As mentioned in the introduction to this lecture, we will be studying fluid flow under certain strict conditions.  That is, we will only be studying fluid flow which displays  certain restrictive characteristics. These characteristics are listed below, followed by a short discussion of the consequences of these restrictions.

Laminar Flow vs. Turbulent Flow:

A fluid is said to display laminar flow (or steady flow) if, at any point in the liquid, the velocity of the flow is always the  same.  That is, let’s say that we put a small drop of ink into a flowing liquid at a certain point, and then watch the direction of the ink drop’s velocity in the fluid.  Some time later, we put another drop of ink at the same point in the fluid. The velocity of the drop will be the same as before if the flow is laminar flow.  If the fluid flow is not laminar, then we say the flow is turbulent flow (or nonsteady flow). We shall only deal with laminar flow in this course. (We can qualitatively think of laminar flow as a smooth fluid flow....)

Compressible vs. Incompressible Fluids:

A fluid is said to be compressible if its density increases as its pressure is increased. (That is, more mass of the liquid can be squeezed into a given amount of volume.) In general, all fluids are compressible.  To a good approximation, however, we may treat many liquids, including water, or sometimes even gasses (at not-too-high speeds!), as incompressible fluids over an ordinary range of pressures.  In this case, the density of the fluid (or gas) may be treated as a constant.   Unless specified otherwise, we shall assume in this course that all fluids are incompressible.

Rotational vs. Irrotational Fluid Flow:

A fluid is said to undergo a rotational flow if a small paddle wheel would rotate when placed in the flow.  If the paddle wheel would not rotate, then the flow is said to be irrotational.  We shall (of course!) deal only with irrotational fluid flow in this course.

Some Results of the Above Simplifications

Streamlines:  Due to the assumption of working with laminar flow, we  can put a drop of ink into a flowing liquid and follow it as far as we want.  For laminar flow, this path would be exactly the same for any drop of ink placed at the same position within that fluid. This path is called a streamline.  Note that no two streamlines can ever cross paths.  (Can you see why not?)

Tubes of Flow:  A bundle (or group) of streamlines is called a tube of flow .  This tube of flow acts exactly as if there were a pipe within the liquid: no liquid can flow into or out of a tube of flow for a fluid undergoing laminar flow, whether or not a pipe is present! (Why not?) It will therefore make no difference if we are speaking of fluid flowing within a pipe, or flowing in a river, as long as the flow is laminar.