Transit Time Ultrasonic Flowmeter:
A pair (or pairs) of transducers, each having its own transmitter and receiver, are placed on the pipe wall, one (set) on the upstream and the other (set) on the downstream. The time for acoustic waves to travel from the upstream transducer to the downstream transducer t_{d} is shorter than the time it reqires for the same waves to travel from the downstream to the upstream t_{u}. The larger the difference, the higher the flow velocity.
t_{d} and t_{u} can be expressed in the following forms:
where c is the speed of sound in the fluid, V is the flow velocity, L is the distance between the transducers and is the angle between the flow direction and the line formed by the transducers.
The difference of t_{d} and t_{u} is
where X is the projected length of the path along the pipe direction (X = L cos).
To simplify, we assume that the flow velocity V is much smaller than the speed of sound c, that is, . We then have
or,
Note that the speed of sound c in the fluid is affected by many factors such as temperature and density. It is desirable to express c in terms of the transit times t_{d} and t_{u} to avoid frequent calibrations:
The speed of sound c becomes
The flow velocity is now only a function of the transducer layout (L, X) and the measured transit times t_{u} and t_{d}.
The above formula can be further simplified by utilizing the following approximation:
The flow velocity can therefore be written as
