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TECQUIPMENT H10 FLOWMEASURING APPARATUS 1.0 INTRODUCTION The FlowMeasuring Apparatus is designed to accustom students to typical methods of measuring the discharge of an essentially incompressible fluid, whilst at the same time giving applications of the SteadyFlow Energy Equation (Bernoulli's Equation). The discharge is determined using a venturi meter, an orifice plate meter and a rotameter. Head losses associated with each meter are determined and compared as well as those arising in a rapid enlargement and a 90degree elbow. The unit is designed for use with the TecQuipment HI Hydraulic Bench, which provides the necessary liquid service and gravimetric evaluation of flow rate.
Figure 1. Flow measuring apparatus. The TecQuipment HI0 FlowMeasuring Apparatus is shown Figure 1. Water from the HI Hydraulic Bench enters the equipment through a Perspex venturi meter, which consists of a graduallyconverging section, followed by a throat, and a long graduallydiverging section. After a change in cross section through a rapidly diverging section, the flow continues along a settling length and through an orifice plate meter. This is manufactured in accordance with BSI042, from a plate with a hole of reduced diameter through which the fluid flows. Following a further settling length and a rightangled bend, the flow enters the rotameter. This consists of a transparent tube in which a float takes up an equilibrium position. The position of this float is a measure of the flow rate. After the rotameter the water returns via a control valve to the Hydraulic Bench and the weigh tank. The equipment has nine pressure tappings as detailed in Figure 2 each of which is connected to its own manometer for immediate read out. Figure2. Explanatory diagram of a flow measuring apparatus. 1.2 Installation and Preparation
1.3 Routine Care and Maintenance
2.0 THEORY Figure 3. The steadyflow energy equation For steady, adiabatic flow of an incompressible fluid along a stream tube, as shown in Figure 3, Bernoulli's equation can be written in the form; (1) Where is termed the hydrostatic head. is termed the kinetic head ( is the mean velocity i.e. the ratio of volumetric discharge to crosssectional area of tube). z is termed potential head represents the total head. The head loss may be assumed to arise as a consequence of vortices in the stream. Because the flow is viscous a wall shear stress then exists and a pressure force must be applied to overcome it. The consequent increase in flow work appears as increased internal energy. Also, because the flow is viscous the velocity profile at any section is nonuniform. The kinetic energy per unit mass at any section IS then greater than V^{2}/2g and Bernoulli's equation incorrectly assesses this term. The fluid mechanics entailed in all but the very simplest internal flow problems is too complex to permit the head loss to be obtained by other than experiential means. Since a contraction of stream boundaries can be shown (with incompressible fluids) to increase flow uniformity and a divergence correspondingly decreases it, is typically negligibly small between the ends of a contracting duct but is normally significant when the duct walls diverge. Figure 4. Construction of the orifice meter 3.0 EXPERWENT AL PROCEDURE With the equipment set as in Section 1.2, measurements can be taken in the following manner. Open the apparatus valve until the rotameter shows a reading of about 10mm. When a steady flow is maintained measure the flow with the TecQuipment HI Hydraulic Bench as outlined in its manual. During this period, record the readings of the manometers in a table of the form of Figure 5. Repeat this procedure for a number of equidistant values of rotameter readings up to a maximum of approximately 220mm.
Figure 5 form of result table. 4.0 RESULTS AND CALCULATIONS 4.1 Calculations of Discharge The venturi meter, the orifice plate meter and the rotameter are all dependent upon Bernoulli's equation for their principal of operation. The following have been prepared from a typical set of results to show the form of calculations. Venturi Meter Since ΔH_{12} is negligibly small between the ends of a contracting duct it, along with the Z terms, can be omitted from Equation (1) between stations (A) and (B). From continuity The discharge, Q = ABV_{B} (2) With the apparatus provided, the bores of the meter at (A) and (B) are 26mm and 16mm respectively. Thus: A_{B}/A_{A} = 0.38 and AB = 2.01 x 10^{4} m^{2}, since g = 9.81 m/s^{2} and p_{A}/ρg, p_{B}/pg are the respective heights of the manometric tubes A and B in meters, we have from Equation (2). Taking the density of water as 1000 kg/m^{3}, the mass flow will be e.g. if and (The corresponding weigh tank assessment was 0.47 kg/s) Orifice Meter Between tapping’s (E) and (F) ∆H_{12} in Equation (1) is by no means negligible. Rewriting the equation with the appropriate symbols, i.e. the effect of the head loss is to make the difference in manometric height (h_{E} h_{F}.) less than it would otherwise be. An alternative expression is where the coefficient of discharge K is given by previous experience in BS1042 (1943)* for the particular geometry of the orifice meter. For the apparatus provided K is given as 0.601. Reducing the expression in exactly the same way as for venturi meter, = Since with the apparatus provided, the bore at (E) is 51mm and at (F) is 20mm. Thus e.g. if and (The corresponding weigh tank assessment was o.47 kg/s) *NB It is found that the value of C given in the 1943 BS1042 publication gives better results over the velocity range of the apparatus then the figures given in later editions and has thus been retained for use in this manual. Rotameter Observation of the recordings for the pressure drop across the rotameter (H)(I) shows that this difference is large and virtually independent of discharge. Though there is a term which arises because of wall shear stresses and which is therefore velocity dependent, since the rotameter is of large bore this term is small. Most of the observed pressure difference is required to maintain the float in equilibrium and as the float is of constant weight, this pressure difference is independent of discharge. The cause of this pressure difference is the head loss associated with the high velocity of water around the float periphery. Since this head loss is constant then the peripheral velocity is constant. To maintain a constant velocity with varying discharge rate, the crosssectional area through which this high velocity occurs must vary. This variation of crosssectional area will arise as the float move up and down the tapered rotameter tube. Figure 6. Principle of the rotameter. From Figure 6, if the float radius is R_{f}, and the local bore of the rotameter tube is 2R_{t} then, = Cross sectional area = Discharge/Constant peripheral velocity Now δ = lθ, where 1 is the distance from datum to the crosssection at which the local bore is R, and 8 is the semiangle of tube taper. Hence 1 is proportional to discharge. An approximately linear calibration characteristic would be anticipated for the rotameter. Figure7. Typical rotameter calibration curve 