Cylindrical pipes are widely used in industries such as nuclear power plants and micro total analysis systems (mTAS). Measuring the flow rate of fluid in such pipes is critical. Ultrasonic flowmeters are noncontact, nondestructive, and easy-to-use devices, and are therefore widely used. However, typical bulk-wave-based ultrasonic flowmeters cannot be used for pipes narrower than the wavelength of bulk waves. For such pipes, we are currently developing a ''guide wave flowmeter'' that uses guide waves instead of bulk waves. Previously, we theoretically and experimentally investigated a pipe filled with quiescent fluid for all modes [Jpn. J. Appl. Phys. 45 (2006) 4573]. In this study, we expanded our theoretical investigation to a cylindrical pipe containing flowing fluid, and then compared the results with experimental results. Both the theoretical and experimental results revealed that the flow rate can be determined by measuring the sound velocity (propagation time) of guide waves. This is the operating principle of our guide wave flowmeter.