Relationship between flow coefficient and discharge coefficient. Modeling choked flow through an orifice applied flow technology. Flow coefficient cv and kv pressure drop coefficient zeta. Nozzle discharge coefficientscompressible flow journal of. Fm 308 flow measurement by venturi and orifice meter objectives. Good communication between various groups involved with fluid piping systems is critical for the proper design, operation, and determination of cost for many systems in residential, commercial, and industrial applications. Pressure loss from location 1 to 3 in the pipe written in terms of discharge coefficient. Photograph of the discharge apparatus ilr shown in figures 1 and 2. For rough approximations, the flow coefficient may be assumed to be between 0.
The computed discharge coefficients for cylindrical, conical convergent nozzles and conical divergent orifices are plotted against the radius of curvatures r. The discharge coefficient does not correlate with the throat reynolds number for compressible flow through knifeedge orifices. On the flow of a compressible fluid through orifices by d. The discharge coefficient differs from unity due to the nonuniformity of flow parameters such as mach number at the nozzle exit and presence of boundary layer viscous effect. The method employed in the determinationof all coefficient onsisted in timing the ao\\ of a known volume of liquid and determining lhe eoefficients as the ratio of the adual t the theoretical rate of flow. Pdf this paper presents a study of the compressibleflow behavior of light. This approach made use of the authors omega method applicable for both flashing discharge and nonflashing discharge. A novel method to determine the discharge coefficient of. Combining the results of this paragraph and the preceding one, the discharge q va c v v i c c a o c d a o v i. Friction factor f 4c f discharge coefficient ideal actual d m m c nusselt number. Orifices and nozzles are typically used to deliberately reduce pressure, restrict flow or to measure flow rate. The assumption that a coefficient of discharge common to all orifices from % inch to 12 inches in diameter is reached at a head of 100 feet is erroneous.
Pdf discharge coefficients for compressible flow through small. A theory on the discharge coefficient for safety relief valve. On the compressible flow through an orifice journal. The orifice plate is a typical obstruction type of flow meter, widely used in industries for flow measurement. Discharge coefficients for compressible flow through smalldiameter. The discharge coefficient is a dimensionless number used to characterise the flow and pressure loss behaviour of nozzles and orifices in fluid systems. Discharge coefficients for compressible flow through small. Discharge coefficient c flow rate q flow velocity v head drop. A novel pulsating flow measurement apparatus that allowed.
Compressible flow or gas dynamics is the branch of fluid mechanics that deals with flows having significant changes in fluid density. This article gives typical values of the discharge coefficient for common orifice. Based on the experimental data, a generalized expression characterizing the discharge coefficient for nozzles of different diameters, lengths, and fluid conditions was developed. Steady flow of an incompressible fluid through an orifice based on a discharge coefficient. Chaplygin 19021 solved the subcritical compressible flowfleld of a 90 slot horn. Analysis of compressible effect in the flow metering by. This thesis is brought to you for free and open access by. Parker and kercher 1991 introduced an enhanced method to compute the compressible discharge coef. On the compressible flow through an orifice journal article. Pdf discharge coefficients for compressible flow through. The discharge coefficient could also be found by keeping the head constant and measuring the water discharged in a known time interval. An orifice only works well when supplied with a fully developed flow profile.
Discharge coefficient for nozzles and orifices neutrium. Compressibility becomes important for high speed flows where m 0. Lets go on to apply the knowledge of entropy to the flow of compressible fluids starting with isentropic flow. In fluid dynamics, the drag coefficient commonly denoted as.
Apr 05, 2010 this publication is an extract of the underlying widespread and more detailed asme paper huening, 2008, comparison of discharge coefficient measurements and correlations for several orifice designs with crossflow and rotation around several axes, asme paper no. A theory on the discharge coefficient for safety relief. The results suggest that many aspects of compressible pulsating flow through. Calculate the reynolds numbers for these flow rates by hand you know the area of pipe before orifice and flow rate, so you know the velocity. The flow does act as a compressible fluid of low speed of sound and exhibits shock structure. This text is based on practical applications, worked examples, and. C d, the coefficient of discharge, allows us to use the ideal velocity and the orifice area in calculating the discharge. The coefficient of velocity is usually quite high, between 0. Jan 30, 2019 flow is considered to be real and compressible. To find the coefficient of discharge for venturi meter.
In the present work, an attempt is made to study and develop a computational model of flow through an orifice plate which can be used as an. For a first approximation, a flow coefficient of 0. Jobson by making certain basic assumptions, the author has determined a theoretical expression for the contraction coefficient, c, appropriate to an orifice when transmitting a compressible fluid, either. Discharge coefficient iso, 1998 corner pressure taps. Iso51671 and bs1042 standards provide the value of discharge coefficient for both standard orifice plate and quarter circle orifice plate. In this case we will consider the flow to be adiabatic also, that is, with no heat transfer. U csqrt1b4 sqrt 2 papbrho u is velocity through orifice. Download limit exceeded you have exceeded your daily download allowance.
In a nozzle or other constriction, the discharge coefficient is the ratio of the actual discharge to the theoretical discharge, i. Relationship between flow coefficient and discharge. What is the relationship between the flow coefficient c v and the discharge coefficient c d by jeff sines, senior product engineer, engineered software, inc. Orifice plate calculator find size free online calculations. Fundamentals of compressible flow stanford university. Orifices at different heights could be made to flow simultaneously, demonstrating the increase in velocity with head. Pressure loss characteristics of primary devices 0 0. Theory for this calculator can be found on pages 42 thru 45 in the 2009 edition of tp410. Pdf discharge coefficients for flow through holes normal to. Handbook of hydraulics for the solution of hydraulic problems.
The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of liftinduced drag. The table given below gives the discharge of air through an orifice in cu. Discharge of air through an orifice equation engineers edge. Large diameter orifice flow meter calculation for gas flow. B is ratio of orifice diam to pipe diam rho is density of the fluid. Pdf discharge coefficients for flow through holes normal. A wide range of unsteady compressible flow phenonema exist and these are covered in the works of glass and sislian 1994 and kentfield. Other relation between pressure and specific volume are called polytrophic and interpretation for each individual case is almost impossible. While all flows are compressible, flows are usually treated as being incompressible when the mach number the ratio of the speed of the flow to the speed of sound is less than 0. Consider gas flowing in a duct which varies in size. The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag.
Therefore, information concerning the edges of both the inlet and outlet of all flow elements, discharge coefficient for incompressible flow repres in light of all the possible differences between the ents an important limiting case of compressible flow. The discharge coefficient of a squareedged orifice placed in the exhaust stream. The drag coefficient is always associated with a particular surface area. Daniel measurement and control white papersfundamentals of orifice meter measurement page 1 fluid meters are divided into two functional groups one measures quantity positive displacement. Discharge coefficients for compressible flow through smalldiameter orifices.
The data have been reduced for correlation purposes to a discharge coefficient defined as the fraction of the isentropic, adiabatic mass flow rate attained by real. Discharge coefficient news newspapers books scholar jstor december 2012 learn how and. Measurement and prediction of discharge coefficients in. On the flow of a compressible fluid through orifices. Discharge coefficient performance of venturi, standard. Metger lewis research center cleveland, ohio national aeronautics and space administration washington, d.
All fluid meters, however, consist of two distinct parts, each of which has different functions to perform. Appears in 5 books from 19081941 page 3 it is denned as the quantity of water which will flow through an orifice 1 inch square under a stated head which varies from 4 to 6j inches in. Liquid flow will become choked when the trims vena contracta is filled with vapor from severe cavitation or flashing. Nozzle geometry variations on the discharge coefficient. Equations for flow rate measurement top of page the flow rate measurement calculations on this page are for orifices carrying a gas as described in iso 1991 and 1998. Fm 308 flow measurement by venturi and orifice meter. Heat transfer in gas turbine engines htd188, 5363 asme 1991. Discharge coefficients for compressible flow 1699 vi fig. For such flows, a correction factor in the form of a discharge coefficient is. They should not be in the same vertical line, so that each.
Comparing the flow through an srv to that through an orifice, a simple theory is proposed to relate the discharge coefficient in twophase compressible flow to the value in liquid incompressible flow. The discharge coefficient of an orifice is a function of both geometric and flow effects, such as inlet corner radius, orifice length, inlet velocity orientation, and reynolds number. Brahma i 2019 measurement and prediction of discharge coefficients in highly compressible pulsating flows to improve egr flow estimation and modeling of engine flows. Venturi meter and orifice meter are the commonly used flow meters for measuring massvolumetric flow rate or velocity of the flowing fluid. Moreover, an analogous behavior of the discharge coefficient for larger. Vapor flow also will become choked when the flow velocity at the vena contracta reaches sonic. Comparison of discharge coefficient measurements and. Isothermal compressible flow is the flow at constant temperature.970 350 520 687 379 1402 419 1466 1449 1485 1426 330 864 464 960 1253 1059 117 1528 196 1385 161 211 168 174 1363 1132 134 462 566 655 287 1389 1062 987 1023 1420 1304 661 796 1239 466 683 1058