Moving fluids

Fluid dynamics is the study of how fluids behave when they're in motion. This can get very complicated, so we'll focus on one simple case, but we should briefly mention the different categories of fluid flow. Fluids can flow steadily, or be turbulent. In steady flow, the fluid passing a given point maintains a steady velocity. For turbulent flow, the speed and or the direction of the flow varies. In steady flow, the motion can be represented with streamlines showing the direction the water flows in different areas. The density of the streamlines increases as the velocity increases. Fluids can be compressible or incompressible. This is the big difference between liquids and gases, because

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If the equation was multiplied through by the volume, the density could be replaced by mass, and the pressure could be replaced by force x distance, which is work. Looked at in that way, the equation makes sense: the difference in pressure does work, which can be used to change the kinetic energy and/or the potential energy of the fluid.

Pressure vs. speed

Bernoulli's equation has some surprising implications. For our first look at the equation, consider a fluid flowing through a horizontal pipe. The pipe is narrower at one spot than along the rest of the pipe. By applying the continuity equation, the velocity of the fluid is greater in the narrow section. Is the pressure higher or lower in the narrow section, where the velocity increases?

Your first inclination might be to say that where the velocity is greatest, the pressure is greatest, because if you stuck your hand in the flow where it's going fastest you'd feel a big force. The force does not come from the pressure there, however; it comes from your hand taking momentum away from the