# UNIVERSITY OF MINNESOTA DULUTH DEPARTMENT OF CHEMICAL ENGINEERING ChE MEASUREMENTS WITH FLOW METERS

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1 UNIVERSITY OF MINNESOTA DULUTH DEPARTMENT OF CHEMICAL ENGINEERING ChE MEASUREMENTS WITH FLOW METERS OBJECTIVE The purpose of this experiment is to calculate the coefficient of discharge from experimental data for a venturi meter and an orifice meter. Determine the relationship between volumetric flow rate, Q, and the pressure drop, ΔP, for each meter Is it linear? Determine the pressure recovery for each meter. Determine the relationship between Reynolds number and the coefficient of discharge and the pressure recovery for each meter. INTRODUCTION The chemical, paper, and minerals processing industries and pollution control facilities all have various fluid streams entering and leaving different processes. In order to control these processes and to calculate mass balances for these processes it is important to be able to accurately measure the flow rate of these fluids as they move through pipes, conduits, or channels. There are many different types of instruments used to measure the flow rates, but the most common flow measurement instruments are the variable head meters and the variable area meters. Variable head meters work on the principle that a variation of the flow rate through a constriction with a constant cross-sectional area causes a pressure drop suffered by the fluid as it flows through the constriction. The pressure drop is related to the flow rate, and hence variations of the pressure drop can be used to measure variations in the flow rate. The most common examples of variable head meters used in industry are the venturi meter and the orifice meter. The venturi meter A sketch of a typical venturi meter is shown in Figure 1. It is made up of an inlet section A, consisting of a short truncated cone with a recommended cone angle around 21E, a throat section B one throat diameter in length, and an outlet section C consisting of a long truncated cone with a recommended cone angle between 5E and 15E. Pressure drop between the inlet and the throat sections can be measured either by piezometers or manometers. The behavior of the fluid as it passes through the venturi is understood by writing the Bernoulli equation using the conditions at the entrance and the throat, and at the throat and the 1

2 exit. As the fluid passes from the entrance to the throat, its velocity increases and its pressure decreases. Upon passing from the throat to the exit, the velocity of the fluid decreases and its pressure increases, largely recovering to its value at the entrance. Venturi meter. A, inlet section; B, throat section; C, outlet section; D, G, piezometer chambers; E, holes to piezometer chambers; F, upstream pressure tap; H, liner; I, downstream pressure tap. Figure 1. Venturi meter The venturi meter is designed to recover most of the pressure drop. The angle of the downstream cone is sufficiently small to prevent separation in the boundary layer and so friction is minimized. Friction can not be eliminated completely and so there is always a pressure drop across the venturi meter. However, in a well-designed meter, about 90% of the entrance pressure is recovered. In the use of a venturi as a flow meter, the average velocity of the fluid in the throat is obtained from the Bernoulli equation applied to the entrance and the throat. The volumetric flow rate is then calculated from the average velocity. However, it is generally found that the flow rates calculated in this way are slightly higher than the observed flow rates (Why?). The empirical parameter, the coefficient of discharge C v is introduced to make them equal; that is, the meter is calibrated. C v is typically about 0.98 for a well-designed venturi meter. The orifice meter A standard sharp-edged orifice meter is shown in Figure 2. It consists of an accurately machined and drilled plate mounted between two flanges with the hole concentric with the pipe in which it is mounted. Pressure taps, one before and one after the orifice plate, are connected to a manometer to measure the pressure drop. The position of the taps are arbitrary. The principle of operation of the orifice meter is identical with that of the venturi meter. As in the case of the venturi meter, the empirical coefficient, the coefficient of discharge is introduced. For accurate work, an orifice meter must be calibrated to get the coefficient of discharge, C o. The value of C o depends on the position of the pressure taps and is a function of the diameters of the orifice hole and the pipe. It is important that enough straight pipe be provided both before and after the orifice to ensure a flow that is undisturbed by fittings, valves or other equipment. C o is typically about 0.63 for an orifice meter. 2

3 Figure 2. Orificemeter The variable area meter The variable area meter works on the principle of varying area of flow at different flow rates so as to produce a constant pressure head differential. The most common example of a variable area meter is the rotameter. Figure 3 shows a sketch of a rotameter. Figure 3. Rotameter, A-tapered tube, B-float 3

4 A rotameter consists of a gradually tapered glass tube mounted vertically in a frame with the large end up. The fluid flows up through the tube and suspends freely a float. As the flow varies, the float rises or falls thus varying the area of the annular space between it and the tube, so that the head loss across this annulus is equal to the weight of the float. The tube is marked in divisions and the reading of the meter is taken from the scale reading and the reading edge of the float, which is taken at the largest cross section of the float. Rotameters must always be used with a calibration chart to convert observed scale readings to flow rate. Floats are constructed of metals of various densities, glass or plastic. They also may have various shapes and proportions for different applications. The aim of this experiment is to use a venturi meter, orifice meter, and rotameter in a flow circuit for various flow rates of water. A study of their characteristics will also be made. The apparatus consists of a hydraulic circuit consisting of a venturi meter, an orifice meter and a rotameter. Pressure drops are measured using water piezometers. A sketch of the hydraulic circuit is shown in Figure 4. A B C D E F G H I J - Bench valve - Flow Control valve - Centrifugal pump - Venturi meter - Rotameter - Orifice meter - 8 bank manometer - Sump tank - Air bleed screw - volumetric tank Figure 4. Flow diagram of Apparatus 4

5 REFERENCES de Nevers, N., "Fluid Mechanics for Chemical Engineers", McGraw-Hill, New York, 1991 McCabe, W.L., and Smith, J.C., "Unit Operations of Chemical Engineering", 4th Edition, McGraw-Hill, New York, N.Y., 1985, pp Perry, R.H., and Chilton, C.H., (Editors), "Chemical Engineers' Handbook", 5th Edition, McGraw-Hill, New York, N.Y., 1973, pp. 5-10, EQUIPMENT 1. Hydraulic circuit-flowmeter demonstration rig mounted on the hydraulics bench. 2. Stopwatch. 3. Digital thermometer liter graduated cylinder CHEMICALS/MATERIALS 1. Tap water EXPERIMENTAL PROCEDURE Close the drain valve on the sump tank. Close the stopper on the drain of the volumetric tank. Use a hose and fill the volumetric tank full until it begins to overflow into the sump tank. Open the stopper and allow the water to drain into the sump tank. The next step is to check the calibration of the volumetric tank. This can be done using the two liter graduated cylinder. The sight glass and the scale found on the front of the hydraulic bench indicates the volume of water in the volumetric tank. First check the zero point. If the zero mark on the left hand side scale (black lines) does not correspond to the water level when the volumetric tank is empty, check with the Lab Services Coordinator. If the zero mark is correct measure 2 L of water into the graduated cylinder and pour it into the volumetric tank. Compare the water level with the left hand scale (black lines), it should be 2 L. If it is not, record the actual difference. Continue to add water in 2 L increments and compare the scale reading with the actual amount added with the graduated cylinder. Record any differences. If there are differences, then a calibration graph of scale reading versus actual volume should be used to determine the volume in the tank. Use the hose to fill the remainder of the volumetric tank until it overflows into the sump tank. Drain the volumetric tank a second time. There will now be enough water in the sump tank to run the experiment. 5

7 From the manometer bank readings the following data can be obtained. 1. Venturi reading Manometer 1 - Manometer 2 2. Loss in Venturi Manometer 1 - Manometer 3 3. Loss in variable area meter Manometer 4 - Manometer 5 4. Orifice plate reading Manometer 6 - Manometer 7 5. Loss in orifice plate Manometer 6 - Manometer 8 SAFETY NOTES 1. Safety Glasses with side shields shall be worn during the running of this experiment. Tap water is used in this experiment. As stated in number 2 below, it is possible for hoses or tubing to pop off and spray water. 2. Be careful of the outlet hose position and the position of the bench and flow control valves when starting the pump. It is easy for the outlet hose to spray water. It is also possible to blow off the pressure tap hoses and spray water all over. WASTE DISPOSAL PROCEDURES There will not be any waste to dispose of in this experiment. 7

8 TECHNICAL DATA SHEET For the venturi meter For the orifice meter Upstream pipe diameter = mm hence A 1 = 7.92 x 10-4 m 2 Throat diameter = 15 mm hence A 2 = 1.77 x 10-4 m 2 Upstream taper = 21E inclusive Downstream taper = 14E inclusive Upstream pipe diameter = mm hence A 1 = 7.92 x 10-4 m 2 Orifice diameter = 20 mm hence A 2 = 3.14 x 10-4 m 2 07/2012 8

9 Department of Chemical Engineering Stockroom Checkout slip Measurements with Flow Meters ChE 3211 Name: (print name) Date: Lab No.: Lab 1 Tuesday 12:00-4:50 PM Lab 2: Thursday 12:00-4:50 PM Lab No.: Lab 3 Tuesday and Thursday morning (9:30-11:50 AM) (circle one) Equipment Out In Equipment Out In 2-liter grad cylinder Digital Thermometer Stopwatch Name: (Signature) 9

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