Pumps continuity equation

Normally a Roots pump will be operated in connection with a dovmstream rough vacuum pump having a nominal pumping speed Sy. The continuity equation gives ... 

The gas ballast pump has the function of pumping the fraction of air, which is often only a small part of the water-vapor mixture concerned, without simultaneously pumping much water vapor. It is, therefore, understandable that, within the combination of condenser and gas ballast pump in the stationary condition, the ratios of flow, which occur in the region of rough vacuum, are not easily assessed without further consideration. The simple application of the continuity equation is not adequate because one is no longer concerned with a source or sink-free field of flow (the condenser is, on the basis of condensation processes, a sink). This is emphasized especially at this point. In a practical case of non-functioning of the condenser - gas ballast pump combination, it might be unjustifiable to blame the condenser for the failure. 

As far as modelling the decrease of flow rate with time after the loss of electric power is concerned, the codes used balance the momentum in each cooling circuit and in the core. This momentum balance is combined with the continuity equations, with the momentum balance of the pumps and with the pump characteristic curves. In these calculations the head losses are overestimated for sake of conservatism. 

Because electron transport is a nonequilibrium process, we anticipate that static DFT will not be able to accurately predict some features of electron transport. A number of methods have been developed that allow one to use TDDFT for these purposes. For example, Kurth et al. ° present a practical scheme using TDDFT to calculate current. The basic idea is to pump the system into a nonequilibrium initial state by some external bias and then allow the KS orbitals to evolve in time via the TDKS equations. The RG theorem then allows one to extract the longitudinal current using the continuity equation. Using transparent boundary conditions that solve problems with... 

Example 2 Simplified Ejector Figure 6-6 shows a very simplified sketch of an ejector, a device that uses a high velocity primary fluid to pump another (secondary) fluid. The continuity and momentum equations may he... 

As will be shown later the equation above is identical to the mass balance equation for a continuous stirred-tank reactor. The recycle can be provided either by an external pump as shown in Fig. 5.4-18 or by an impeller installed within the reaction chamber. The latter design was proposed by Weychert and Trela (1968). A commercial and advantageously modified version of such a reactor has been developed by Berty (1974, 1979), see Fig. 5.4-19. In these reactors, the relative velocity between the catalyst particles and the fluid phases is incretised without increasing the overall feed and outlet flow rates. 

The oil-water dynamic interfacial tensions are measured by the pulsed drop (4) technique. The experimental equipment consists of a syringe pump to pump oil, with the demulsifier dissolved in it, through a capillary tip in a thermostated glass cell containing brine or water. The interfacial tension is calculated by measuring the pressure inside a small oil drop formed at the tip of the capillary. In this technique, the syringe pump is stopped at the maximum bubble pressure and the oil-water interface is allowed to expand rapidly till the oil comes out to form a small drop at the capillary tip. Because of the sudden expansion, the interface is initially at a nonequilibrium state. As it approaches equilibrium, the pressure, AP(t), inside the drop decays. The excess pressure is continuously measured by a sensitive pressure transducer. The dynamic tension at time t, is calculated from the Young-Laplace equation... 

Piping systems often involve interconnected segments in various combinations of series and/or parallel arrangements. The principles required to analyze such systems are the same as those have used for other systems, e.g., the conservation of mass (continuity) and energy (Bernoulli) equations. For each pipe junction or node in the network, continuity tells us that the sum of all the flow rates into the node must equal the sum of all the flow rates out of the node. Also, the total driving force (pressure drop plus gravity head loss, plus pump head) between any two nodes is related to the flow rate and friction loss by the Bernoulli equation applied between the two nodes. 

Polynomial equations are used to describe continuous curves of pump flowrate versus head, power, and NPSHR. A 6th order polynomial equation is written in the form ... 

If the high vacuum pump is only to be used at intake pressures below 10 mbar, a smaller backing pump will do in the case of the example given this will be a pump offering a pumping speed of 6 m /h. If the continuous intake pressures are even lower, below 10" mbar, for example, the required pumping speed for the backing pump can be calculated from equation 2.41a as ... 

Procedure. To form a BLM, a small amount (.— 0.005 ml.) of lipid solution was applied via a Teflon capillary attached to a micrometer syringe. The formation characteristics leading to the black state were observed under reflected light at 20-40 X magnification. Other precautions that should be exercised are essentially those described previously (10). The bifacial tension of BLM was measured as follows. After the membrane had become completely black (except at the Plateau-Gibbs border), the infusion-withdrawal pump was started. The pressure difference across the BLM was continuously monitored and reached a maximum when the membrane was hemispherical. The interfacial tension was calculated from this point using Equation 3. 

If the same vessel is arranged with suitable openings near the center and also around the periphery, and if it is provided with vanes, it becomes either a centrifugal pump impeller or a turbine runner. These vanes constrain the flow of the liquid and determine both its relative magnitude and its direction. If the area of the passages normal to the direction of flow is a, then the equation of continuity fixes the relative velocities, since ... 

Chapter 2 begins by defining essential terms in vacuum technology - gas flow rate, pumping speed, conductance, etc. It also emphasises a basic assumption for calculation - that continuity is established in a system (what enters must eventually leave). Simple equations are stated and their use demonstrated. 

---