1. Practical Use of Straight line Theory Prepared by Bernie Lafferty Bsc(Hons) GIMA Mathematical Sciences

2. Typical Reservoir Site An ultrasonic level probe measures the level of the reservoir and displays it on an instrument panel at site. ( Range typically 0 - 5 metres ) The Industrial standard output for an Instrument’s low - high range is 4mA - 20 mA DC (Direct Current ) Display Reading 0 m5 m 4mA20mA Valid range for instrument

3. Interface to Telemetry The output from the Instrument (4mA-20mA DC) is fed into the Telemetry Unit and then converted using Analogue to Digital conversion into a count value between 0 - 4095. The Industrial standard output is 4mA - 20 mA DC Valid Instrument Range 4mA-20mA Bad value Instrument Faulty ! 4mA20mA 8194095 < 819 means bad value instrument fault Telemetry Unit Conversion Fixed for all analogues no matter the Instrument scaling 4mA20mA 8194095 under 819 i.e. under 4mA means bad value Telemetry Unit Conversion DC current value Count value 0mA 0

4. Scanner Radio Communications The Count value ( between 0 - 4095 ) which represents the DC current value ( 0 - 20 mA ) which in turn represents the value on the instrument at site is then transmitted to Scottish Water Control Centre. Communications types are Satellite Scanning Radio Private Wire (BT) PSTN (dial-up BT) 4mA20mA 8194095 under 819 i.e. under 4mA means bad value Telemetry Unit Conversion DC current value Count value 0mA 0 0 - 4095

5. Scottish Water Control Centre The count value (between 0 - 4095) is received at Master Station at the Water Control Centre and using Digital to Analogue conversion is converted back into the original analogue value and then displayed on computer screens.

6. Summary of Process Mathematics Summary Fixed graph for all analogues Master Station Conversion Standard Telemetry Conversion Instrument Conversion = half scale

7. Overview Multi-Analogues Level meter PH meter Flow meter Instrument 4mA-20mA 4mA-20mA 4mA-20mA Value between 0-4095 Range 0- 5 m 0 - 100 l/s 0 - 14 PH l/s = litres per second m= metres Graph 2 Graph 1 Graph 3 Range 0- 5 m 0 - 14 PH 0 - 100 l/s Control Centre Telemetry Outstation Computer Screen Probes

8. Mathematical Overview y=0.0000048842x Level meter PH meter Flow meter Range 0- 5 m Range 0 - 100 l/s Range 0 - 14 PH Graph 2 / equation 2 Graph 1 / equation 1 Graph 3 / equation 3 y=0.0032x + 0.04 y=0.001143x + 0.04 y=0.00016x + 0.04 y=0.001526x - 1.25 y=0.004274x - 3.5 y=0.031x - 25 Notes Gradients are less than 1 ( this will stop errors being compounded ) Gradients are less than 1 ( this will stop errors being compounded ) Equation 2 is FIXED no matter the instrument scaling due to the Equation 2 is FIXED no matter the instrument scaling due to the Industrial Standard Output for instruments ( 4mA-20mA ) Industrial Standard Output for instruments ( 4mA-20mA ) Typical value on Instrument 3.75725 y=16mAy=12mAy=8mA DC current value on Graph y=3276y=2457y=1638 Count value on Graph y=3.75y=7y=25 Analogue value on Graph

9. Graphical Example Level meter Range 0 - 5 m present value 3.75 Value on Computer Screen 3.75 m