Conduit Interior Diameter Conduit d Current Operational Density

B The interior diameter of the conduit has a great impacton the accuracy of the flow calculation. For this reason we recommend that you determine the exact interior diameter measurement at the sampling point when conducting measurements which require a high degree of accuracy. The mathematical average from multiple measurements can be used when dealing with non-round conduits.The interior diameter can change at high temperaturesdue to the thermal expansion of the material. For this reason, the calculation sheet of your deltaflow specifies the “warm” interior diameter of your conduit. This means that it is only necessary—and practical—to calculate the actual interior diameter at a given moment ( The density of a medium depends upon its composition, the temperature, and the pressure which is applied to it.The density of liquids is only affected in a very slightway by the pressure. For this reason, liquids are also referred to as “incompressible media.” Likewise, the effect that temperature has on liquids is substantially less than the effect it has on gasses or steams.There are basically two principal approaches tocalculating the density of media: calculation based on tables and calculation based on equations.Calculating density based on tables is very simple andexact, but it does require that a density table exist and be available. Density tables for many common media can be found in the appendix of this booklet. It is permissible to construct a linear interpolation between sampling points when there is no phase transition (i.e. boiling or melting point) located between the sampling points.There are many formulas for calculating density basedon equations. These formulas vary in their ease of use and in their accuracy. A few common formulas are detailed below.
d B ) if the process temperatures changedramatically during the course of operation. The warm interior diameter is calculated as follows:

1 TTdd

DBDB In this formula, represents the vertical (length)expansion coefficient of the conduit material. For moststeels, the value of falls between 10*10e-6 and16*10e-6. A temperature increase of 100K, for example, would result in an increased diameter measurement of 0.13% based on the material, and the flow would be increased by 0.26%.A table containing the vertical expansion coefficientvalues of various materials is located in the Appendix.

Calculating the Density of Liquids Using a VolumeExpansion Coefficient

One simple method of calculating the medium density of liquids is to use constant volume expansion coefficients.

Measured Differential Pressure dp

20 BCB

15.29311 KT

As you can see in Equation (1), the differential pressure is located below the radical when calculating flow. Many differential industrial pressure transducers can automatically extract the root given the measured differential pressure signal. The output signal from this type of transducer is then no longer proportional to the differential pressure, but is instead proportional to the root of the differential pressure.It is therefore extremely important to be aware ofwhether or not the root extraction is automatically performed within the transducer when evaluating themeasurement signals from differential pressure transducers. Example: Water at 50°C and 1 bar
70 C mkgKKemkg ³0.992301510*7.2011³2.998 Consult a volume of tables, and you will find an actualdensity of 988.0 kg/m³ at 1 bar and 50 C. The error inthe density calculation in this example equals 0.4%, deltaflow Basic Calculation Information 07/03Page4