Ones body movement to the side when a car makes a sharp turn. Revisiting viscosity from the macroscopic to nanoscale regimes. Derivation of the viscous flow equations to obtain the equation for viscousdominated inertialfree flow, we need to start with the local force balance in the fluid, which is the same expression we used previously in a solid, ij 0 1. Per newtons law of viscosity, this momentum flow occurs across a velocity gradient, and the magnitude of the corresponding momentum flux is determined by. Newtons second law describes the affect of net force and mass upon the acceleration of an object. It is used to predict how an object will accelerated magnitude and direction in the presence of an unbalanced force. Newton s method is an application of derivatives will allow us to approximate solutions to an equation. Newtons viscosity law s states that, the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers. Newtons law of viscosity properties of fluid fluid mechanics duration. Newtons law of viscosity, pressure and temperature. Newtons law of viscosity defines the relationship between the shear stress and shear rate of a fluid subjected to a mechanical stress. Newtons law of viscosity video lecture from properties of fluid chapter of fluid mechanics for mechanical engineering students.
The derivation of such a terms form is not as simple as that of the shear terms, but. Newtons law of viscosity properties of fluid fluid mechanics. Newtonian fluids the fluids that obey the newtons law of viscosity are known as newtonian fluids. The driving force on the cylinder due to the pressure difference is.
Every body continues to be in its state of rest or uniform motion. They arise from the application of newtons second law in combination with a fluid stress due to viscosity and a pressure term. Newtons law of viscosity states that the stress on fluid layers is directly proportional to the rate of shear strain. The viscous drag force opposing motion depends on the surface area of the cylinder length l and radius r.
The ratio of shear stress to shear rate is a constant, for a given temperature and pressure, and is defined as the viscosity or coefficient of viscosity. We have seen that, in the absence of shear forces, newtons law requires that the. Viscosity is defined as the measure of fluid resistance to the flow of one layer of fluid over adjacent layer. Newtons law of viscosity newtons law of viscosity states that shear stress is directly proportional to velocity gradient du du. Consider a solid cylinder of fluid, of radius r inside a hollow cylindrical pipe of radius r. Newtons law of viscosity, given above, is a constitutive equation like hookes law, ficks law, ohms law. There are many equations that cannot be solved directly and with this method we can get approximations to the solutions to many of those equations. Newtons law of viscosity, newtonian and nonnewtonian. Inertia was best explained by sir isaac newton in his first law of motion. Often expressed as the equation a fnetm or rearranged to fnetma, the equation is probably the most important equation in all of mechanics. The derivation of the hagenpoiseuille equation for laminar flow in straight, circular pipes is based on the following two assumptions.
531 840 128 155 119 657 1008 191 1247 1302 878 454 753 917 781 253 1114 221 366 1496 555 802 967 1322 1458 169 793 1130 321 1097 1277 1433 1333 270 941 544 889 1156 679