venturimeter equation – What Is Piping

Venturimeter is a type of flowmeter that works on the principle of Bernoulli’s Equation. This device is widely used in the water, chemical, pharmaceutical, and oil & gas industries to measure the flow rates of fluids inside a pipe. The pipe cross-sectional area is reduced to create a pressure difference which is measured with a manometer to determine the rate of fluid flow. So, the venturi meter is a differential head type flowmeter. The principle of the Venturimeter was demonstrated by Giovanni Batista Venturi (Hence the name Venturimeter), But it was first used in practical metering applications by Clemens Herschel. In this article, we will explore the parts, working principles, equations, and applications of Venturimeter. Venturimeter Diagram and Parts A venturimeter consists of four parts: Cylindrical Inlet SectionConical convergent SectionCylindrical throat andConical divergent outlet Fig. 1 below shows a typical venturimeter diagram with its parts. Fig. 1: Typical Venturimeter Diagram with Parts There are two tappings on the venturi meter for pressure measurement; the upstream pressure tapping is located at a distance of one half of pipe diameter (D/2) upstream of the convergent entry, while the downstream pressure tapping is located in the throat (d/2) as shown in Fig. 1. Cylindrical Entrance Section: Venturimeter entrance is a straight cylindrical section with a length equal to 5 to 8 times the pipe diameter.Convergence Conical Section: In this section, the venturi meter tube diameter gradually decreases. The conical angle is normally 210 ± 20. While the liquid flows inside the venturimeter, the velocity of fluid increases at the expense of a decrease in pressure.Cylindrical Throat: Throat consists of the minimum venturemeter diameter. In the throat section, the velocity is maximum and pressure is minimum. Normally, throat diameter = 1/3 to 1/4th of inlet pipe diameter.Diverging Conical section: At this section of venturimeter, the tube diameter gradually increases. So, the pressure is build up again to the original inlet pressure. The cone angle is 5-70. British Standard BS-1042 specifies two conical angles, 5–70 and 14–150 for the outlet cone. Materials for Venturimeter Small-size venturimeter are made of brass, glass, or bronze and large venturimeters are made of cast iron, steel, or stainless steel. Working principle of Venturimeter When a fluid flows through a venturimeter, it accelerates in the convergent section and then decelerates in the divergent section. The pressure difference between an upstream section and throat is measured by a manometer. Using that differential pressure, applying Bernoulli’s Equation and Contininuity Equitation the volumetric flow rate can be estimated. In the next section, the equations of venturimeter to find the discharge value is discussed. Venturimeter Equations Bernoulli’s principle states the relation between pressure (P), kinetic energy, and gravitational potential energy of a fluid inside a pipe. The mathematical form of Bernoulli's equation is given as: Where, p= pressure inside the pipeρ =density of the fluidg =gravitational constantv = velocityz=elevation or heada = cross-sectional area of the piped= diameter of the pipe Suffix 1 and 2 are used to denote two different areas; 1 denotes cylindrical inlet section and 2 denotes throat section. Now as the pipe is horizontal; there is no difference in elevation of pipe centerline; So, z1=z2. Re-arranging the above equation we get the following: (p1-p2)/ρg = (v22-v12)/2g (p1 – p2)/ ρg is the difference of pressure heads in sections 1 and 2 which is equal to h that can be measured in the differential manometer. So the above equation becomes h=(v22-v12)/2g..........eqn. 1 Now applying continuity equations between the same sections 1 and 2, we get a1v1=a2v2 or v1=(a2v2)/a1 Putting this value of v1 in eqn. 1 and solving we get, So, the rate of flow through the throat (Q) can be calculated as Q=a2v2; Substituting the above value of v2 we get, This Q represents the theoretical discharge of Venturi Meter in ideal condition. But in actual practice, there will be always be some frictional loss. Hence, the actual discharge will always be less than the theoretical discharge. So, to calculate the actual discharge, the above Q value is multiplied by Cd, called the Coefficient of discharge of venturimeter. So the actual flow rate through the throat of the venturimeter will be given by the following equation. Coefficient of Discharge of Venturimeter (Cd) The coefficient of discharge for Venturimeter, Cd is defined as the ratio of the actual flow rate through the venturi meter tube to the theoretical flow rate. So the venturi meter discharge coefficient is given by: Cd=Qact/Q As Qactual will always be less than Qtheoretical due to frictional losses, the value of Cd is always less than 1.0. The typical range of the discharge coefficient of a Venturi meter is 0.95-0.99 but this can be increased by proper machining of the convergent section. The value of venturimeter discharge coefficient differs from one flowmeter to the other depending on the venturimeter geometry and the Reynolds number. ISO-5167 code provides the values of venturimeter discharge coefficients. For accurate flow measurement, normally straight length requirement upstream and downstream of venturimeter is specified. Types of Venturimeters Normally three types of venturimeters are available: Horizontal Venturimeter: This type of venturimeter has the highest kinetic energy and the lowest potential energy.Vertical Venturimeter: This type has the maximum potential energy and the minimum kinetic energy.Inclined Venturimeter: Both potential and kinetic energy are in between the above two types mentioned. Applications of Venturimeter Venturimeters find wide application in fluid industries. The major application of venturimeters include Used in Engine Carburetors (Automobile Sector) to measure airflowUsed in process industries (Process and Power Piping Industries) to measure and control process flow.In the medical industry, blood flow in the arteries is measured by venturimeters.Measures the fluid flow inside pipelines (Oil & Gas Industries) Advantages and Disadvantages of venturimeter Advantages of venturimeter: They provide accurate results.The accuracy of venturimeter is not dependent on temperature and pressure inside the pipe.No moving part.Very low energy loss.Wide applicability for Water, suspended solids, gases, slurries, chemicals, dirty liquids, etc.High discharge coefficient and very low-pressure drop.Venturimeters can be installed in a horizontal, inclined, or vertical direction.Very less chance of being clogged.The pressure recovery of venturimeter is very high. The discharge pressure is almost near to inlet pressure. Disadvantages of venturimeter: Venturi meters are large in size; so difficult to install where there is space constraint.Expensive as compared to other types of flowmetersLimited range of flow measurementNot suitable for very small diameter pipes. Codes and Standards of Venturi meter The codes and standards that provide guidelines related to venturi meters are ISO 5167ISO 9300AWWA M33ISO TR 15377BS 1042ASME MFC-8MASTM D2458AGA 9 Installation of a venturi meter Proper installation of venturi meter is the key for ideal operation. So, the installation of venturi meters must be performed following manufacturer guidelines. Normally, the following guidelines to be followed while installing a venturi meter in a piping or pipeline system: The flow direction arrow in the venturi meter should be checked and installed to agree with the direction of the flow.Flanges at the venturi meter ends should be properly aligned with the piping flanges.Pipe Support should not be placed on venturi meters.Bolts should not be over-torqued.Installation tolerances should be within industry standards.Pressure taps should be oriented horizontally for liquid service applications. Fig. 2: Venturi meter Pressure Connections Venturi meter Upstream and Downstream Pipe Straight Leg Requirement For proper functioning and accurate results, the flow through the venturi meters should stabilize. This calls for minimum straight pipe length requirements upstream and downstream of the venturi meter. Depending on the type of fitting, type of venturi meter, and beta ratio (the throat diameter divided by the inlet diameter) the straight leg requirement varies. The following image (Fig. 2) provides a sample table that provides typical strength leg requirements while installing a venturi meter in a piping system. Fig. 3: Venturi meter Piping Requirements Difference between Venturi meter and Orifice meter The major differences between a venturimeter and an orifice meter are tabulated below: Venturi MeterOrifice MeterComplex DesignEasy to fabricateLarge Space requirementRelatively lower space requirementLow Energy LossComparatively more energy lossExpensiveCheaperHigh discharge coefficientLow coefficient of dischargeHigh Pressure RecoveryPressure Recovery relatively lessVenturimeter vs Orificemeter