Water flow analogy

Because the transaldolase and transketolase reactions are symmetrical with respect to types of bonds cleaved and formed, their equilibrium constants are near 1. The pool of sugar phosphates is thus near equilibrium in cells that contain these enzymes. In a water-flow analogy, the sugar phosphates and the reactions that interconvert them resemble a large swamp, with ill-defined flows along many interconnecting channels. Water may be fed in from any direction and may leave the swamp in any direction. 

Derive the Taylor-Prandtl modification of the Reynolds Analogy between momentum and heat transfer. In a shell and tube condenser, water flows through the tubes which are 10m long and 40 mm diameter. The... 

To understand why this is so, recall that cell potentials are analogous to altitude differences for water. Whether 10,000 or 20,000 L of water flows down a spillway, the altitude difference between the top and bottom of the spillway is the same. In the same way, multiplying a reaction by some integer changes the total number of moles of electrons transferred, but it does not change the potential difference through which the electrons are transferred. We return to this point in Section 19-1. 

Electric current, which is the flow of electrons, is in many ways directly analogous to the flow of water. Think of a river flowing over a waterfall. The volume of water flowing past a point in the river each second is analogous to electrical current, and the height of the waterfall is analogous to a voltage drop. 

Current is a measure of electron flow rate in an electrical circuit, analogous to water flow rate through a pipe, and is symbolized by I. Current is measured in amperes (amps), symbolized as A miUiamperes (milliamps), symbolized as mA or microamperes (microamps), symbolized as ptA. An ampere is an electron flow of 6.23 xlO18 electrons per second passing through the circuit. 

Apparently no attempts have been made to prepare a complete chart for the prediction of flow patterns in vertical flow, analogous to Fig. 4. Kozlov (K5) has stated, on the basis of his experiments with air and water in a 1-in. diameter tube, that the flow pattern can be defined by plotting the volumetric gas fraction fed and the average Froude number, Vii /gD- He gives equations for the boundary lines between types of flow (assumed to be straight lines on a log-log plot of the type suggested). 

This paper is a progress report of an experimental study underway at ANL on the interaction of flowing simulated ground-water and the components that may be used in a nuclear waste repository constructed in basalt The components are placed in the water stream analogously to the configuration that could occur from a breach of the repository hence, the experiments... 

In all cases, an understanding of the physics of groundwater movement is necessary to adequately estimate the direction and rate at which contaminated water is moving in an aquifer. An analogy can be made with tracking a contaminant in a river, as discussed in Chapter 2, except that the underground water flow is out of sight and much more expensive to sample. 

The deep water flow in the ocean is often depicted as a conveyor belt in which water that originates at the surface in the North Atlantic Ocean (NADW) flows through the Atlantic, Indian and Pacific Oceans before it upwells and returns (Fig. 1.12). The analogy... 

Step one is to draw a system diagram similar to Figure 10-7. Only one analog/digital input and two discrete outputs are necessary. The analog/digital input is the make-up water flow transmitter and the two discrete outputs are the contact closures to start the chemical pumps. 

To understand this think of the analogy of water flowing through a pipe. The greater the pressure on the water, the more vigorously the water flows. The "pressure" on electrons to flow from one electrode to the other in a battery is called the potential of the battery and is measured in volts. For example, each cell in a lead storage battery produces about 2 volts of potential. In an actual automobile battery, six of these cells are connected to produce about 12 volts of potential. 

When it is necessary for a reaction to proceed through several successive elementary steps before the product is formed, the rate of the reaction is determined by the rates of all these steps. If one of these reactions is much slower than any of the others, then the rate will depend on the rate of this single slowest step. The slow step is the rate-determining step. The situation is analogous to water flowing through a series of pipes of different diameters. The rate of delivery of the water will depend on the rate at which it can pass through the narrowest pipe. An apt illustration of this feature of consecutive reactions is offered by the Lindemann mechanism of activation for unimolecular decompositions. 

This is Laplace s equation, which describes potential flow. It is widely used in heat flow and electrostatic field problems an enormous number of solutions to Laplace s equation are known for various geometries. These can be used to predict the two-dimensional flow in oil fields, underground water flow, etc. The same method can be used in three dimensions, but solutions are more difficult. The solutions to the two-dimensional Laplace equation for common problems in petroleum reservoir engineering are summarized by Muskat [3]. The analogous solutions for groundwater flow are shown in the numerous texts on hydrology, e.g., Todd [4]. See Chap. 10 for more on potential flow. 

Write the equation analogous to Eq. 12.37 for water flowing upward through a bed of sand. Note that in this case the gAz term in Eq. 12.36 cannot be neglected,... 

This relation seems necessary to solve the problems that students have with non-additivity of temperatures as it is the formal expression distinguishing heat from temperature. Arnold s teaching design (Arnold Millar, 1996), in which heat flow is compared to water flow, offers some promise because this analogy can be extended to include the heat capacity. 

Besides, the water flow causes mechanical mixing, which together with the diffuse one determines the value of hydrodynamic dispersion, the value dependent on the direction and seepage velocity of flow. The coefficient of longwise hydrodynamic dispersion by analogy with the diffusion coefficient may be associated with the dispersion of statistical distribution by equation... 

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