Instantaneous flow

Water Hammer When hquid flowing in a pipe is suddenly decelerated to zero velocity by a fast-closing valve, a pressure wave propagates upstream to the pipe inlet, where it is reflected a pounding of the hne commonly known as water hammer is often produced. For an instantaneous flow stoppage of a truly incompressible fluid in an inelastic pipe, the pressure rise would be infinite. Finite compressibility of the flmd and elasticity of the pipe limit the pressure rise to a finite value. The Joukowstd formula gives the maximum pressure... 

Condensate pumps usually operate with an on/off action, so that the instantaneous flow rate during the on period is greater than the average rate of flow of condensate to the pump receiver. This increased instantaneous flow rate must be kept in mind when sizing the delivery lines. 

In reciprocators hf is calculated at peak instantaneous flow, including maximum loss through a dirty filter, and an additional head loss to allow for pulsation acceleration is used ... 

Flow instabilities or even pipeline blockage during start-up procedures due to surge effects caused by the initial high pressure drop across the blow tank (and hence high instantaneous flow rate of material),... 

Fig. 12. Snapshot from a two-phase DNS of colliding particles in an originally fully developed turbulent flow of liquid in a periodic 3-D box with spectral forcing of the turbulence. The particles (in blue) have been plotted at their position and are intersected by the plane of view. The arrows denote the instantaneous flow field, the colors relate to the logarithmic value of the nondimensional rate of energy dissipation.

Gould KL, Lipscomb K, Hamilton GW. Physiologic basis for assessing critical coronary stenosis. Instantaneous flow response and regional distribution during coronary hyperemia as measures of coronary flow reserve. Am J Cardiol 1974 33 87-94... 

Type 2 Characterized by slow change of Re with with the instantaneous flow pattern similar to that in steady motion at the instantaneous Re. 

Consider a straight tubular runner of length L. A melt following the power-law model is injected at constant pressure into the runner. The melt front progresses along the runner until it reaches the gate located at its end. Calculate the melt front position, Z(f), and the instantaneous flow rate, Q t), as a function of time. Assume an incompressible fluid and an isothermal and fully developed flow, and make use of the pseudo-steady-state approximation. For a polymer melt with K = 2.18 x 10 N s"/m and n = 0.39, calculate Z(t) and Q(t)... 

It is usually very important to design separation equipment for the maximum flow rate of both gas and liquid rather than a 24-hour average rate. Only when the maximum possible rate is of a short duration, infrequent, and the application will allow occasional liquid carryover, can equipment be designed for less than the maximum instantaneous flow rate. 

The preceding sections are concerned with the time-averaged flow behavior in a macroscale. The time-variant flow behavior is complex. Analyses of the instantaneous flow... 

With the preceding assumption, the instantaneous flow rate Q(t), at given constant inlet pressure, Pq, and instantaneous fill length, Z(t) at time, t, is given by (see Example 3.4 or Table 12.2) ... 

The previous section has shown that turbulence combined with a different domain decomposition (i.e. a different number of processors for the following) is sufEcient to lead to totally different instantaneous flow realizations. It is expected that a perturbation in initial conditions will have the same effect as domain decomposition. This is verified in runs TC3 and TC4 which are run on one processor only, thereby eliminating issues linked to parallel implementation. The only difference between TC3 and TC4 is that in TC4, the initial solution is identical to TC3 except at one random point where a 10 perturbation is applied to the streamwise velocity component. Simulations with different locations of the perturbation were run to ensure that their position did not affect results. 

On the flow curves, this slip is accompanied by a discontinuity in the instantaneous flow values (Fig. 1). Its occurrence differs depending on whether or not the installation involves any storage of elastic energy connected with the compressibihty of the polymer upstream of the die. 

By analyzing the variations in instantaneous pressure, it was possible to show that slip in this config iration is accompanied by oscillations in pressiu-e between two regimes (fig. 4). During the compression phase, the pressime increases in time and the instantaneous flow rate is low. The polymer sticks to the wall of the extrusion die and cracks at the outlet. During the relaxation phase, the pressure decreases in time and the instantaneous flow rate is high. The polymer shps along the die wall and the surface of the extrudate is more or less smooth. 

Figure 12c Extrudate distortion for LLDPE at the exit of a capillary 0.5mm diameter and 20 mm long, during the second oscillating regime. The polymer flows downwards. The largest instantaneous flow rate is observed for iii). Photograph ii) shows the transition from small (photograph i)) to large instantaneous flow rate.

A continuous process may include batch make-up of minor reagents, such as the catalyst for a polymerization process. Batch flows into a continuous process are usually labeled Normally no flow and show the flow rates that will be obtained when the stream is flowing. It is these instantaneous flow rates that govern the equipment design, rather than the much lower time-averaged flow rates. 

The fluid mixture coming out of the extractor is depressurized to atmospheric pressure by passing it through a heated metering valve and a back pressure regulator. The instantaneous flow rate of the gas leaving the extractor is measured using a rotameter and the total amount of gas flow is measured with a calibrated wet-test meter. 

FIGURE 25-3. Normal flow-volume loop. Flows are measured on the vertical (y) axis, and lung volumes are measured on the horizontal (x) axis. FVC can be read from the tracing as the maximal horizontal deflection. Instantaneous flow (Vmax) at any point in FVC also can be measured directly. FVC = forced vital capacity. 

Although Equation (22.2) is often considered to be a fundamental formula governing filtration, it must be used with caution. It is very useful in analysis when viewed as an empirical approximation. It provides an instantaneous picture of the relationship among the variables, which include the instantaneous flow rate q, applied pump pressure p, and volume co or mass of solids/unit area. 

Loop-based introduction is more suitable for inserting small sample volumes because the analytical repeatability tends to be preserved when the loop dimensions are reduced. For very small inserted sample volumes and the use of pulsed flows, pumping and injection should be synchronised in order to avoid sample insertion under different instantaneous flow rates (see also 5.23.2). 

Thus, in the absence of the forcing and viscous dissipation the vorticity is conserved along the trajectories of fluid elements. Equation (1.30) describes the evolution of the vorticity distribution in a given velocity field. However, u and v are obviously not independent of each other, but are two alternative representations of the instantaneous flow field. The velocity field is a vector, but it is subjected to the incompressibility condition. This constraint can be eliminated... 

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