A method of measuring the flow rate in a pipe is proposed. The method utilizes one-dimensional acoustic pressure signals that are generated by a loud speaker. A microphone array mounted flush with the inner pipe wall is used to measure the signals. A formula for the flow rate, which is a function of the change of wave number, is derived from a simple mathematical model of sound field in the pipe conveying a viscous fluid. The change of the wave number. which is one of the results caused by flow, is estimated from the recursive relation among the measured microphone array signals. Since measurement errors, due to extraneous measurement noise and mismatch of response characteristics between microphones, exist in the estimated flow rate, a method of compensating the errors is proposed. By using this measurement method, the flow rate can be obtained more accurately than that of our previous method. To verify applicability of the measurement method, numerical simulation and experiments are performed. The estimated flow rates are within 5% error bound. (C) 2002 Acoustical Society of America.