2. Fluids Basics and Concepts

2Fluids Basics and Concepts TO PI C PAGE 2.1 Introduction ................................................ 22 2.2 Force, Weight , and Mass ............................ 22 2.3 Density ........................................................ 23 2.4 Specific Gravity ............................................ 23 2.5 Pressure ....................................................... 23 2.6 Temperature ................................................ 25 2.7 Viscosity ...................................................... 26 2.8 Fluid Velocity ............................................... 27 2.9 Mass and Volumetric Flow .......................... 27 2.10 Isentropic Exponent .................................... 28 and is the amount of force needed to move a 1kg mass at an acceleration of 1m/s2.a . Newton’s second law becomes: (2. this factor is often left out of force calculations using the metric system.2.Newton’s Second Law states force is equal to mass times its acceleration. N. Fluids can be liquids. and covers the fundamentals required to understand the theory of measuring flow. Thus.1) Where: 22 . which is presented in Chapter 3. lbf. gc = 1kg-m/(N-s2).1) Units Mass m lbm . one foot at an acceleration of 32. the unit of force is the pound force. mass. (2. and weight. it is important to review the physics behind the concept of force. Acceleration. F m a 2. m A fluid is a substance that continues to deform when subjected to a shear stress. mass and acceleration as: (2. Figure 2.2 – Fluids Basics and Concepts 2. some of the fluid properties can be calculated by knowing other properties. and is the amount of force needed to move 1 pound mass.3) (2. Since the value of gc is 1. a review of basic concepts.2.174 ft/s2.1 INTRODUCTION Force This chapter presents an overview of the physical properties of fluids.2) In SI units. temperature. isentropic exponent and viscosity. lbm. For most fluids. vapors. N The SI unit of force is the Newton. The US Customary unit of mass is the lbm and the SI unit is the kilogram. These properties factor into DP Flow calculations. or gases. MASS AND WEIGHT Property Symbol = The force applied to or by an object = The mass of the object = The resulting acceleration of the object To account for the force of gravity. So: When working with fluids in motion. Thus: Newton’s Second Law of Motion describes the relationship between force. static pressure. a Mass. FORCE. a gravity conversion constant gc is needed. kg Force F lbf . Where: There are five key fluid properties that must be known to properly size and use a DP flowmeter: density or specific weight. The DP flowmeter uses the concept of energy conversion to determine the rate of flow in a pipe by measuring a physical difference in pressures. They are related by: In imperial US units. the volume occupied by that mass will vary with temperature and pressure (see 2. Fluctuations in density are typically small for liquids but is much greater for gases. it is considered a compressible fluid. See Chapter 4 for more information on density and compressibility considerations.9644).4) Where: W gl = The weight in force units = The local acceleration of gravity The value of earth’s gravity is slightly higher at the poles and slightly lower at the equator due to the earth’s rotation.e. pressure. Pa Pressure is the force acting on a surface in the normal direction (i.2 – Fluids Basics and Concepts 2. The reference substance for liquids is generally water at 68°F (20°C). or at 20°C.a). (2. substance. The US unit of pressure is related by: For industrial gas measurement applications it is common to use the Real Gas Law or the Ideal Gas Law.4 SPECIFIC GRAVITY Weight of an object can be defined as: Specific gravity (SG) is the ratio of density of one substance to the density of a second. perpendicularly) per unit area (figure 2. or reference. At 45° latitude. This concept is used to account for the weight of fluids in the energy equation (such as the elevation or “z” term in the Bernoulli flow equation). Specific gravity thus provides a simple number that indicates whether a liquid is lighter or heavier than water.2. gl = gc. degrees Baume (°B). and in fluid statics when converting gravitational head to pressure. The density of distilled water at 68°F is 62. and the force exerted by a Lbm is exactly a Lbf . or location. If the density changes significantly with varying pressures and temperatures. or degrees API (American Petroleum Institute). Fluids whose densities change slightly with moderate temperature and pressure fluctuations are considered incompressible. instruments whose scales read in specific gravities.9 Mass and Volumetric Flow).. When assumptions regarding the Ideal Gas Law do not apply the Real Gas Law is applicable.3 DENSITY Property Symbol Density ρ Units lbm /ft2. The SI unit of pressure is the Pascal and is equal to: Where: N 23 = Newton and is in units of kg-m/s2 . Specific gravity of liquids is generally obtained with hydrometers. The Ideal Gas Law is applicable for moderate temperatures and low pressures. It fails to account for the interaction between gas molecules.4.5 PRESSURE The density of a fluid is its mass per unit volume. as well as accounting for the non-linear behavior of gases. the ratio of molecular weight against that of a reference gas will remain the same regardless of temperature. Specific gravity of a gas is defined as the ratio of the molecular weight of the gas of interest to the molecular weight of air (defined as 28. This method avoids the difficulty of calculating the gas density based on temperature and pressure. Note that for the same quantity of mass. Property Symbol Units Pressure P psi. where the lb /in is force and not mass. The reference fluid for specific gravity of gases is air.316 lbm /ft3. as is done with the manometer. kg/m2 2. As long as the composition of a gas does not change. 2. 998 kg/m3. 325 kPa. thus it is important to know the reference temperature.5. inHg*. Standard orifice plate The value of pressure for a flowmeter application is used to provide information for two separate but important engineering tasks: P1 P2 • For the calculation of fluid parameters– especially gas or vapor density and gas expansion factor • To check the compatibility and safety margins for the mounting hardware Figure 2. 24 Rosemount Conditioning .2 Differential Pressure The Pascal is a very small unit of pressure and is generally expressed in kPa (kiloPascals) or MPa (megaPascals). P1 has higher pressure than P2.08% between the two reference temperatures. Actual atmospheric pressure at any given location depends on that location’s elevation above sea level and dayto-day weather conditions. The gage pressure is the pressure relative to atmospheric pressure. The conversion factors in psi for each of these is: Area Figure 2. it is called the differential pressure or DP (figure 2. As an example a DP of 25 inches H2O at 68°F means that this is the pressure at the bottom of a column of water that is 25 inches high when the temperature of the water is a uniform 68°F. Property Differential Pressure 2. The inches of water unit is a carryover from the past where manometers were used to measure flow rate and indicates the pressure at the bottom of a column of water of the specified height when the water is at a specific temperature.a .5. However local standard atmospheric pressure–adjusted for elevation –is used to determine the atmospheric pressure for purposes of measuring the flow rate. alcohol.Differential pressure. kPa.1 Absolute and Gage Pressure ΔP or DP Units inH20 @ 68°F. The absolute pressure is used to compute the density of gases.69595 psi or101.a). The gage pressure. is used to ensure that pressure retaining parts (ie the pipe or parts of flowmeters that retain the pressure when installed in the pipe) will remain within safe working limits. Thus: (2. as called for in DP Flow calculations. mbar *inches of mercury.a . Another common SI unit of pressure is the bar which is equal to 100 kPa.5.5) When the difference in two pressures is needed. since it is relative to atmospheric pressure.2. oil or other fluid The absolute pressure is the pressure relative to a perfect vacuum. There are two commonly used versions of this unit inches H2O at 68°F (used in the US process control industry) and inches H2O at 60°F (used in the US natural gas industry).2 – Fluids Basics and Concepts 2. or 14. Force Symbol The US unit for DP is psi or inches of water (inH2O) at a specified temperature.5. This is a difference of 0. can also be inches of water.1.2. The SI unit for DP is Pa or kPa. Typically. changes in the atmospheric pressure due to weather are not used when calculating absolute pressure. Standard atmospheric pressure is typically defined as 1atm.5.Pressure is force acting perpendicularly on an area. and the DP expressed as “Inches of Water Column. The differential pressure is then calculated using the relation: e. if water or other liquids are being measured.2.2 – Fluids Basics and Concepts Differential pressure can be calculated with a simple relation: Ambient Fluid (2.2. mercury (S.2.com/temperature.c .Example of how a manometer works.2.b .7) ΔP gl gc P0 Unknown Pressure P = Differential pressure. (2. Where: p m pf h h (Atmospheric pressure in most cases) Reference Fluid Density p (Liquid.5 to 3. or bromide-based fluids are used (S. with the height indicated in inches. a heavier manometer fluid is needed. water or mercury) Figure 2.” Of course.g. with a liquid filling the tubes part-way (figure 2. °K. = 13. but it must be “immiscible. The standard manometer fluid for gas flow DP measurement is water. Rosemount literature reference number 00805-0100-1036 or go to Rosemount. h.5.5.Modern differential pressure transmitter. When the two pressures are applied at the top of each tube. .5.G.5). Any fluid that is heavier than water could be used.6 TEMPERATURE Property Temperature 1 25 Symbol T Units °C. in appropriate units = The local acceleration of gravity = Units conversion constant from mass to force = The density of the manometer fluid = The density of the fluid conveying the pressure = Elevation difference or height of the fluid at the points of measure Figure 2. and can operate over a wide range of ambient temperatures without external correction.6) Fluid of Interest (Gas in most cases) The simplest of instruments used for the measurement of a small difference in pressures is the manometer A manometer uses a U-shaped tube or two vertical tubes connected at the bottom. Current best practices exploit electronic differential pressure and static pressure transmitters (figure 2.b).c).G. °R More in-depth information can be found in The Engineer’s Guide to Industrial Temperature Measurement.” or unable to mix with the fluid in contact with the manometer.5. and a scale fixed to the manometer is used to measure the height or elevation difference. the liquid in the two tubes change height. Note that manometers and mechanical pressure gages are old technology. 2. which provide extremely accurate readings over very large ranges of pressure or DP.0). Typically.. The electronic signal output is easily fed into microprocessors for calculating the flow rate or logging data. °F. = 2. such as RTDs (resistance temperature detectors).b shows the plot for different types of fluids based on the behavior of μ.τ (2. For this reason. It is a measure of the resistance of fluid molecules to velocity change due to shear stress. Stated differently.Viscosity defines the resistance to movement of a fluid. Bingham plastics do not flow until a critical stress yield is exceeded. which changes primarily with temperature. the viscosity increases with temperature.2 – Fluids Basics and Concepts Industrial methods of measuring temperature are based on substances that change electrical resistance with temperature. or those where the slope of the fluid stress/strain curve (μ) is constant. For a liquid. Absolute viscosity is defined as: (2. the viscosity decreases with temperature. lava. or thermocouples that generates a voltage at the junction of dis-similar metals that is based on temperature. or: Units (2.9) The absolute temperature is required in the calculation of the fluid properties (i. Absolute zero Rankine and absolute zero Kelvin are equivalent. Where: τ Outside of the engineering world. Property velocity. Shear-thinning fluid viscosities decrease with increasing shear stress..7 VISCOSITY Absolute Viscosity μ Dynamic Viscosity ν δυ δγ Figure 2. density. moving) fluid boundary plate (2D. flow engineering problems require a different temperature scale.8) 459. fluid viscosity is usually plotted against temperature.e.11) centipoise (μcp). viscosity tends to resist one particle from moving faster than an adjacent particle. stationary) Every real fluid has viscosity. The relationships between absolute temperature and the conventionally used units of °F and °C are: γ dimension boundary plate (2D. examples include ketchup. measurements are generally done on the relative Fahrenheit or Celsius scales. DP flowmeters are restricted to “Newtonian” type fluids. or the force required to move the fluid against a surface per unit area = The change in velocity or “strain” between the wall or surface and the free-stream velocity Kinematic viscosity is the absolute viscosity divided by the density of the fluid at the same temperature. Absolute temperature has units of Kelvin in SI units and Rankine in US customary units.a). for a gas. or polymer solutions and molten polymers. while the Kelvin scale increments by degrees Celsius. centistokes Absolute viscosity defines the resistance to movement of a fluid (figure 2. examples of this type of fluid include toothpaste. which were originally devised to measure the earth’s temperate range. kg/m-s Fluids are classified by the relationship between fluid stress (the force needed to overcome viscosity) and the strain (the fluid velocity). The calculation of thermal expansion effects involves temperature differences so it is common to use °F or °C. (2. 2. viscosity and insentropic exponent). Symbol gradient.7.67 = The shearing stress in the fluid.7. However. Figure 2. lbm/ft-s. ν shear stress.a . one that represents an absolute temperature. and equations are developed that allow the calculation of viscosity once the temperature is known.7. Shear thickening (with viscosity increasing as shear stress increases) include suspensions—corn starch in water for example. The Rankine scale increments by degrees Fahrenheit.10) 26 . the temperature is 68 °F.2 – Fluids Basics and Concepts 2. but in order for the pressure to be at 14. So if the flowing pressure is 146. the velocity of a flowing fluid in a pipe would be uniform across a pipe section. When a fluid flows around an object or through a pipe.Fluid classification based on the behavior of viscosity. Fluid flow in a pipe also defines a velocity field. m/s Velocity is not a fluid property. Mass flow is dependent on density and the volumetric flow rate. with a velocity of zero at the pipe wall and maximum at the pipe centerline for developed flow.b . kg/hr Shear thickening Volumetric flow is measured in terms of volume. when the mass flow rate (units of mass/unit time) is divided by the density at reference conditions. In general. the viscosity of the fluid creates a velocity profile. The flow of fluids through pipes has been studied extensively and velocity fields can be predicted when the rate of flow and fluid properties are known. the flow rate is equivalent to the volume the fluid would occupy if its pressure and temperature were adjusted from the flowing conditions to reference conditions.12) Figure 2. m3/hr Mass Flow Rate Qm lb/hr. As applied to fluid dynamics. shearing between adjacent fluid particles produces a non-uniform velocity profile in the pipe. The mass will remain the same. τ Bingham plastic Newtonian Property μ 1 Symbol Units Volumetric Flow Rate Qv 1/hr. m.7. as the name implies.13) Volumetric flow and mass flow can be related by the following: Units ft/s.696 psia it must occupy 10 times the volume as it did under flowing conditions. but can be used to predict the behavior of fluids in motion and will frame the application of DP flowmeters. however. velocity is the rate of change of an object’s position relative to a reference.9 MASS AND VOLUMETRIC FLOW Shear thinning Shearing stress. δυ δγ (2. With the slightest of viscosity. (2. 27 . velocity defines the speed of a particle of fluid with respect to a stationary reference such as a pipe.696 psia and 68°F when the mass flow rate is converted to standard volume flow rate (by dividing by the density of the fluid at reference conditions) the numerical value will increase by a factor of 10.14) In other words.8 FLUID VELOCITY Property Symbol Velocity v (2. as follows: Rate of shearing strain. as follows: 2. and the reference conditions are 14. yielding how much volume is passing through a given area.96 psia. If there were no viscosity. and is equivalent to the specification of speed and direction of an object. Mass does not change with fluctuations in pressure and temperature.a . Typical values of k can range from 1. turbine.0 to 1. or variable area meters. magmeter. It is common practice to determine k at a nominal temperature and use this value for all flow rates. The relevant fluid property is the isentropic exponent of the gas. while volumetric flow can be acceptable for stable liquids. mass does not change. Volumetric flowmeters include DP flowmeters.10 ISENTROPIC EXPONENT As gases flow through a restriction in a pipe the density changes due to pressure changes. 2. Flowmeters suitable for mass flow include multivariable DP flowmeters or Coriolis meters.4. The measurement of mass flow is preferred for most gases and liquids. The expansion of the gas is assumed to be an isentropic process and the effect of the density changes on the flow rate can be determined theoretically for some obstructions or empirically for others. but volume can. 40.2 – Fluids Basics and Concepts For a given quantity of liquid. This illustration depicts an example of how much volume can change with temperature. 28 .0 gal 60˚F 0.9 gal 2. but volume can with changes in pressure and temperature (figure 2. vortex.0% 342 lb Figure 2.7% 20˚F 342 lb 42. designated by k (sometimes designated by g) and primarily is a function of temperature.9.9.a). com\terms_of_sale. All other marks are the property of their respective owners. The Emerson logo is a trademark and service mark of Emerson Electric Co. © 2015 Rosemount Inc.com Literature reference number: 00805-0100-1041 Rev AA March 2015 .rosemount. All rights reserved. Rosemount and Rosemount logotype are registered trademarks of Rosemount Inc. www.Standard Terms and Conditions of Sale can be found at: www.rosemount.