conservation of momentum in collisions (Sections 7.7 and 7.8)
equilibrium (Section 2.4)
Mastering the Concepts
Fluids are materials that flow and include both liquids and gases. A liquid is nearly incompressible, whereas a gas expands to fill its container.
Pressure is the perpendicular force per unit area that a fluid exerts on any surface with which it comes in contact. (P = F / A). The SI unit of pressure is the pascal (1 Pa = 1 N/m2).
The average air pressure at sea level is 1 atm = 101.3 kPa.
Pascal's principle: A change in pressure at any point in a confined fluid is transmitted everywhere throughout the fluid.
The average density of a substance is the ratio of its mass to its volume <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663817/Img_01.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a>
The specific gravity of a material is the ratio of its density to that of water at 4oC.
Pressure variation with depth in a static fluid: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663817/Img_02.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (5.0K)</a> where point 2 is a depth d below point 1.
Instruments to measure pressure include the manometer and the barometer. The barometer measures the pressure of the atmosphere. The manometer measures a pressure difference.
Gauge pressure is the amount by which the absolute pressure exceeds atmospheric pressure: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663817/Img_03.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (5.0K)</a>
Archimedes' principle: a fluid exerts an upward buoyant force on a completely or partially submerged object equal in magnitude to the weight of the volume of fluid displaced by the object: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663817/Img_04.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a> where V is the volume of the part of the object that is submerged and ρ is the density of the fluid.
In steady flow, the velocity of the fluid at any point is constant in time. In laminar flow, the fluid flows in neat layers so that each small portion of fluid that passes a particular point follows the same path as every other portion of fluid that passes the same point. The path that the fluid follows, starting from any point, is called a streamline. Laminar flow is steady. Turbulent flow is chaotic and unsteady. The viscous force opposes the flow of the fluid; it is the counterpart to the frictional force for solids.
An ideal fluid exhibits laminar flow, has no viscosity, and is incompressible. The flow of an ideal fluid is governed by two principles: the continuity equation and Bernoulli's equation.
The continuity equation states that the volume flow rate for an ideal fluid is constant: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0073512141/663817/Img_05.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>
Bernoulli's equation relates pressure changes to changes in flow speed and height: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0073512141/663817/Img_06.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>
Poiseuille's law gives the volume flow rate DV/Dt for viscous flow in a horizontal pipe: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0073512141/663817/Img_07.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> where DP is the pressure difference between the ends of the pipe, r and L are the inner radius and length of the pipe, respectively, and h is the viscosity of the fluid.
Stokes's law gives the viscous drag force on a spherical object moving in a fluid: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::::/sites/dl/free/0073512141/663817/Img_08.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>
The surface tension g (the Greek letter gamma) of a liquid is the force per unit length with which the surface pulls on its edge.
