Flow and pressure measurement

Sulphuric acid of density 1300 kg/m is flowing through a pipe of 50 mm internal diameter. A thin-lipped orifice, 10 mm diameter, is fitted in the pipe and the differential pressure shown by a mercury manometer is 10 cm. Assuming that the leads to the manometer are filled with the acid, calculate (a) the mass of acid flowing per second, and (b) the approximate loss of pressure caused by the orifice. The coefficient of discharge of the orifice may be taken as 0.61, the density of mercury as 13,550 kg/m, and the density of water as 1000 kg/m.  

The rate of discharge of water from a tank is measured by means of a notch, for which the flowrate is directly proportional to the height of liquid above the bottom of the notch. Calculate and plot the profile of the notch if the flowrate is 0.1 m /s when the liquid level is 150 mm above the bottom of the notch. 

The velocity of fluid discharged as a height h above the bottom of the notch is  

The velocity therefore varies from zero at the bottom of the notch to a maximum value at the free surface. 

For a horizontal element of fluid of width 2w and depth dh at a height h above the bottom of the notch, the discharge rate of fluid is given by  

The second section of the mechanism (the controller) produces an output which is a function of the magnitude of e. This is fed to a control valve in the steam line, so that the valve closes when To increases and vice versa. The system as shown may be used to counteract fluctuations in temperature due to extraneous causes such as variations in water flowrate or upstream temperature — termed load changes. It may also be employed to change the water temperature at Y to a new value by adjustment of the desired value. 

It is very important to note that in this loop system the parameter To, which must be kept constant, is measured, though all subsequent action is concerned with the magnitude of the error and not with the actual value of To. This simple loop will frequently be complicated by there being several parameters to control, which may necessitate considerable instrumental analysis and the control action will involve operation of several control valves. 

This represents a simple form of control for a single variable, though in a modem plant many parameters are controlled at the same time from various measuring instmments, and the variables on a plant such as a distillation unit are frequently linked together, thus increasing the complexity of control that is required. 

On industrial plants, the instruments are therefore required not only to act as indicators but also to provide some link which can be used to help in the control of the plant. In this chapter, pressure measurement is briefly described and methods of measurement of flowrate are largely confined to tho.se which depend on the application of the energy 

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Measurement versus Equipment Performance Pumps that are in reasonable condition typically operate within 5 percent of their pump curve. Consequently, pressures and flows that are inconsistent with the pump curve imply that the indicated flow and/or pressure are incorrecl . Figure 30-16 shows a single impeller curve plotted as head versus flow. The point shown is inconsistent with the pump operation. Therefore, that pair of flow and pressure measurements is not validated and should not be used in the subsequent steps. 

Fryer, P.J. 210,229 Fuller, E. N. 584,655 Fully developed flow 61.681 Fundamental units, choice of 12 Further reading, flow and pressure measurement (Chapter 6) 272... 

In Section II,C we have deliberately chosen a simple set of problem specifications for our steady-state pipeline network formulation. The specification of the pressure at one vertex and a consistent set of inputs and outputs (satisfying the overall material balance) to the network seems intuitively reasonable. However, such a choice may not correspond to the engineering requirements in many applications. For instance, in analyzing an existing network we may wish to determine certain input and output flow rates from a knowledge of pressure distribution in the network, or to compute the parameters in the network element models on the basis of flow and pressure measurements. Clearly, the specified and the unknown variables will be different in these cases. For any pipeline network how many variables must be specified And what constitutes an admissible set of specifications in... 

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