Will a prism widen a monochromatic beam? The representation of the experiment which demonstrates that white light consists of many colors, invariably shows that the beam of white light is broadened inside the prism and is some what more broadened when it exits in the form of the separated colors. I am not able to figure out if this broadening of the beam will occur in the case of a strictly monochromatic light.
For a more complete background, the following is what I am trying to achieve. I have a laser pointer out of which I am trying to get a sheet of laser. For this I am exploring the use of prisms (one or more prisms). Using this beam I plan to setup a crude preliminary demo of flow visualization. Any inputs are appreciated.
 A: Provided the prism is of high quality (broadly speaking its faces need to be optically flat, and its material free of defects), then there should be no broadening.  What the prism does is disperse different colours in different directions. Since the source is monochromatic there will be no dispersion.  However if the source isn't monochromatic (within a small tolerance) then there will be some dispersion, but it's likely to be minimal.
A: Typically sheets of laser light are usually achieved by bouncing the laser off an oscillating mirror, though you could achieve a similar effect by passing the light through an oscillating or rotating prism. If the frequency of oscillation of the mirror is fast enough persistence of vision makes it look like a steady sheet of light.
Prisms broaden a beam of multichromatic light because the refractive index varies with wavelength so each colour bends by a different amount. With monochromatic light there is just a single refractive index and single angle of bending.
A: 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?
