Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: William Moebs, Samuel J. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the The precise relationship between flow rate Q and average speed v is The volume flow rate is Q = d V d t = A v, Q = d V d t = A v, where A A is the cross-sectional area of the pipe and v is the magnitude of the velocity.

Figure 14.26 illustrates the volume flow rate. A rapid mountain stream carries far less water than the Amazon River in Brazil, for example. But flow rate also depends on the size and shape of the river. The greater the velocity of the water, the greater the flow rate of the river.

To make the distinction clear, consider the flow rate of a river. įlow rate and velocity are related, but quite different, physical quantities. Note that a liter (L) is 1/1000 of a cubic meter or 1000 cubic centimeters ( 10 −3 m 3 or 10 3 cm 3 ). The SI unit for flow rate is m 3 /s, m 3 /s, but several other units for Q are in common use, such as liters per minute (L/min). Here, the shaded cylinder of fluid flows past point P in a uniform pipe in time t. This can occur when the speed of the fluid reaches a certain critical speed.įigure 14.26 Flow rate is the volume of fluid flowing past a point through the area A per unit time. In turbulent flow, the paths of the fluid flow are irregular as different parts of the fluid mix together or form small circular regions that resemble whirlpools. 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.By the end of this section, you will be able to:

Fluid dynamics book