FLOW MEASUREMENT IN PIPES EXPERIMENT

Transcription

1 University of Leicester Engineering Department FLOW MEASUREMENT IN PIPES EXPERIMENT Page 1

2 FORMAL LABORATORY REPORT Name of the experiment: FLOW MEASUREMENT IN PIPES Author: Apollin nana chaazou Partner during the experiment: Hassan ali Date of the experiment: 19 th February 2010 Place of the experiment: Engineering department of the University of Leicester Page 2

3 TABLE OF CONTENTS 1. Summary.4 2. Introduction.4 3. Description of the apparatus Theory.5 5. Procedure Results Discussion Conclusions References Appendices Page 3

4 1. Summary This experiment was conducted to investigate flow measurement in pipes using a venturi meter and an orifice plate meter. It was carried out to find discharge coefficients for each of the two meters mentioned above. Results obtained for discharge coefficients were 0.71 and 0.92 for orifice plate meter and venturi meter respectively. These were then compared with published values obtained from British standard (1042 pt 1:1964) and found to be different. 2. Introduction Flow is the movement of something in one direction. In this experiment the flow that was being measured was that of fluid called water. By definition a fluid is a substance that deforms continuously to shearing force no matter how small that shearing force may be. Fluid flow can be laminar, that is when layers of water flow over one another at different speeds with virtually no mixing between layers; it can also be turbulent when characterised by irregular movement of the fluid. The orifice plate meter consists of a flat orifice plate with a circular hole drilled in it; there is a pressure tap upstream from the orifice plate and another just downstream. [1] In the venturi meter the fluid is accelerated through a converging cone and the pressure difference between the upstream side of the cone and the throat is measured and provide a signal for the rate of flow. [2] Piezometers are tubes that allow the change in static head between two points in the meters to be determined. [3] The discharge coefficient is the ratio of the actual flow rate to the theoretical discharge; it is dimensionless. 3. Description of the Apparatus The below picture shows the apparatus, which consists of a vertical Perspex tube containing a venturi meter underneath an orifice meter. A pump provides water to the lower end of the tube through a tap. A weight tank through which water returns to the reservoir is used to measure the flow rate. The orifice plate meter and the venturi meter are fitted with piezometers. Just next to the weight tank is a handle which is used to empty or fill the tank with water by pulling it downward or pushing it upward. The weight tank is also fitted with a handle on which there a little platform supporting a certain number of masses that will balance the mass of water in the tank and help to determine the mass flow rate. As can be seen on the picture below, the weight tank and the water reservoir are fitted underneath the experiment table and the orifice plate meter and the venturi meter are fitted on the table. Page 4

5 4. Theory The orifice plate meter and the venturi meter are calibrated on the same principle; the tap through which water enters the lower end of the tube is set such that the flow rate through each meter is constant. Because the meter uses a narrowing throat in the pipe which then expands back to the original pipe diameter, the velocity of the water increases; this is due to the theory of continuity, which states that the total flow must remain constant, provided the liquid is incompressible: Q = V1 A1 = V2 A2 (m³/s) (1) The cross sectional area of each meter is recorded to help compute the equation. As the velocity of the water increases the static head exerted by water on the tube wall also changes consequently, decreasing. Based on the principle of Bernoulli s equation: P1 + ρv1² +ρgz1 = P2 + ρv2² +ρgz2 (B) Since Q1 = Q2 = V1 A1 = V2 A2 it is shown from the Bernoulli's equation that: V2² - V1² = 2g h (m² s²) (2) Equations (1) and (2) combined give the below equation, which allows flow rate to be predicted from the difference between the piezometer readings. Page 5

6 Q = A1A2 (3) Given that the actual discharge is the one that occurs and which is affected by friction as the jet passes through the orifice, the ideal discharge would be the discharge achieved without friction. It follows from the equation (3) that the coefficient of discharge is directly related to the volumetric flow rate of the fluid flow and the cross sectional area of the meter. Furthermore it is also related to the gravitational constant and the head pressure. In order to develop equations (B), (1) and (2) to get the equation of flow, assumptions are made regarding the flow. And with regard to that, the flow must be inviscid, incompressible, laminar and steady. [4] 5. Procedure Before starting the experiment checks were made to ensure that there was no water leak from the pipes; the tap was then opened slowly at the base of the apparatus to allow the flow of water through the meters; as water in one of the piezometers was almost off scale, a control-valve was use to adjust and set height differences for the venturi meter and that of the orifice plate meter; as water returned and filled up the tank it was emptied and a certain mass put against it to measure the time it took to be Page 6

7 fill up with water and balance the mass at various heights. The time it took for the tank to be filled up without mass at various heights was also recorded. A total of three readings were made in each case at a certain height and the average reading used to determine the mass flow rate following a quantitative estimation of errors on each set of readings. Repeated readings were made for lower flow rates obtained with the reduction of the flow of water using the tap and checking carefully the apparatus. Following the readings, graphs of mass flow rate against height difference were plotted for each of the two meters. 6. Results Below is a table of results which discloses all the data obtained and recorded as the experiment proceeded. It emphasises the number of readings in each case as explained in the procedure above and provides detailed data for all the different variables. TABLE OF THE EXPERIMENT RESULTS OBTAINED AND RECORDED Readings Time taken to fill tank without mass (s) Time taken to fill Tank with mass (s) Height difference for the venturi meter (mm) Height difference for the orifice meter (mm) Experimental Mass flow rate (kg/s) Average Average Average Average Average Using the values for the cross sections of each meter we obtained theoretical values in m³/s and then converted to kg/s. Page 7

8 The below two tables of results show the theoretical values of flow rate obtained for each of both meters at various height difference. Table of results: Venturi meter VENTURI METER Q (m³/s) Height difference Δh (m) Q (kg/s) Orifice plate meter ORIFICE PLATE METER Q (m³/s) Height difference Δh (m) Q (kg/s) The graphs below show the plots of mass flow rate against height difference for both meters. Also there are plots of theoretical flow rates against experimental flow rates for each of the two meters. Theoretical flow rates were calculated using equation (3). The plots illustrate graphical presentations of results and calculations. Page 8

9 experimental flow rate (kg/s) heigth difference (mm) plot of mass flow rate against height difference venturi meter orifice plate mass flow rate (kg/s) plot of theoretical flow rate against experimental flow rate orifice plate meter venturi meter theoretical flow rate (kg/s) With the plot of theoretical flow rate against experimental flow rate showing two straight lines, the discharge coefficients for both meters were determined by computing the gradients of the lines. The values obtained were 0.92 and 0.71 for venturi meter and orifice plate meter respectively. Page 9

10 7. Discussion: Results obtained showed in light of the plot (mass flow rate against height difference) that the mass flow rate of water through each meter increases with the height difference. With regard to the values of theoretical and experimental flow rates obtained, it is observed clearly that although quite close, they are not the same; this is emphasised graphically by the above plot of the theoretical values against the experimental values showing two straight lines close to each other. More importantly discharge coefficients obtained for both meters compared with published British standard 1042 pt 1:1964 were different. As assumptions are made with regard to the principle of Bernoulli s equation which, were referred to as for the theory in this experiment that, the flow be steady, inviscid and incompressible; and in light of the experimental values of flow rates that were not correct as far as the theory is concerned, one reason for this can be the apparatus and its sensitiveness, but more likely the explanation for the inconsistency between theory prediction and experimental results in this case is that, water used could have been contaminated by particles from the pipes or from other sources which then made it becoming not ideal fluid due to viscosity and as a result turbulence is developed in the flow, hence not a laminar flow and not obeying the Bernoulli s equation. Because of the presence of turbulence in the flow there is energy produced in the form of heat; this makes it very difficult to account for that effect using the Bernoulli s equation, hence the coefficient is used to reduce the complexity and make the computation simple. 8. Conclusions: The results obtained in this experiment show that the volumetric flow rate of a fluid through a venturi meter and an orifice plate meter can be determined easily due to the law of continuity. Observations made during this experiment back up the fact that if the fluid is not ideal, then results obtained of the discharge coefficients and flow rate for the two meters would be different of the ones predicted by the theory. Hence the values contained in the published British standard 1042 pt 1:1964, to which experimental Page 10

11 data were compared has been obtained with the conditions and assumptions for the Bernoulli s equation to be valid. For low velocities flow the venturi meter and the orifice plate meter can be importantly calibrated for the purposes of flow measurement. In the light of the theory of flow through the two meters and their practical use in the flow rate measurement the choice of one or another would depend on several factors amongst which: The cost Adaptability Permeability The likeliness to create turbulence 9. References: [1] [2] [3] university of Leicester engineering department, handbook first year laboratory work page F1-1 [4] university of Leicester engineering department, handbook first year laboratory work page F1-3 [5] [6] Appendices: Q is the volumetric flow rate (m³/s) V1 is the upstream velocity (m/s) A1 is the upstream pipe cross sectional area (m²) V2 is the downstream velocity (m/s) A2 is the downstream pipe cross sectional area (m³) P is static pressure head (N/m²) which is the pressure when the liquid is at rest Page 11

12 (½)ρV² is the velocity head (N/m²) which is expressed in terms of static pressure needed to produce it. ρgz is the potential head (N/m²) linked to the elevation or height ρ is fluid density (kg/m³) V is fluid velocity (m/s) Z is height of fluid above a datum (m). g is the acceleration due to gravity (m/s²) h is the change in static head measured by the piezometers or height difference. (m) Laminar flow: flow in which the fluid flow in parallel layers without disruption between the layers. Steady flow: fluid flow in which at any one point conditions are constant with respect to time. Inviscid flow: flow in which there is no friction or viscosity. Gradient: slope of the graph. Bernoulli's principle is named after the Dutch-Swiss mathematician Daniel Bernoulli who published his principle in his book Hydrodynamica in [5] Volumetric flow rate: this is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m 3 s -1 ] in SI units, or cubic feet per second [cu ft/s]). It is usually represented by the symbol Q. [6] Mass flow rate: mass of fluid passing a point per unit time. Calculations: Theoretical flow rates using equation (3) Q = A1A2 1. For the venturi meter: Diameter = D1 =0.026m areas venturi A1=πD1²/4 =5.31 D2= 0.016m A2= πd2²/4= 2.01 Having values for A1 and A2 and knowing the various height differences ( h), values of Q for different h are computed and are presented in the first table of results on page 9 of this report. 2. For the orifice plate meter: Diameter D1= 0.051m D2= 0.024m A2=πD2²/4 =4.52 A1= πd1²/4 = 2.04 Using equation (3) for different ( h) give the results obtained and presented in the second tables of values on page 7 of this report. Gradient of the line in the graph on page 9 corresponding to the orifice plate meter were obtained by picking two points on the line and calculating the slope of the line as presented below: ( )/ ( ) = 0.71 = discharge coefficient Page 12

13 Similarly for the Venturi meter, ( )/ ( ) = 0.92 discharge coefficient. Comparing them with published values from British standard, We computed: for venturi: = =0.38 coefficient 1 For the orifice plate meter: = 0.22 coefficient Derivation of the flow equation from the information given on the experiment sheet: Q = V1 A1 = V2 A2 (1) V2 = Q/ A2 V1= Q/ A1 V2² - V1² = 2g h (2) Substituting V1 and V2 into (2) (Q/ A2)² - (Q/ A1)² = 2g h (Q² / A2²) (Q² / A1²) = 2g h [Q² A1² - Q²A1²]/ A2² A1² =2g h Q² (A1² - A2²) = A2² A1² (2g h) Q = A1A2 Thursday, 06 May 2010 Page 13