The second diagram represents turbulent flow, in which streamlines are irregular and change over time. This is a special case of laminar flow, where the friction between the pipe and the fluid is high, known as no slip boundary conditions. Note that in the example shown in part (a), the velocity of the fluid is greatest in the center and decreases near the walls of the pipe due to the viscosity of the fluid and friction between the pipe walls and the fluid. The first fluid exhibits a laminar flow (sometimes described as a steady flow), represented by smooth, parallel streamlines. The diagrams in Figure 14.25 use streamlines to illustrate two examples of fluids moving through a pipe. The velocity is always tangential to the streamline. A streamline represents the path of a small volume of fluid as it flows. (credit: modification of work by Joseph Trout, Stockton University)Īnother method for representing fluid motion is a streamline. The colors represent the relative vorticity, a measure of turning or spinning of the air. Notice the circulation of the wind around the eye of the hurricane. Figure 14.24 shows velocity vectors describing the winds during Hurricane Arthur in 2014.įigure 14.24 The velocity vectors show the flow of wind in Hurricane Arthur. For example, wind-the fluid motion of air in the atmosphere-can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. In a few examples, we examine an incompressible fluid-one for which an extremely large force is required to change the volume-since the density in an incompressible fluid is constant throughout. Viscosity is a measure of the internal friction in a fluid we examine it in more detail in Viscosity and Turbulence. An ideal fluid is a fluid with negligible viscosity. For this reason, we limit our investigation to ideal fluid s in many of the examples. Even the most basic forms of fluid motion can be quite complex. The rest of this chapter deals with fluid dynamics, the study of fluids in motion. The first part of this chapter dealt with fluid statics, the study of fluids at rest. Explain the consequences of the equation of continuity to the conservation of mass.Describe the relationship between flow rate and velocity.Which schematically measures the turbulence intensity of the flow.By the end of this section, you will be able to: For instance, the relative importance of viscous and Coriolis forces is measured by the Ekman number The main obstacle to quantitative modeling and understanding of planetary hidden flows stands in the extreme character of the involved physical dimensionless parameters, which translates to highly turbulent regimes implying an extremely wide range of time and length scales. Generally speaking, and even though the deeper interior dynamics is not directly observable, gravity data, magnetic field, and the rotation state of a planet are influenced by ongoing flows and hence offer indirect clues for their understanding. Also, motions in conducting fluids are the main mechanism for generating planetary magnetic fields (Larmor 1919), a possible ingredient for planetary habitability. Indeed, turbulent flows in cores and oceans significantly influence the planets thermal and orbital evolution, because of heat advection, viscous dissipation, and coupling with the overlying/underlying solid shells. Beyond the challenge in fundamental fluid dynamics to understand these complex motions involving turbulence, rotation, and buoyancy effects at typical spatial and temporal scales well beyond our day-to-day experience, a global knowledge of the involved processes is fundamental to a better understanding of the global dynamics of planets. Understanding the flows taking place in these spherical shell envelopes remains a tremendous interdisciplinary challenge, despite more than one century of intense research. Numerous planetary bodies have or had a global, internal fluid layer, such as a liquid iron-rich core in the deep interior of terrestrial planets and moons, or a salty water ocean below the solid surface of icy satellites.
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