For an accurate flow metering without considering the influences of flow control devices such as valves and elbows in closed conduits, velocity distribution in the cross-sectional area must be integrated. However, most flow meters, including multi-path ultrasonic, electromagnetic or Coriolis mass flow meters, require assumptions on the fully-developed turbulent flows to calculate flow rates from physical quantities of their own concern. Therefore, a long straight pipe has been a necessary element for accurate flow metering because the straight pipe can reduce flow disturbances caused by flow control devices. To reduce costs due to the installation of long straight pipes, another flow metering technique is required. For example, flow rates can be estimated by integrating velocity distributions in the cross-section of conduits. In the present study, ultrasound tomography was used to find the velocity distribution in the cross-section of a closed conduit where flow was disturbed by a Coriolis mass flow meter or a butterfly valve. A commercial multi-path ultrasonic flow meter was installed in the pipeline to measure the line-averaged velocity distribution in the pipe flow. The ultrasonic flow meter was rotated $180^{circ}$ at intervals of $10^{circ}$ to construct line-averaged velocity distributions in Radon space. Flow images were reconstructed by using a back-projection algorithm (inverse Radon transform). Flow diagnostic parameters were defined by calculating statistical moments, i.e., average, standard deviation, skewness, and kurtosis, based on the normalized velocity distribution. The flow diagnostic parameters were applied to flow images to find whether the parameters could discern flow disturbances in the reconstructed velocity distribution.