KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY FACULTY OF MECHANICAL AND AGRICULTURAL ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING MECHANICAL ENGINEERING LAB III (ME 395) CALIBRATION OF A VENTURI METER DATE: 14THTH SEPTEMBER, 2011 GROUP 13 NAME INDEX NO Fianya, Laud Kweku 3758509 Fosu, Mark 3758309 Yeboah, Benjamin 3758109 Puni, Richard 3756809 SUMMARY Even though this topic has not yet been treated in class, this experiment has enlightened our understanding on the relationship between the rate of flow and pressure with respect to a Venturi meter. It also helped us understand how the Bernoulli’s equation is applied practically. All group members were present and actively partook of the experiment which was conducted in the Fluid Mechanics lab on 7 thth September, 2011. Mark wrote the summary and introduction of the report. Kofi Yeboah worked on the theory aspect of the report. Richard described and drew the Experimental Setup. Laud compiled and analysed the data results and finished up with the conclusion. INTRODUCTION The Venturi tube is a device used for measuring the rate of flow along a pipe. A fluid moving through it accelerates in the direction of the tapering contraction with an increase in the velocity in the throat. This is accompanied by a fall in pressure, the magnitude of which depends on the rate of flow. The flow rate may therefore be inferred from the difference in pressure in as measured by piezometers placed upstream at the throat. The effect that the meter has on the pressure change is termed as the Venturi effect. A venturi can also be used to mix a liquid with a gas. If a pump forces the liquid through a tube connected to a system consisting of a venturi to increase the liquid speed (the diameter decreases), a short piece of tube with a small hole in it, and last a venturi that decreases speed (so the pipe gets wider again), the gas will be sucked in through the small hole because of changes in pressure. At the end of the system, a mixture of liquid and gas will appear. OBJECTIVE The aim of this experiment was to: 1.1. Obtain the calibration curve for the meter. 2.2. Investigate the variation in pressure at inlet and throat at various rates of flow. 3.3. Present the results in a non-dimensional form so that they could be used to estimate the flow through any similar meter. THEORY The Venturi effect is a jet effect; as with an (air) funnel, or a thumb on a garden hose, the velocity of the fluid increases as the cross sectional area decreases, with the static pressure correspondingly decreasing. According to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through a constriction to satisfy the principle of continuity, while its pressure must decrease to satisfy the principle of conservation of mechanical energy. Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is negated by a drop in pressure. An equation for the drop in pressure due to the Venturi effect may be derived from a combination of Bernoulli's principle and the continuity equation. The limiting case of the Venturi effect is when a fluid reaches the state of choked flow, where the fluid velocity approaches the local speed of sound. In choked flow the mass flow rate will not increase with a further decrease in the downstream pressure environment. However, mass flow rate for a compressible fluid can increase with increased upstream pressure, which will increase the density of the fluid through the constriction (though the velocity will remain constant). This is the principle of operation of a de Laval nozzle. Increasing source temperature will also increase the local sonic velocity, thus allowing for increased mass flow rate. Consider the flow of an incompressible and inviscid fluid through the convergent-divergent Venturi tube. Given that both the velocity and piezometer head are constant over each of the sections considered, we might assume that flow to be one-dimensional so that the velocity and the piezometric head vary only in the direction of the tube length. Treating the convergent- divergent pipe as a stream-tube and applying the Bernoulli’s theorem at sections 1,2,3,…………… and have ++ ℎℎ == ++ ℎℎ == ++ ℎℎ---------------------- 1 The Continuity equation is given by == == == -------------------------- 2 Substituting equation 1 for U11 in equation two gives ++ == ++ ------------------------------ 3 ℎℎ ℎℎ This implies (( )) == --------------------------- 4 (( )) The flow rate Q = A22 (ideal discharge rate) ------------------------- 5 The actual discharge is given by (where C = Discharge coefficient) (( )) Q = C. A22 -------------------------------------- 6 The velocity head /2g at the throat can be conveniently used to express a dimensionless way of expressing the distribution of piezometric head along the length of the Venturi meter. Accordingly, the Piezometer Head Coefficient == (n = 2,3,…) ----------------------------- 7 ℎℎ / / The ideal distribution Cpph along a Venturi meter (in terms of its geometry) is given. == ------------------------------- 8 ℎℎ −− == ------------------------------- 9 ℎℎ −− APPARATUS 1. Venturi meter 2. Two supply hoses 3. Measuring tank DESCRIPTION OF EXPERIMENTAL SETUP - A tube is connected to each to the inlet and outlet of a Venturi meter. - The tube connected to the outlet of the Venturi meter is connected to the measuring tank. - The adjustable screws are adjusted to level the Venturi meter. Fig. 1 - Venturi Meter www. tecquipment.com EXPERIMENTAL PROCEDURE - The apparatus was leveled by opening both the Bench Supply valve and the control valve downstream of the meter to allow water to flow and clear air pockets from the supply hose. This was achieved by connecting the apparatus to a power supply. - The control valve was then gradually closed causing water to rise up in the tubes of the manometer thereby compressing the air contained in the manifold. - When the water level had risen to a convenient height, the bench valve was also closed gradually so that as both valves are finally shut off, the meter was left containing static water at moderate pressure. - The adjustable screws were operated to give identical reading for all of the tubes across the whole width of the manometer board. To establish the meter coefficient measurements of a set of differential heads (h11-h-h22) and flow rate Q were made. - The first reading was taken with the maximum possible value when (h22 – h11) i.e. with h11 close to the top of the scale and h22 near to the bottom. This was obtained by gradually opening both the bench valve and the control valve in turn. - Successive opening of either valve increased both the flow and the difference between h11 and hh22. The rate of flow was found by timing the collection of a known amount of water in the weighing tank, in the mean time valves h11 and h22 was read from the manometer. Similarly, readings were then taken over a series of reducing values of h11 – h22 roughly equally spread over the available range from 250mm to zero. About ten readings sufficed. DATA/RESULTS Table 1 – Experimental Values obtained for h22 and h11 1/21/2 -4-4 hh22 (D)/mm h11 (A)/mm Discharge/litres Time/s h11 – h22/mm (h11 – h22)) /mm Q/(litre/s) C (x 1010 )) 230 250 5 49.75 20 4.472 0.101 5.377 210 252 5 31.81 42 6.481 0.157 5.768 190 254 5 25.12 64 8.000 0.199 5.922 170 256 5 19.19 86 9.274 0.261 6.700 150 258 5 17.06 108 10.392 0.293 6.712 130 262 5 15.97 132 11.489 0.313 6.486 110 264 5 14.56 154 12.410 0.343 6.580 90 268 5 13.72 178 13.342 0.364 6.495 70 270 5 13.00 200 14.142 0.385 6.481 50 274 5 12.04 224 14.967 0.415 6.601 Table 2 – Experimental values for Ideal Curve Discharge (5) A/mm B/mm C/mm D/mm E/mm F/mm G/mm H/mm J/mm K/mm L/mm 11stst 250 250 240 230 230 236 240 244 246 248 250 55thth 258 254 214 150 162 198 218 230 238 244 248 1100thth 274 266 182 50 84 150 190 214 232 244 25500 Area/mm22 530.9 422.7 265.9 261.1 221.4 267.9 319.2 374.6 434.8 499.2 530.9 ANALYSIS 1166 1144 1122 1100 m m // 22 // )) 11 88 11 h -- 22 h (( 66 44 22 00 00 00..0055 00..11 00..1155 00..22 00..2255 00..33 00..3355 00..44 00..4455 Q/ (litres/s) 11//22 Fig 2 – Graph of (h22-h-h11)) versus the flow rate Q 0.45 00..44 0.35 00..33 )) ss // 0.25 rr ee ii tt (( ll // 00..22 Q 0.15 00..11 0.05 00 0 550 11000 11550 22000 225500 hh11 – – hh22/mm Fig 3 – Graph of flow rate (Q) against differential head (h11 – h22)) 88 77 66 55 )) 44 -- 00 1144 (( xx CC 33 22 11 00 00 00..0055 00..11 00..1155 00..22 00..2255 00..33 00..3355 00..44 00..4455 Q/(litre/s) Fig 4 - Graph of Discharge coefficient (C) against flow rate (Q) DISCUSSION OF RESULTS 1/21/2 From the curve for fig. 2, it could be seen that (h11-h-h22)) rises steadily with respect to the flow rate Q. Despite this, there is a sudden decrease in rise rate at h 22=170. It can then be said that 1/21/2 (h(h11-h-h22)) is directly proportional to the flow rate of the liquid.