Although the physics in the other answers is correct, their conclusions unfortunately aren't. Prisms can be used to make a laser beam wider in one dimension. This is, in fact, common practice in circularizing the output of laser diodes which are typically highly elliptical (they go by the name anamorphic prism pairs). Here is an example from Thorlabs.com.
Why does this happen? As the other answers correctly point out, there is no dispersion; this effect is purely geometrical. Think of the beam as a cylinder with an elliptical cross-section. By taking the correct cross section through this cylinder which isn't perpendicular to the direction of propagation we can get something whose cross-section is circular (or vice versa). This is what a prism does to a laser beam; by inserting it into the beam at a steep angle of incidence, the projected cross-section at the output of the prism is larger in the dimension in which the prism is tilted.
However, the other answers are correct in that you would not want to use this method to obtain a large laser beam. For that you should use a lens or two; cylindrical lenses can be used to make only one dimension larger. I could offer some suggestions on your project, but I don't understand what you mean by flow visualization. Do you want to build something like a Fizeau interferometer? What optical property of the fluid are you trying to visualize?