# Density Compensation

Specific Volume

Before examining an example which shows the effects of density, the unit “specific volume” must be defined. Specific volume is defined as volume per unit mass as shown in Equation 3-1.

Specific Volume = Volume/Mass (3-1)

Specific volume is the reciprocal of density as shown in Equation 3-2.

Specific volume is the standard unit used when working with vapors and steam that have low values of density. For the applications that involve water and steam, specific volume can be found using “Saturated Steam Tables,” which list the specific volumes for water and saturated steam at different pressures and temperatures.

The density of steam (or vapor) above the liquid level will have an effect on the weight of the steam or vapor bubble and the hydrostatic head pressure. As the density of the steam or vapor increases, the weight increases and causes an increase in hydrostatic head even though the actual level of the tank has not changed. The larger the steam bubble, the greater the change in hydrostatic head pressure.

Figure 12 illustrates a vessel in which the water is at saturated boiling conditions.

A condensing pot at the top of the reference leg is incorporated to condense the steam and maintain the reference leg filled. As previously stated, the effect of the steam vapor pressure is cancelled at the DP transmitter due to the fact that this pressure is equally applied to both the low and high pressure sides of the transmitter. The differential pressure to the transmitter is due only to hydrostatic head pressure, as stated in Equation 3-3.

Hydrostatic Head Pressure = Density x Height (3-3)

Reference Leg Temperature Considerations

When the level to be measured is in a pressurized tank at elevated temperatures, a number of additional consequences must be considered. As the temperature of the fluid in the tank is increased, the density of the fluid decreases. As the fluid’s density decreases, the fluid expands, occupying more volume. Even though the density is less, the mass of the fluid in the tank is the same. The problem encountered is that, as the fluid in the tank is heated and cooled, the density of the fluid changes, but the reference leg density remains relatively constant, which causes the indicated level to remain constant. The density of the fluid in the reference leg is dependent upon the ambient temperature of the room in which the tank is located; therefore, it is relatively constant and independent of tank temperature. If the fluid in the tank changes temperature, and therefore density, some means of density compensation must be incorporated in order to have an accurate indication of tank level. This is the problem encountered when measuring pressurizer water level or steam generator water level in pressurized water reactors, and when measuring reactor vessel water level in boiling water reactors.

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