Roughness, relative Chart

Figure 10-143 is useful in roughly predicting the relative economic picture for adapting low finned tubes to the heat or cooling of oil on the shell side of conventional shell and tube units. This is not a design chart. 

Lewis et al. (entry 11 of Table 2) examined the temperature-dependence of isotope effects in the action of both the human enzyme and the soybean enzyme, by measuring the relative amounts of per-protio and per-deuterio-13-hydroperoxy-products by HLPC. The observed effects are, therefore, composed of primary, secondary, and perhaps remote isotope-effect contributions. Isotope effects on fecat/ M for both enzymes (determined by competition between labeled substrates) are increased by high total substrate concentration, an effect previously observed but stiU ill-understood. At 100 /rM substrate, the effects are roughly independent of temperature below about 15 °C, and are about 60 (H/D) for the human enzyme and 100 (H/D) for the soybean enzyme. Above 15 °C, the effects decline to about 50 for the human enzyme and about 60 for the soybean enzyme, perhaps because non-isotope-sensitive steps become more nearly rate-limiting (see Chart 4). 

Kinetic complexity can produce apparently temperature-independent isotope effects. For example, a rise in temperature produces a smaller intrinsic isotope effect, in agreement with the conventional expectations of Chart 3, for an isotope-sensitive step that is partially rate limiting. If at the same time the rise in temperature makes other steps relatively more rapid so that the isotope-sensitive step then becomes more nearly rate-limiting, then the intrinsic isotope effect will be more fully expressed (Chart 4). If these effects roughly balance, then the isotope effect may appear to be independent of temperature while in fact fully in accord with semiclassical expectations. Seymour and Klinman have discussed in detail the problem of kinetic complexity in isotope-effect temperature dependences. 

At high Reynolds numbers (Re > 2500), the surface roughness is an important parameter and must be allowed for in the calculations. Friction factor charts [53] include curves relating to various values of the relative roughness, that is the ratio of the mean height of surface roughness to the tube diameter. 

Figure 1. Value at stake over range 0-100% free allocation. The chart shows value at stake (see text) relative to total value-added by sector, plotted against UK trade intensity. The bars span the range from (NVAS) 100% free allocation, to (MVAS) the theoretical impact of zero free allocation or equivalent carbon tax. Results are for a carbon price of 15 /tC02 and an electricity cost pass-through that increases power prices by lO/MWh, consistent with a coal-dominated power system (CCGTs could roughly halve this rate of electricity price impact for the same carbon price). Scaling the electricity price moves the lower point of the bars in proportion scaling the carbon price scales the length in proportion.

Figure 6 was created in this manner for a series of decade values of He. It may be used in place of the Moody chart for standard pipeline design problems. Because of the manner in which the empirical correlation for B was determined, no correction for pipe relative roughness is needed when one is dealing with commercial grade-steel line pipe. 

Commercially available pipes differ from those used in the experiments in that the roughness of pipes in the market is not uniform and it is difficult to give a precise description of it. Equivalent roughness values for some commercial pipes are given in Table 8-3 as well as on the Moody chart. But it should be kept in mind that these values are for new pipes, and the relative roughness of pipes may increase with use as a result of corrosion, scale... 

The friction factor corresponding to this relative roughness and the Reynolds number can simply be determined from the Moody chart. To avoid the reading error, we determine it from the Colebrook equation ... 

Absolute roughness commercial steel pipe. Table 5.2 = 0.046 mm Relative roughness = 0.046/(25 x 10 3) = 0.0018, round to 0.002 From friction factor chart. Figure 5.11, f = 0.0032... 

Figure 4.2 gives the Moody Friction Factor Chart. This chart allows Ito be read as a function of pipe roughness, e, divided by pipe diameter (e/D, the so called relative roughness) and the Reynolds number (Re= Dvp/p), where p is the viscosity of the fluid. One can also solve the Colebrook equation iteratively to find f ... 

For turbulent flows, the friction factor is a function of both the Reynolds number and the relative roughness, where s is the root-mean-square roughness of the pipe or channel walls. For turbulent flows, the friction factor is found experimentally. The experimentally measured values for friction factor as a function of Re and are compiled in the Moody chart [1]. Whether the macroscale correlations for friction factor compiled in the Moody chart apply to microchannel flows has also been a point of contention, as numerous researchers have suggested that the behavior of flows in microchannels may deviate from these well-established results. However, a close reexamination of previous experimental studies as well as the results of recent experimental investigations suggests that microchannel flows do, indeed, exhibit frictional behavior similar to that observed at the macroscale. This assertion will be addressed in greater detail later in this chapter. 

Method for calculation of major losses of liquids. First determine fluid properties such as the density, and dynamic viscosity at the operating temperature. Determine the inner diameter of the pipe, and evaluate its absolute roughness based on Table 20.3. Then calculate the Reynolds number for average velocity of the liquid. Afterwards, either use the Moody chart to evaluate the Fanning friction factor based on the Reynolds number and relative roughness, or compute the Colebrook equation by successive iterations. Finally, use the Darcy-Weisbach equation to determine the friction head loss. 

We now have to thank Stanton and PanneU, and also Moody for their studies of flow using numerous fluids in pipes of various diameters and surface roughness and for the evolution of a very useful chart (see Fig. 48.6). This chart enables us to calculate the frictional pressure loss in a variety of circular cross-section pipes. The chart plots Re)molds numbers (Re), in terms of two more dimensionless groups a friction factor < ), which represents the resistance to flow per unit area of pipe surface with respect to fluid density and velocity and a roughness factor e/ID, which represents the length or height of surface prelections relative to pipe diameter. 

Moody plot, chart, diagram A dimensionless representation of friction factor with Reynolds number tor a fluid flowing in a pipe. Presented on log-log scales, the diagram includes laminar, transition, and turbulent flow regimes. It also includes the effects of pipe relative roughness as a dimensionless ratio of absolute roughness with internal pipe diameter. The plot was developed in 1942 by American engineer and professor of hydraulics at Princeton, Louis Ferry Moody (1880-1953). 

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