11.7

Fluids in Motion

Fluids can move or flow in many ways. Water may flow smoothly and slowly in a quiet stream or violently over a waterfall. The air may form a gentle breeze or a raging tornado. To deal with such diversity, it helps to identify some of the basic types of fluid flow.
Fluid flow can be steady or unsteady. In steady flow the velocity of the fluid particles at any point is constant as time passes. For instance, in Figure 11-23 a fluid particle flows with a velocity of past point 1. In steady flow every particle passing through this point has this same velocity. At another location the velocity may be different, as in a river, which usually flows fastest near its center and slowest near its banks. Thus, at point 2 in the figure, the fluid velocity is , and if the flow is steady, all particles passing through this point have a velocity of . Unsteady flow exists whenever the velocity at a point in the fluid changes as time passes. Turbulent flow is an extreme kind of unsteady flow and occurs when there are sharp obstacles or bends in the path of a fast-moving fluid, as in the rapids in Figure 11-24. In turbulent flow, the velocity at a point changes erratically from moment to moment, both in magnitude and in direction.

Figure 11-23 Two fluid particles in a stream. At different locations in the stream the particle velocities may be different, as indicated by and .

Figure 11-24 The flow of water in white-water rapids is an example of turbulent flow. (Gary M Prior/Allsport/ Getty Images Sport Services)

Fluid flow can be compressible or incompressible. Most liquids are nearly incompressible; that is, the density of a liquid remains almost constant as the pressure changes. To a good approximation, then, liquids flow in an incompressible manner. In contrast, gases are highly compressible. However, there are situations in which the density of a flowing gas remains constant enough that the flow can be considered incompressible.
Fluid flow can be viscous or nonviscous. A viscous fluid, such as honey, does not flow readily and is said to have a large viscosity*. In contrast, water is less viscous and flows more readily; water has a smaller viscosity than honey. The flow of a viscous fluid is an energy–dissipating process. The viscosity hinders neighboring layers of fluid from sliding freely past one another. A fluid with zero viscosity flows in an unhindered manner with no dissipation of energy. Although no real fluid has zero viscosity at normal temperatures, some fluids have negligibly small viscosities. An incompressible, nonviscous fluid is called an ideal fluid.
When the flow is steady, streamlines are often used to represent the trajectories of the fluid particles. A streamline is a line drawn in the fluid such that a tangent to the streamline at any point is parallel to the fluid velocity at that point. Figure 11-25 shows the velocity vectors at three points along a streamline. The fluid velocity can vary (in both magnitude and direction) from point to point along a streamline, but at any given point, the velocity is constant in time, as required by the condition of steady flow. In fact, steady flow is often called streamline flow.

Figure 11-25 At any point along a streamline, the velocity vector of the fluid particle at that point is tangent to the streamline.

Figure 11-26a illustrates a method for making streamlines visible by using small tubes to release a colored dye into the moving liquid. The dye does not immediately mix with the liquid and is carried along a streamline. In the case of a flowing gas, such as that in a wind tunnel, streamlines are often revealed by smoke streamers, as part b of the figure shows.

Figure 11-26 (a) In the steady flow of a liquid, a colored dye reveals the streamlines. (b) A smoke streamer reveals a streamline pattern for the air flowing around this pursuit cyclist, as he tests his bike for wind resistance in a wind tunnel. (b, Nicholas Pinturas/Stone/ Getty Images)

In steady flow, the pattern of streamlines is steady in time, and, as Figure 11-26a indicates, no two streamlines cross one another. If they did cross, every particle arriving at the crossing point could go one way or the other. This would mean that the velocity at the crossing point would change from moment to moment, a condition that does not exist in steady flow.

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