We are now ready to consider motion of a fluid. Fluid flow can be extremely complex, as shown by the currents in river rapids or the swirling flames of a campfire. But we can represent some situations by relatively simple idealized models. An ideal fluid is a fluid that is incompressible (that is, its density cannot change) and has no internal friction (called viscosity). Liquids are approximately incompressible in most situations, and we may also treat a gas as incompressible if the pressure differences from one region to another are not too great. Internal friction in a fluid causes shear stresses when two adjacent layers of fluid move relative to each other, as when fluid flows inside a tube or around an obstacle. In some cases we can ignore these shear forces in comparison with forces arising from gravitation and pressure differences.
The path of an individual particle in a moving fluid is called a flow line. In steady flow, the overall flow pattern does not change with time, so every element passing through a given point follows the same flow line. In this case the “map” of the fluid velocities at various points in space remains constant, although the velocity of a particular particle may change in both magnitude and direction during its motion. A streamline is a curve whose tangent at any point is in the direction of the fluid velocity at that point. When the flow pattern changes with time, the streamlines do not coincide with the flow lines. We’ll consider only steady-flow situations, for which flow lines and streamlines are identical.
The flow lines passing through the edge of an imaginary element of area, such as area A in Fig. 12.18, form a tube called a flow tube. From the definition of a flow line, in steady flow no fluid can cross the side walls of a given flow tube.
Figure 12.19 shows the pattern of fluid flow from left to right around an obstacle. The photograph was made by injecting dye into water flowing between two closely spaced glass plates. This pattern is typical of laminar flow, in which adjacent layers of fluid slide smoothly past each other and the flow is steady. (A lamina is a thin sheet.) At sufficiently high flow rates, or when boundary surfaces cause abrupt changes in velocity, the flow can become irregular and chaotic.
This is called turbulent flow (Fig. 12.20). In turbulent flow there is no steady-state pattern; the flow pattern changes continuously.
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