraulic mean diameter which is four times the ratio of the cross-sectional area to the wetted perimeter. 

The hydraulic mean diameter for such a flow passage has been shown in Volume 1, Chapter 3 to be ... 

Use equation 12.18 for estimating the pressure drop, taking the friction factor from Figure 12.24. As the hydraulic mean diameter will be large compared to the roughness of the jacket surface, the relative roughness will be comparable with that for heat exchanger... 

---