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: 14TH 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 7th 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. Obtain the calibration curve for the meter. 2. Investigate the variation in pressure at inlet and throat at various rates of flow. 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 convergentdivergent pipe as a stream-tube and applying the Bernoulli’s theorem at sections 1,2,3,…………… and have +ℎ =
+ℎ =
+ ℎ ---------------------- 1
The Continuity equation is given by =
=
= -------------------------- 2
Substituting equation 1 for U1 in equation two gives +ℎ =
+ ℎ ------------------------------ 3
This implies (
=
)
--------------------------- 4
The flow rate Q = A2
(
)
(ideal discharge rate) ------------------------- 5
The actual discharge is given by (where C = Discharge coefficient) Q = C. A2
(
)
-------------------------------------- 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
ℎ =
/
(n = 2,3,…) ----------------------------- 7
The ideal distribution Cph along a Venturi meter (in terms of its geometry) is given. ℎ =
−
------------------------------- 8
ℎ =
−
------------------------------- 9
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 (h1-h2) and flow rate Q were made. - The first reading was taken with the maximum possible value when (h2 – h1) i.e. with h1 close to the top of the scale and h2 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 h1 and h2. 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 h1 and h2 was read from the manometer. Similarly, readings were then taken over a series of reducing values of h1 – h2 roughly equally spread over the available range from 250mm to zero. About ten readings sufficed.
DATA/RESULTS Table 1 – Experimental Values obtained for h2 and h1 h2 (D)/mm 230 210 190 170 150 130 110 90 70 50
h1 (A)/mm 250 252 254 256 258 262 264 268 270 274
Discharge/litres 5 5 5 5 5 5 5 5 5 5
Time/s 49.75 31.81 25.12 19.19 17.06 15.97 14.56 13.72 13.00 12.04
h1 – h2/mm 20 42 64 86 108 132 154 178 200 224
(h1 – h2)1/2/mm 4.472 6.481 8.000 9.274 10.392 11.489 12.410 13.342 14.142 14.967
Q/(litre/s) 0.101 0.157 0.199 0.261 0.293 0.313 0.343 0.364 0.385 0.415
C (x 10-4) 5.377 5.768 5.922 6.700 6.712 6.486 6.580 6.495 6.481 6.601
Table 2 – Experimental values for Ideal Curve Discharge (5) A/mm B/mm C/mm D/mm E/mm 1st 250 250 240 230 230 th 5 258 254 214 150 162 th 10 274 266 182 50 84 Area/mm2 530.9 422.7 265.9 261.1 221.4
F/mm G/mm H/mm 236 240 244 198 218 230 150 190 214 267.9 319.2 374.6
J/mm 246 238 232 434.8
K/mm 248 244 244 499.2
ANALYSIS 16
14
12
(h2 - h1)1/2/mm
10
8
6
4
2
0 0
0.05
0.1
0.15
0.2
0.25
0.3
Q/ (litres/s)
Fig 2 – Graph of (h2-h1)1/2 versus the flow rate Q
0.35
0.4
0.45
L/mm 250 248 250 530.9
0.45 0.4 0.35
Q/(litre/s)
0.3 0.25 0.2 0.15 0.1 0.05 0 0
50
100
150
200
250
h1 – h2/mm
Fig 3 – Graph of flow rate (Q) against differential head (h1 – h2)
8 7 6
C (x 10-4)
5 4 3 2 1 0 0
0.05
0.1
0.15
0.2 0.25 Q/(litre/s)
0.3
0.35
0.4
Fig 4 - Graph of Discharge coefficient (C) against flow rate (Q)
0.45
DISCUSSION OF RESULTS From the curve for fig. 2, it could be seen that (h1-h2)1/2 rises steadily with respect to the flow rate Q. Despite this, there is a sudden decrease in rise rate at h2=170. It can then be said that (h1-h2)1/2 is directly proportional to the flow rate of the liquid. From the curve for fig. 3, it could be noticed that the flow rate Q rises steadily with respect to the differential head. But at h2=170, there is a sharp rise in flow rate before the liquid assumes it steady flow rate. It can also be said here that Q is directly proportional to the differential head (h1 – h2). From the curve for fig, 4, a similar effect is noticed as in fig 2 and 3 that the discharge coefficient rises steadily with respect to the flow rate and increases sharply at h2=170. Aside that the discharge coefficient is directly proportional to the flow rate Q.
CONCLUSION It can therefore be concluded that the experiment was successful. This is because from the results, it can be seen clearly that a rise in differential head of two tubes causes the flow rate of the liquid in the tubes to increase and this proves the Venturi effect. However, there is a significant change in the rise in flow rate when h2 is equal to 170mm and the reason for this change could not be accounted for.
RECOMMENDATION The operation of the Venturi meter can be applied in the following mechanisms: 1. Pressure transducers 2. Robotic Fueling System
REFERENCES 1. http://en.wikipedia.org/wiki /Venturi_effect 2. www.tecquipment.com 3. Instruction manual from Fluid Mechanics Laboratory.
