A system for precision measurement of fluid velocity is developed and applied to determine the laminar flow distribution in a square duct. The experimental technique consists of measuring the Doppler shift of laser radiation scattered by particles moving with the fluid. From this frequency shift, the fluid velocity is inferred. Measurements in the entrance region and fully developed flow region of a square duct indicate that the velocity profile development takes place in a somewhat longer section of the duct than had been predicted. Measurements of the f ully developed flow indicate that the optical technique used is capable of measuring velocity within an accuracy of at least 0.1 percent.