This document describes the ultrasonic time-of-flight (TOF) based algorithms for water flow measurement. Figure 1-1 shows different configurations that are used in practice for the ultrasonic TOF technique.

Figure 1-1 Configurations for Ultrasonic TOF Based Measurement

This document uses the structure in Figure 1-2 for analysis of ultrasonic TOF techniques.

Figure 1-2 Transmit and Receive Transducers for Ultrasonic Measurements

In Figure 1-2, the two transducers are numbered 1 and 2, T₁₂ is the propagation time for the ultrasonic signal from transducer 1 to 2, and T₂₁ is the propagation time for the signal from transducer 2 to 1. Equation 1 and Equation 2 calculate the propagation times in the two directions as a function of the velocity of ultrasound in water and the velocity of water flow. The parameters in the equation are c = velocity of ultrasound in water, v = velocity of water flow, and L = the propagation length of the pipe along the flow of water. Because this length is much larger than the radius r of the pipe, the propagation length of the wave perpendicular to the flow is neglected in this analysis.

The objective is to solve for the velocity v of the water flow so that can be used to indicate the water flow volume which would be given by volume = A × v, with the assumption that the cross sectional area A of the pipe is known.

Equation 3 calculates the differential TOF of the upstream and downstream signals.

There are two methods to solve Equation 1 and Equation 2. One method can be used when the velocity of ultrasound in water is known (see Section 1.1.1), and the other method can be used when the velocity of ultrasound in water is not known (see Section 1.1.2).

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

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).

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

Figure 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.