SLAA889A March   2019  – July 2021 MSP430FR6041 , MSP430FR6043 , MSP430FR60431 , MSP430FR6045 , MSP430FR6047 , MSP430FR60471

 

  1.   Trademarks
  2. 1Flow Metering Background
    1. 1.1 Water Flow Velocity Estimation
      1. 1.1.1 Velocity of Ultrasound in Water is Known
      2. 1.1.2 Velocity of Ultrasound in Water is Unknown
  3. 2Algorithms for Ultrasonic Water Flow Metering
    1. 2.1 Correlation Based Technique for Differential TOF Estimation
    2. 2.2 Absolute Time-of-Flight (AbsTOF) Measurement (Tup and Tdn)
      1. 2.2.1 AbsTOF Calculation
        1. 2.2.1.1 Acquisition Algorithm for AbsTOF
        2. 2.2.1.2 Tracking Algorithm for AbsTOF
  4. 3References
  5. 4Revision History

1.1.1 Velocity of Ultrasound in Water is Known

When the velocity c of ultrasound in water is known, Equation 4 uses this velocity to solve for the water flow velocity v.

Equation 4. ΔT=T21–T12=2Lvc2–v2

However, the velocity c of ultrasound in water is a function of temperature. Based on the data in Figure 1-3, Equation 5 gives a first-order simple expression for the dependence of ultrasound velocity in water. The temperature in the equation is in degrees Celsius (°C).

Equation 5. c=1404.3+4.7Ttemp–0.04Ttemp2

Figure 1-3 shows the change of velocity c of ultrasound in water as a function of temperature.

GUID-BEB2B9D3-8546-45A3-965C-DFDD8875E296-low.pngFigure 1-3 Velocity of Ultrasound in Water as a Function of Water Temperature

If the water meter does not take this temperature dependence into account and only assumes a nominal 25°C temperature, an error of up to ±3.5% can occur in the absolute time-of-flight estimation. Therefore, a temperature sensor is needed for the estimation of velocity c of ultrasound in water using Equation 4.