Elevation change

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

I. Hs - the static head, or the change in elevation of the liquid across the system. It is the difference in the liquid surface le el at the suction source or ve.s.sel, subtracted from the liquid surface level where the pump deposits the liejuid. The Hs is measured in feet of elevation change. Some systems do not have Hs or elevation... 

The Hp also can exist with the pump running or off VVe can represent this value with an O or oval on the vertical line of the below graph. The Hp is added to and. stacked on top of the Hs. Let s say that our system is pumping cold water and requires 50 ft of elevation change and 10 psi of pressure change across the system. Now, our pump not only has to lift the liquid 50 ft, but it must also conquer 23 ft of Hp. Remember that 10 psi is 23.1 ft of Hp ... 

AP = 21.2 psi friction pressure loss only (no elevation change)... 

In most applications, it is relatively straightforward to confirm the total elevation change of the pumped liquid. Measure all vertical rises and drops in the discharge piping, then calculate the total difference between the pump s centerline and the final delivery point. 

HRSG), a furnace or a NO treatment unit. The backpressure created by such a device decreases the power generation. Even if there is no device, changes in elevation changing the ambient pressure also change the machine performance. 

FIG. 23-31 Configuration modeled for pipe flow with elevation change. 

HEM for Inclined Pipe, Discharge If a pipe leak occurs at an elevation above or below the pump or source tank the elevation change can be idealized between the starting and ending points as shown in Fig. 23-38. That is, elevation changes can be treated as an inclined pipe with a non-zero inclination factor Fj. This is an approximation to the actual piping isometrics, but is often an adequate approximation. 

As the process model is made more accurate and complicated, you can lose the possibility of obtaining an analytical solution of the optimization problem. For example, if (1) the pressure losses through the pipe fittings and valves are included in the model, (2) the pump investment costs are included as a separate term with a cost exponent (n) that is not equal to 1.0, (3) elevation changes must be taken into account, (4) contained solids are present in the flow, or (5) significant changes in density occur, the optimum diameter will have to be calculated numerically. 

Figure 1. Map of St. Mary s City, Maryland area (adapted with permission from Reference 13 copyright 1989, Maryland Geological Survey). Inset shows elevation changes along Mattapan Road, up the St. Mary s Hill, with transect sampling sites marked by boxes. Triangles on larger map indicate most recent sampling locations. Sample sites A-F were examined by Armitage et al. (14).

Surface-elevation changes (Figure 3), brought about by the explosive work, ranged from 1.20 in. at well 1 to 1.92 in. at well 3 in the five-spot test pattern to 0.84 and 0.60 in., respectively, at off pattern wells 6 and 7. The contours of surface elevation change indicated that the change was almost proportional to the distance from the NG1 injection well 3. 

Void volume based on the elevation-change contours and the area enclosed by the dashed line in Figure 3 was calculated to be nearly 150 cu ft. The total area affected by explosive fracturing could not be determined because of the lack of elevation-measuring stations outside of the contoured area. 

Figure 3. Contours of surface elevation change resulting from 300-qt. NGl snot, Rock Springs site 4...

The range of techniques discussed in this volume measure local elevation, local relief, erosion and several environmental variables including precipitation, temperature, seasonality, and enthalpy. Relief, erosion and environmental records are related to paleoaltimetry through (1) empirically and theoretically determined climate-elevation relationships, and (2) assumptions about how erosion and relief relate to elevation change. While reading this volume, the reader should consider the specific measurement provided by a particular technique and its sensitivities to other factors. A broad range of approaches provides the opportunity to be both circumspect and comprehensive with tectonic and geomorphic interpretations based on paleoaltimetry data. 

In the following sections, I review a few, commonly-cited models of widespread compressional and extensional deformation and consider their respective elevation predictions. This review is not meant to be an exhaustive list of all possible mechanisms of elevation change due to continental deformation. Rather, the purpose is to illustrate the role of elevation as a parameter that can be used to constrain mechanisms of continental deformation. 

Looking forward, the techniques discussed in this volume will not only elucidate elevation histories, but applied in combination may also explore how climate, relief, erosion and elevation change independently or interdependently during orogenesis. Such combinations will ultimately advance our understanding of deformation processes on the continents and the interrelationships between climate, erosion and tectonics. 

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