Physical properties commonly used in flow measurement

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In flow measurement and calculation, certain physical properties of fluids are required; these properties have a significant impact on the accuracy of flow measurement as well as on the choice of flow meters. Due to space constraints in this book, we only provide an introduction to the basic concepts and some simple calculation formulas for these physical properties; detailed data can be found in relevant manuals. 1. Density of the fluid The density of a fluid is defined by the following formula: http://www.chinaflow.com.cn/basic/IMAGES/jilian1.jpg Where: ρ – density of the fluid, in kg/m3 ； m — mass of the fluid, kg ； V — volume of the fluid, m3. (1) Density of liquids: At constant pressure, the formula for the density of a liquid is: ρ = ρ20 [μ (t–20)] (4.10-6) Where: ρ – the density of the liquid at temperature t, in kg/m3 ； ρ20 —— density of the liquid at 20°C, kg/m3 ； μ —— the coefficient of volume expansion of the liquid, 1/℃ ； t — the temperature of the liquid, °C. When the temperature remains constant, the formula for calculating the liquid density is: ρ1 = ρ0β(ρ0 – ρ1) (4.10-7). Here, ρ1 represents the density of the liquid at pressure p1, in kg/m3 ； ρ0 —— the density of the liquid at pressure p0, ； kg/m3 ； β —— volume compressibility coefficient of the liquid, in 1/Mpa ； p0, p1 —— pressure of the liquid, in Mpa. Generally, changes in pressure have little effect on the density of liquids, and this effect can be ignored at pressures below 5 Mpa; however, for hydrocarbons, pressure corrections should be applied even at lower pressures. (2) Density of gas: The formula for calculating the density of dry gas under operating conditions is: http://www.chinaflow.com.cn/basic/IMAGES/jilian2.jpg Where: ρ – density of dry gas under operating conditions, in kg/m3 ； ρn —— density of dry gas under standard conditions (293.15 K, 101.325 kPa), kg/m3 ； p — absolute pressure of the gas under operating conditions, kPa ； pn——absolute pressure under standard conditions, kPa ； T — absolute temperature of the gas under operating conditions, K ； Tn——absolute temperature under standard conditions, 293.15K ； Zn——Compression coefficient of the gas at standard conditions ； Z — Compressibility coefficient of the gas under operating conditions. 2. Viscosity of fluids: The property of a fluid that resists the relative sliding of its particles is known as the viscosity of the fluid. The degree of fluid viscosity is measured by viscosity. The viscosity of the same fluid changes with its temperature and pressure. Generally, as temperature rises, the viscosity of liquids decreases, while the viscosity of gases increases. The viscosity of liquids only requires pressure correction at very high pressures, whereas the viscosity of gases is closely related to pressure and temperature. The following two methods are commonly used to characterize fluid viscosity: (1) Dynamic viscosity http://www.chinaflow.com.cn/basic/IMAGES/jilian3.jpg Where: η – dynamic viscosity of the fluid, Pa·s ； τ — internal friction force per unit area, Pa ； http://www.chinaflow.com.cn/basic/IMAGES/jilian4.gif —— Velocity gradient, 1/s ； u —— fluid flow velocity, m/s ； h —— distance between the two fluid layers, in m. (3) Kinematic viscosity: The ratio of a fluid’s dynamic viscosity to its density is called kinematic viscosity. http://www.chinaflow.com.cn/basic/IMAGES/jilian5.jpg Where: v —— dynamic viscosity. 3. Coefficient of thermal expansion The coefficient of thermal expansion refers to the relative rate of change in volume of a fluid when its temperature changes by 1°C; that is: http://www.chinaflow.com.cn/basic/IMAGES/jilian6.jpg Where: β —— the coefficient of thermal expansion of the fluid, 1/℃ ； V —— original volume of the fluid, m3 ； ?V——Volume of the fluid that expands due to temperature changes, in m3 ； ?T——Change in fluid temperature, °C. 4. Compressibility coefficient The compressibility coefficient refers to the rate of change of volume of a fluid when the pressure applied to it changes, while its temperature remains constant. That is: http://www.chinaflow.com.cn/basic/IMAGES/jilian7.jpg Where: K —— the compressibility coefficient of the fluid, in 1/Pa ； V —— Volume of the fluid at pressure p, in m3 ； ?V——The change in fluid volume when pressure increases by p, in m3. 5. Reynolds number The Reynolds number is a dimensionless quantity that represents the ratio of the inertial forces to the viscous forces in a fluid. It is defined as: http://www.chinaflow.com.cn/basic/IMAGES/jilian8.jpg Where: v – the average velocity of the fluid, in m/s ； ι —— the characteristic length of the flow velocity; for example, in a circular pipe, it is the inner diameter of the pipe, in meters ； υ —— dynamic viscosity of the fluid, m2/s. If the Reynolds number is low, viscous forces play a dominant role, and viscosity has a significant impact on the entire flow field. If the Reynolds number is high, inertial forces are dominant, and viscosity’s effect on the flow is significant only within the boundary layer or in areas with large velocity gradients.