Instantaneous flow rate

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. 

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),... 

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. 

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) ... 

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. 

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). 

However, there is a price to be paid for this elimination of steady-state error. When P control was used, the flow rates simply increased to their new steady-state values. With PI control these flow rates increase above their final steady-state values for a period of time. This occurs because the only way that the level can be lowered back to its desired value is to have the instantaneous flow rate out of the tank be larger than the flow rate into the tank. 

Here we assume that the dVIdi) is small we check that assumption later. Then the instantaneous flow rate is assumed to be given by Bernoulli s equation, which here takes the form of Torricelli s equation ... 

This is the instantaneous flow rate. As the flow continues, the pressure and flow rate both decrease. ... 

This equation describes the instantaneous flow rate through a filter it is analogous to Ohm s law for two resistors in series, so the fj, Ax/k terms are called the cake resistance and the cloth resistance. 

The most complete information regarding the hydrodynamic structure of reactant flows in reactors can be obtained from the instantaneous flow rate values at every point of a device. This parameter is the basis for the formation of temperature and... 

Instantaneous flow rate measurements for every point of an industrial device are very difficult and often practically impossible, which is why the hydrodynamic mode of a reaction mixture is determined indirectly by the distribution of liquid particles using the duration of their pass through the reaction zone. A random value (the duration of a particle pass) measurement requires marking of the particles in a way which allows detecting the input and output moments and therefore, drawing the curve of concentration distribution in the flow and at the output. This curve is called the output curve/response curve, responding pulsed input of inert indicator [117,118]. 

The following argument assumes that tests have provided values of specific and medium resistances and the data is to be used to check, predict, control or design a pressure filter where information on the cycle time to filter a given volume of filtrate, or slurry, is required. The instantaneous flow rate q is assumed to be (neglecting the volume of the cake) ... 

The punq> characteristic ciuve gives qr as a fimction of pressure drop, and the value of the instantaneous flow rate given at an arbitrary pressure taken fi-om the characteristic can be used in a rearranged and integrated form of Equation (2.29) ... 

For exan le if the data provides a straight line on a plot of inverse instantaneous flow rate q i ainst time t then an intermediate blocking model is apparent, or a hnear relation on a plot of time over cumulative filtrate volume t/V against time t suggests standard blocking. 

During storms, the first water to fall washes the ground and is the most polluted. The flow may be from 500 to 3000 m -h Since it is not feasible to treat this amount at its instantaneous flow rate, the water must be stored in a storm basin designed on the basis of historical meteorological statistics. 

Flow rates of nitrogen at 2500 psi are 65 000 L/min through a 7.13 mm (0.281-in.) cylinder valve opening 27 000 L/min through a severed 0.89 mm (0.035-in.) wall thickness, 6.35 mm (1/4-in.) tube and 30 L/min through a 0.006-in. limiting orifice. These are instantaneous flow rates which decrease as the cylinder pressure decreases. The decrease in the first two instances is very rapid as the cylinder quickly vents. 

Suppose the mold is filled to a radius R(i) at time t the pressure relation between the instantaneous fill pressure, the instantaneous flow rate, and the amount of material in the mold ... 

Formalism for Combined Reaction and Semibatch Flow The following summarizes the ACOMP approach presented in [38]. Expressions were derived for the concentration of monomer and polymer in the reactor, while reactions are occurring, when N solutes in solution are allowed to flow into the reactor, each at their own rate, which need not be constant, such that solute s has caused a change in reactor volume at time t of AVft), where Qft) is the instantaneous flow rate of liquid from a reservoir containing component s into the reactor. In the following, q is a constant withdrawal rate from the reactor q (ernes ) that feeds the ACOMP extraction/dilution/conditioning front end. 

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