1. Pressure gauges using liquids Third measurement MEASUREMENT OF PRESSURE U tube manometers are the simplest instruments to measure pressure with. In Fig.22 there can be seen three kinds of U tube manometers connected with different points of a pipe-line delivering water. The indicating liquid is mercury or other liquid which in both legs of the U tubes reach the same height according to the law of communicating vessels. The availability of the U tube manometers is limited partly by the length increasing proportionally with the measured pressure-differences partly again because of the bearing capacity of the common glass (about 250 kpa). For reading the level difference a wooden, metal or glass scale of mm division is used. The reading is taken in the height of the level in the horizontal tangent-plane of meniscus (the curved liquid surface) (Fig.21). Precise reading in horizontal plane can be helped by a mirror put behind the glass-tube. Fig. 21. When using liquid manometers we have to make sure that the connecting-pipes are filled with fluid communicating pressure. In most cases this is the same fluid whose pressure is required. In order to remove the air from the connecting pipes and the air bubbles trapped in the liquid communicating pressure an air cock must be put at the uppermost point of the connecting pipe. (The bubbles of air move up the tube) (Fig.22). When using U tube manometer two readings must be made in measuring the difference of levels. In the simple manometer (shown in Fig.23) there is a wide, shallow container whose cross section is essentially larger than that of the glass tube. If we connect the point 1 to a place of higher pressure than 2, the mercury level elevates in the glass-tube while the level in the container remains practically at the 0 level of the scale. So works also the simple barometer with which the atmospheric pressure can be measured. 2. Metal manometers During the operation of machines generally there are used direct reading instruments having dial plates. The Bourdon pressure gauge is shown in Fig.24. The tube is of bronze or steal, depending upon pressure, usually of elliptical cross section and it is curved into a circular arc. When pressure is applied the tube tends to straighten out and rotates the pointer. This gauge can be
used both for overpressure and vacuum. In the former case the dial plate is calibrated for bar-s in the latter one for percentage proportional to the negative gauge-pressure. The metal manometers have to be calibrated before being used. Fig. 22. Fig. 23. For calibration the instrument of Fig. 25 can be used. A plunger protruding into an oil-filled cylinder is loaded by forces. So known pressures are generated in a confined liquid. When loaded with known pressure the instrument is synchronously read. The result of the calibration can be seen in Fig. 28. This is the so-called calibration-diagram. In an ideal case - with equal scales in both coordinates - it is a straight line at an angle of 45 degrees. The principle of operation of a diaphragm gauge is that there is a relationship between the deformation of the diaphragm and its cause i.e. the pressure p. Fig. 26 shows a plane-
diaphragm while in Fig. 27 the sketch of an aneroid (meaning "without liquid") barometer is presented. It consists of an evacuated metal box which-has corrugated sides-to increase its strength. In up-to-date pressure gauges the deformation of the membrane is transformed into electric signal. Fig. 24. Fig. 25. Fig. 26. Fig. 27. Fig. 28.
3. Measurement of flow-rate On the rig presented in Fig. 22 there are two possibilities to measure the flow-rate (i.e. the quantity of liquid delivered per unit time) in the pipe drawn with heavy line. In the horizontal pipe-section an orifice (OR) is built in while at the end the liquid flows into a volume meter tank VMT. Fig. 29. The orifice is a contraction as seen in Fig. 29. In the contraction the fluid flows with greater velocity so the pressure decreases. The difference between the pressures in the tappings before and after the orifice can be well measured. The flow-rate is proportional to the square root of the pressure drop. In Fig. 30 there is shown the diagram of the orifice (OR of Fig. 22). On the abscissa we have not drawn the pressure-drop but the square root of the level-difference read on the U-tube manometer and so the flow-rate is given directly after the reading of the manometer. Fig. 30. The structure of a measuring turbine can be seen in Fig. 31. In the field of the permanent magnet (7) a rotor (4) rotates with a revolution number proportional to the flow-rate. The blades of the rotor rhythmically brake off the magnetic field. By this a series of signs are generated in the signalling coil (5). The frequency of the series of signs is shown by the instrument the flow-rate can be read on the scale plate. Volume meter tank can be used only in a system which is open, or can be opened. In a tankof known cross-section (VMT) the rising of the level can be followed in a glass tube
connected to the tank on the principle of the law of communicating vessels. Time is measured by stop watch. So the quantity of liquid where α [dm 3 /mm] m [mm] t [s] 4. Measuring exercise m dm Q = α t s 3 is the constant of the tank being the volume of a 1 mm high quantity of liquid in the tank, is the rising of the level is the time taken for rising. The first task is to determine p and p s pressures in the indicated spots on the instrument shown in Fig. 22 in the case of flow-rate Q w. The pg overpressure is shown on a Bourdon pressure gauge, too. Q w must also be determined both with volume meter tank and with the aid of the orifice built in the system. The pressure difference measured on the orifice must also be calculated although - as we have seen - flow-rate can be got from the difference on the manometer. For regulating Q w serves the valve V1. Pressure p is higher than the atmospheric one because of resistance of the pipe section reaching till the outlet end of the pipe. So here a positive over-pressure is measured. Pressure p s is less than the atmospheric pressure because here a nozzle is built in from which the liquid departs with greater velocity and this causes a local pressure drop. So there can be measured a negative over-pressure (suction). The role of the OR orifice and the volume meter tank VMT was explained previously. With cautious closing the valve V2 pressure p s can be made greater than the atmospheric one. So this valve ensures the possibility of expulsion the air from all of the four connecting pipes. During the measurement it must be kept open. When evaluating we need the value of the atmospheric pressure. Its value will be read on the mercury barometer. The atmospheric pressure p 0 (calculated into Pa) and all the lengths a, a s, e, e s should be measured at the beginning of the measurement. The density of mercury (m) and that of water (w), also can be regarded as known with the data: ρ m = 13600 kg/m3 and ρ w = 1000 kg/m 3. So we can write the balance equations of the manometers from which p and p s pressures can be calculated. The balance equation for p: p0 + ( h1 h2 ) ρmg = p + ( a ( e + h2 )) ρwg The balance equation for p s : p0 = ps ( es + hs 1 as ) ρwg + ( hs 1 hs 2 ) ρmg The suffix 1 denotes the higher while suffix 2 the lower levels. We read round mm values on the manometers (Fig. 21) but the numerical solutions of the equations have to be calculated with m units. The starting data and the results should be given also in tables (Fig. 32)! p g is the gauge pressure read directly on the Bourdon gauge. Let us measure the flow-rate with the orifice that is with the aid of a manometer and the diagram of Fig. 30. This flow-rate is measured also with volume meter tank (Fig. 22). While doing this we have to watch synchronously the rising of the level and the stop watch. Therefore it is advisable to watch only the former one and to start and stop the watch at round level values. To decrease the random failures the measurement should last at least 30 seconds. (Here we measure the time of a rising of m = 100 mm!) The constant of the volume meter tank α = 0,1086 dm 3 /mm.
The second task is the calibration of a Bourdon pressure gauge with the aid of an instrument shown in Fig. 25. Pressure transmitted through the fluid: ( m + m0 ) g p = [ Pa] a In our case the mass of the plunger with the plate m 0 = 1 kg, the cross section of the plunger a = 2*10-4 m 2. To change the pressure there are used steal disks of 1 and 2 kg masses. It is recommendable to increase the loading evenly and having reached the maximum to decrease it evenly again. It is advisable to measure 8 points. When reading the gauge-data the plate should be turned in order to avoid the disturbing affect of the vertical plunger friction During the measurement the table of Fig. 33 should be filled in. Finally we draw the calibration diagram according to the Fig. 28. Our report will consist of 3 papers of A4 form and one A4 form mm-paper. On the first A4 blank paper the whole instrument shown in Fig. 22 must be drawn. On the upper part of the second blank paper the tables of Fig. 32 should be drawn. Beneath these the balance equations of the manometers must be written. The upper part of the third blank paper is kept blank for the calculations of the flow-rate. On the lower part the sketch of the instrument shown in Fig. 25 and the table shown in Fig. 33 must be put at home! You will have to draw the calibration diagram on the A4 form mm-paper!
Fig. 33.
Determination of pressure p Data a= e= b= ρ w = ρ m = p 0 = h 1 h 2 h 1 - h 2 p g p absolute pressure p relative pressure [mm] [mm] [m] [bar] [Pa] [bar] [Pa] [bar] Determination of pressure p s Data a s = e s = b= ρ w = ρ m = p 0 = h s1 h s2 h s1 - h s2 p s absolute pressure p s relative pressure [mm] [mm] [m] [Pa] [bar] [Pa] [bar] Fig. 32.