PS-2 PRESSURE TO LEVEL CONVERSION FACTOR SOFTWARE

The software program PS2.EXE may be run to determine the optimal conversion factor UF between water-level and measured water pressure.  The setting of the value UF to the calculated conversion factor to achieve an accuracy of 0.01 feet over the range 0 to 50 feet of water depth may then be performed. 

Hydrostatic water-level gauging with pressure sensors is based on the principle that the pressure increases with water depth.  In a bubbler system, a bubbler line is pressurized with gas until the gas pressure is equal to the water pressure at the orifice.  The Paroscientific PS-2 Bubbler System measures the gas pressure of the bubbler line at the inlet port of the pressure sensor inside the PS-2 box.  The gas pressure is measured as gauge pressure relative to the ambient air pressure.  The pressure sensor first determines the pressure in engineering units of psi (pounds per square inch).  Since the pressure increases nearly linearly with the water-level, the output can be rescaled by a linear conversion factor (called UF, or user factor).  The water-level equation is simply

H= UF x P

Where H is the height or water-level above the orifice.  UF is approximately 2.31 feet per psi of gauge pressure. 

UF varies slightly between different locations.  The software program PS2 calculates the best UF factor taking into account six input values: 

-average water density

-local gravity

-air density

-gas density

-PS-2 height above orifice

-normal (typical) water-level

Help calculations are provided to determine all densities from temperature values.  Gravity can be determined from a local geodetic survey, or can be calculated from the altitude and latitude.  Height measurements must be obtained from the location of deployment. 

P = density x gravity x H

Comparing this equation with the water-level equation above gives a conversion factor of

UF = 1 / (density x gravity)

Using a water density of 1 gm/cm³ and standard gravity, the conversion factor is 2.307 ft/psi.

Water density varies, mostly due to temperature.  The water density at 15 deg C is 0.99913 gm/cm³, or 0.09 percent lower. 

Gravity varies by up to 0.45% comparing different locations in North America between latitudes of 10 to 70 degrees.

As an example, assume that a Paroscientific PS-2 system with a range of 0 to 50 feet with an accuracy of 0.01 ft is installed.  Assume that the measured water-level agrees perfectly at 20 feet between the PS-2 system and the staff gauge.  How well will the staff gauge agree at 40 feet?  Any uncertainty in the UF factor will show up as a percentage of excursion.  If gravity is off by 0.2 percent, the PS-2 system will indicate an error of 0.2 percent over 20 feet, or 0.04 feet.  To match the high performance of the PS-2 system (e.g., 0.01 feet accuracy over 50 feet), it is advantageous to customize the conversion factor. 

Other Corrections

If the PS-2 sensor is located above the orifice, the pressure at the inlet is slightly lower than the hydrostatic pressure at the orifice due to the mass of gas column inside the bubbler line.  This effect depends on the PS-2 height above the orifice.  The software program folds this correction into the conversion factor.  The improvement is about 0.035 percent water variation per 10 feet of PS-2 height.  The gas temperature should be entered as the weighted mean temperature of the bubbler line. 

Other corrections include an air density correction and a water compressibility correction that only becomes noticeable if the level variations exceed 200 feet. 

The program PS2 is DOS based and will run on most standard color or monochrome monitor in 25x80 text mode.  To start the program, type PS2.  To select a blue background on VGA monitors, type PS2/c.  Select input parameters with the cursor key.  Insert new values with numeric characters, followed by a carriage return.  If the value is within reasonable values, UF will be recalculated accordingly. 

For special calculation, enter <C>.  Any change in the help menu will also change the main entry and UF.

The program PS2 can also be used to enter pressure values to calculate water-level or vice versa.

Accuracy of Input Values

With reasonable input values, the water-level can be determined from pressure to within 0.01 feet over 50 feet.  The following is an estimate of how well one should know temperatures and local gravity among other values. 

Water density: to 0.02 percent or better

Water temperature: to 2 deg C at 10 deg C

Local gravity: to 0.02 percent or better

Altitude: to 2000 feet (suggested within 1000 feet)

Latitude: to 2 degrees (suggested within 1 degree)

Air density: Enter correct altitude

Air temperature: use default value

Nitrogen gas density: change if different gas is used

Gas temperature: to 15 degrees or better

Height of PS-2 sensor: to 10 feet (suggested to 2.5 feet)

PS-2 reference mark is at inlet port of sensor

Nominal water-level: only important beyond 200 feet (use typical range)

The three most important input values are:

-water density

-gravity

-PS-2 height

Of the three most important input values, only the water density is likely to change as the seasons change.  If an average water density value is used, the water stage will be somewhat higher than expected in summer as the water expands, and somewhat lower in the winter.  In applications that are accessible (e.g., power dams), the value could be readjusted periodically to achieve the highest accuracy. 

Consult the SDI-12 programming manual on how to configure the UF parameter.  The UN parameter must be set to 0 to activate the UF parameter.  The PS-2 boxes are usually configured to a default value of UF = 2.307.  A printout option in the program can be used to establish a record of chosen input values.  The document should be stored with the PS-2 system at the place of deployment for future reference.

The PS-2 Bubbler System can also be used for high precision hydrostatic tank gauging.  Change the water density to the appropriate tank fluid density to calculate the optimal conversion factor. 

Software Program PS2.EXE, V 1.0, Copyright 11-24-92

To download the PS-2 Conversion Software, click here.

©2007 Paroscientific, Inc.