# Effects of Velocity Profiles on Measuring Accuracy of Transit-Time Ultrasonic Flowmeter
## 1 Introduction  
Flow measurement is necessary in engineering field for fluid metrology and process control [1; 2]. A variety of flow measurement techniques were invented, such as differential pressure flowmeter [3], float flowmeter [4], volumetric flowmeter [5], electromagnetic flowmeter [6], and vortex shedding flowmeter [7]. However, the common disadvantage of these flow measurement techniques is that the fluid properties are tightly restricted due to direct contact with the flowmeters. In order to overcome the above disadvantage, non-contact ultrasonic flowmeter was developed, which is immune to temperature, causticity, and conductivity of measured fluid [8].  
There is a great variety of ultrasonic flowmeters for measurement of liquid and gas flow [9; 10; 11; 12]. Today, ultrasonic flowmeters utilize clamp-on and wetted transducers, single and multiple paths, paths on and off the diameter, passive and active principles, contra-propagating transmission, reflection (Doppler), tag correlation, vortex shedding, liquid level sensing of open channel flow or flow in partially-full conduits, and other interactions. Due to the simplicity of the measurement principle, the ultrasonic transit-time method is one of the most common techniques in industrial applications. Flowrate measurement using the ultrasonic transit-time method is based on the apparent difference of the sound velocity in the flow direction and in the opposite direction [13; 14]. It was pointed out in reference [15] that the transit-time ultrasonic flowmeter has a relatively high uncertainty, approximately 5%. The uncertainty is mainly caused by three factors, the first is the installation method of transducers; the second is the measurement of transit time, especially for pipe with a small inner diameter; the last isvelocity distribution across the pipe [16]. A large amount of studies have been carried out to reduce the uncertainty caused by these three reasons [17; 18; 19; 20]. For the first reason, [PERSON] et al. [21; 22] improved measurement accuracy by changing the distance between transducers. [PERSON] et al. [23] indicated that multipath ultrasonic flowmeters can provide more accurate flow velocities than a single path. For the second reason, several research focused on developing new algorithms to obtain more accurate time differences [24]. And high time resolution electronic components have significant progress in recent years to achieve nanosecond measurement of transit time. However, there is a limited amount of information available on the effect of velocity profile on the measurement uncertainty. [PERSON] et al. [13] have proved that the flow rate is overestimated by the effects of the assumption of uniform velocity distribution, and a correction factor is obtained empirically based on numerical simulation results for fully developed turbulence. [PERSON] et al. [25] gave a correction factor for the transition region with Reynolds number in the range of 2000-20000 based on experiment results by Particle Image Velocimetry (PIV) measurement. Little attention was paid to obtain correction factor for transit time ultrasonic flowmeter through theoretical analysis.  
In this paper, we put emphasis on the effects of velocity profiles across the pipe on the time of ultrasonic wave propagation. Theoretical correction factors for transit-time ultrasonic flowmeters were proposed for laminar and turbulent flow to improve measurement accuracy. Flow measurement experiments were performed for laminar and turbulent flow, respectively, and experiment data of ultrasonic flowmeter and weighting method are compared to verify the proposed theoretical correction factors.