In the measurement and calculation of the flowmeter, the physical properties of some fluids (fluid properties) are used, which have a great influence on the accuracy of the flow measurement and the selection of the flowmeter. Due to the limited space of the book, we only introduce basic concepts and some simple calculations for these physical parameters. Detailed data sheets need to be consulted in the relevant manuals.

1. Flowmeter fluid density

The density of the fluid is defined by the following formula

Where: ρ - fluid density, kg/m3;

m - the mass of the fluid, kg;

V - Volume of fluid, m3.

(1) Density of flowmeter liquid

When the pressure is constant, the liquid density is calculated as:

ρ=ρ20[1-μ(t-20)]

Where: ρ - the density of the liquid at temperature t, kg/m3;

Ρ20——density of liquid at 20°C, kg/m3;

μ - the volume expansion coefficient of the liquid, 1/°C;

t - the temperature of the liquid, °C.

When the temperature is constant, the liquid density formula is:

Ρ1=ρ0[1-β(ρ0-ρ1)]

Where: ρ1 - the density of liquid at pressure p1, kg/m3;

Ρ0——density of liquid at pressure p0, kg/m3;

β - the volume compression coefficient of the liquid 1/Mpa;

P0, p1 - the pressure of the liquid, Mpa.

Usually the pressure change has little effect on the liquid density and can be ignored below 5 Mpa, but for hydrocarbons, the pressure correction should be performed even at lower pressures.

(2) Flowmeter gas density

The dry gas density formula under working conditions is:

Where: ρ - dry gas density in the working state, kg/m3;

Ρn - the density of dry gas under standard conditions (293.15k, 101.325kPa), kg/m3;

p - the absolute pressure of the gas at work, kPa;

Pn - absolute pressure in standard state, kPa;

T - the absolute temperature of the gas in the working state, K;

Tn - Absolute temperature in the standard state, 293.15K;

Zn - the compression coefficient of the gas under standard conditions;

Z - The compression factor of the gas at work.

2. Flowmeter fluid viscosity

The property that the fluid itself blocks the relative sliding of its mass is called the viscosity of the fluid. The viscosity of the fluid is measured by viscosity. The viscosity of the same fluid changes with the temperature and pressure of the fluid. Usually the temperature rises, the viscosity of the liquid drops, and the viscosity of the gas rises. Liquid viscosity only needs to be corrected under very high pressure, and the viscosity of gas is closely related to pressure and temperature. The following two kinds of characterization of fluid viscosity are commonly used:

(1) Dynamic viscosity

Where: η - hydrodynamic viscosity, Pa · s;

Ï„ - Internal friction on a unit area,

Pa - speed gradient, 1/s;

u - fluid velocity, m/s;

h - distance between two fluid layers, m.

(3) Flowmeter kinematic viscosity

The ratio of the dynamic viscosity of a fluid to its density is called the kinematic viscosity.

Where: v - kinematic viscosity.

3. Thermal expansion rate

The thermal expansion rate refers to the relative change rate of the volume when the fluid temperature changes by 1°C, ie:

Where: β - the thermal expansion rate of the fluid, 1/°C;

V - original volume of fluid, m3;

â–³ V - the volume of fluid expansion due to temperature changes, m3;

ΔT—change in fluid temperature, °C.

4. Compression coefficient

Compression coefficient refers to the change rate of the volume when the fluid temperature is constant and the pressure is changed, ie:

Where: K - the compression coefficient of the fluid, 1/Pa;

V - fluid volume m3 at pressure p;

ΔV—The change in volume of the fluid when the pressure increases, p, m3.

Reynolds number

The Reynolds number is a dimensionless quantity that characterizes the ratio of the fluid's inertial force to the viscous force. It is defined as:

Where: v - the average velocity of the fluid, m/s;

ι - the characteristic length of the flow rate, such as the value of the inner diameter of the tube taken in the circular tube, m;

Ï… - The kinematic viscosity of the fluid, m2/s.

If the Reynolds number is small, the viscous force plays a major role, and the effect of viscosity on the entire flow field is important. If the Reynolds number is large, the inertial force is the main one. The effect of viscosity on the flow is only important in the boundary layer or in the area where the velocity gradient is large.

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