Erosion rate equation

How these factors affect erosion can be determined from the empirical equation shown in Table 4-14. The equation shows erosion rate proportional to a constant, the mass of the particle, its velocity, and angle of attack. 

Figure 6.31 demonstrates the validity of Equation (6.134) and Equation (6.141) via noncross-linked poly(methyl methacrylate-co-methacrylic acid) (PMMA/MAA) beads. The swollen gel thickness initially increases because the rate of erosion is slow. Then a constant gel thickness follows (i.e., synchronization of swelling rate and erosion rate) and continues until the core disappears. Afterwards, the gel thickness decreases. According to Equation (6.139), the release of peptide should be linear with time, but Figure 6.31 shows a nonlinear release profile due to the decrease of surface area of spherical geometry. 

We let a beam of atomic hydrogen and a beam of methyl radicals interact with the film surface simultaneously. This can be considered the simplest of all multi-species experiments first, H and CH3 are the simplest radicalic hydrocarbon species. Second, by restricting ourselves to radicals, the interaction of the beams with the film is purely chemical and expected to be limited to the very surface. Third, the effect of each species separately is already known the previous section described the temperature dependent interaction of CH3 radicals with the a-C H surface. The interaction of atomic hydrogen with carbonaceous materials has been studied extensively in the past by various groups [53,56,57]. A rate equation model describing chemical erosion by atomic hydrogen is well-established [53,58]. 

Using this equation, the erosion rate of crystalline region (Rc) can be roughly estimated from the data in Figure 22.4. The estimated value of Rc (0.1-0.2 [ig/(mm h)) is much smaller than the R value obtained from completely amorphous film (2.5 [ig/(mm h)). Thus, the hydrolysis of the crystalline regions is a rate-limiting step in the enzymatic degradation of semicrystalline PLLA film. 

The basic equation for erosion rate is of the form (Karri, 1990)... 

The result of these modern soil conservation measures was to greatly curtail soil erosion. While a highly imperfect model, use of the Universal Soil Erosion Equation suggests that the erosion rates of 1975 had been reduced to about one-fourth those of 1934 (Trimble Lund, 1982). However, the measured rates of downstream sediment accumulation were only about 6% of the earlier rates (Trimble, 1999) The disparity between erosion rates from the uplands and the sedimentation rates in valleys is explained by sediment entrained from tributaries and also from errors of estimation of erosion and measurement of sediment deposits. 

Roberts et al. (1998) proposed the following equation to approximate the results of their erosion rate study ... 

The erosion rate data discussed above were measured using quartz particles grouped into size classes with a fairly narrow size distribution, which allowed for examination of the effects of particle size and bulk density on erosion rates. As discussed for the critical shear stress, several other sediment properties also influence the erosion rate, including particle size distribution, ionic strength, mineralogy, gas content, and benthic and bacterial colonization. As a result of the many bulk properties that influence the erodibility of a given sediment, the parameters A, n, and m for Equation... 

It should be noted that SEDZLJ assumes that particles less than 200 xm in diameter are transported entirely as suspended load for the purpose of the model calculations. Using Equation 10.21 the suspended load and bed load components of the erosion rate can be calculated as follows ... 

Basically there are two approaches to predicting the occurrence of erosion corrosion. Practical or experience based methods typified by Keller s approach for carbon steels in wet steam. Keller developed an equation that related the erosion corrosion rate as a function of temperature, steam quality, velocity and geometric factor. In recent years this approach has... 

Fig. 9-8 Histogram of dissolved solids of samples from the Orinoco and Amazon River basins and corresponding denudation rates for morpho-tectonic regions in the humid tropics of South America (Stal-lard, 1985). The approximate denudation scale is calculated as the product of dissolved solids concentrations, mean armual runoff (1 m/yr), and a correction factor to account for large ratios of suspended load in rivers that drain mountain belts and for the greater than average annual precipitation in the lowlands close to the equator. The correction factor was treated as a linear function of dissolved solids and ranged from 2 for the most dilute rivers (dissolved solids less than lOmg/L) to 4 for the most concentrated rivers (dissolved solids more than 1000 mg/L). Bedrock density is assumed to be 2.65 g/cm. (Reproduced with permission from R. F. Stallard (1988). Weathering and erosion in the humid tropics. In A. Lerman and M. Meybeck, Physical and Chemical Weathering in Geochemical Cycles," pp. 225-246, Kluwer Academic Publishers, Dordrecht, The Netherlands.)...

The pressure peaks observed in the combustion tests shown in Fig. 14.19 are computed as a function of L/D as shown in Fig. 14.20. The peak pressures computed by means of the Lenoir-Robillard empirical equation are confirmed by the measured pressure at the head-end of the motor. It is evident thatp values predicted without erosive burning are significantly lower than the measured maximum pressures. Fig. 14.21 shows the erosive ratio, 8 = r/to, as a function of the mass flow rate per unit cross-sectional area in the port, G. The erosive ratio increases with increasing Mach number in the port at constant L/D. 

When the rate of drug diffusion is much slower than the rate of polymer erosion (i.e., B2 A), Equation (6.134) becomes ... 

Zero-order release kinetics expressed by Equation (6.139) agree with Equation (6.126) for heterogeneous erosion-controlled systems. However, when the rate of polymer erosion is very slow, the rate of drug diffusion through the swollen gel layer controls drug release kinetics (i.e., B2 A), and Equation (6.134) becomes ... 

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