Vortex formation and shedding downstream obstructions may be assumed to be one of the main sources of flow induced vibration and noise in pipes, ducts, and control valves. The level of the produced noise depends on the size of the formed vortex and its shedding frequency hence, controlling the size of the formed vortex may be one of the main factors that help in attenuation of the generated noise. The vortex size may be estimated from the reattachment length of the separated flow downstream these obstructions. In the present work, vortex formation downstream a single orifice and two orifices in series in a rectangular duct have been investigated numerically and experimentally. A numerical solution has been coded to solve the flow governing equations in the primitive variables using the finite difference technique. The solution has been carried out for laminar, 2-D and incompressible flow field at Reynolds number ranges from 50 to 400 for orifice height to duct height ratio of 0.5 and for the inter distance between the two orifices from 0.2H to 7H. The velocity field, the streamlines, and the vorticity field have been determined. The code is written in visual C-language to achieve low computational time and lower number of iterations. An experimental investigation has been carried out on 2-D laminar flow visualization table. The streamlines of water flow throughout the single orifice and two orifices in the rectangular duct have been visualized for various Reynolds number and orifice height to duct height ratio, D/H, values. The experimental and the theoretical results showed a considerable agreement. The results showed a minimum vortex size as well as lowest circulation in case of using an inter distance of about (1-D/H). Finally, the results showed that the control of the inter distance between the two orifices or similarly between any two obstructions in a rectangular duct may be of special interest to reduce the size of the generated vortex and consequently to attenuate the vibration and noise.