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96 CHAPTER 4 1950 Guide downstream in any degree, a suction effect is produced to falsify the reading. In instruments having the static pressure opening pointed down stream, the coefficient may be as low as 0.86. Consequently, for accurate work, Pitot tubes should be calibrated, and the pertinent coefficient should be applied to Equation 72. In a sense, this coefficient is advantageous, since it results in a higher differential reading, which, in turn, enables more accurate readings at low flows. In using Pitot tubes, it is generally necessary to make a traverse of the pipe or duct to determine the course of the velocity pattern., In a pipe, for instance, one of the profiles shown in Fig. 5 would be obtained. Near a valve or fitting, however, the profile might be quite distorted, a fact which would be revealed by the traverse. If the pipe or duct is divided Fluid Flow 97 VARIABLE AREA FLOW METERS In the routine measurements of many liquids and gases, satisfactory results may be obtained by the use of variable area flow meters freouentlv cafled rotameters. In their most common form these devices consist essentially of a float which is free to move vertically in a tapered tube. The fluid to be metered enters at the narrow bottom end ofofrmtheedtubbeetwaenednmthoevefslouaptwaanrdd,inpsaidsseinwgaallt osof mtheeptouibnet.thrAout gahnythpeaarntincuullua?s rate of flow the Vflwoamt wamssaumoef sa acadleibfrinaitteedpsocsailteioonninthtehetubtueb.e' its loca"tion Fig. 19. Relation op Expansion Factor, so, forNozzi.es to Diameter Ratio and Pressure Loss for Air and Other Diatomic Gases. Factor,y, for Nozzles to Diameter Ratio and Pressure Loss forSteam, Carbon Dioxide and Natural Gas. into equal areas, and a determination of is made for each, the average velocity would be. obtained by using the average of the square roots of in Equation 73. INSTALLATION OF NOZZLES AND ORIFICES A final note should be made of the installation of orifices and nozzles. Generally speaking, the orifice or nozzle, together with a holding arrange ment, including pressure taps, is available from the manufacturer. In making the installation, the user should make certain that the flow ap proaching the nozzle or orifice is steady and evenly distributed, t'.e., with velocity profiles similar to those shown in Fig. 5. Fittings and valves, which tend to direct the flow to one side and which in some cases cause it to rotate as it advances, must be far enough upstream from the orifice or nozzle to permit the disturbed stream to straighten out to the even form before reaching the meter. Minimum conditions in the installation for avoiding trouble from fittings and valves are shown in Fig. 21. If neces sary, straightening vanes may be used upstream from the orifice or nozzle at a distance of not less than 8 pipe diameters. Fig 21. Minimum Conditions to be Observed When Installing Orifices and Nozzles Between Fittings and Valves The position of the float is established by a balance between the fluid pressure forces across the annulus and the weight of the float itself. The buoyant force which must support the float, vt(pi -- p), is balanced by the pressure difference acting on the cross section area of the float, AtAp, where pt, At, v,, are, respectively, the float density, float cross section area, and float volume. Accordingly, the difference in head across the annulus is given by Ap _ vi(fit -- p) hi P Aip (74) The volume flow follows from equation (51) as Q. -- KA.V2ffPi(p -- p)/pAi (75)