![]() ![]() The numerator, in contrast, describes inertial stress recall that the larger the density, the more massive material is, and mass is a measure of inertia. In equation, we see that the denominator represents characteristic shear stress in the flow because it is the product of the viscosity of the fluid and a characteristic velocity gradient obtained by dividing the average velocity by the diameter of the tube. If we multiply the equation both the numerator and theĭenominator by the average velocity V, we get The ratio ν = µ/ρ = is termed the kinematic viscosity. Here, µ is the dynamic viscosity of the fluid, and ρ is the density of the fluid. Re = Inertial force / Viscous force = DV ρ/ µ. The Reynolds number is the ratio of inertial forces to viscous forces. The SI unit for flow rate is =Av, where A is the cross-sectional area of the pipe and v is the magnitude of the velocity.The Reynolds number is a dimensionless number used to categorize the fluids systems in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. Viscosity is the resistance to flow, or how thick a fluid is. From fluid mechanics, for a Newtonian fluid, the shear stress,, on a unit area moving parallel. Here, the shaded cylinder of fluid flows past point P in a uniform pipe in time t. Put simply, the less viscous the fluid is, the greater. 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 coefficient of viscosity is defined as the tangential force F required to maintain a unit velocity gradient between two parallel layers of liquid of unit. The second diagram represents turbulent flow, in which streamlines are irregular and change over time. Fig shows two fluid layers at distance y and. For example, high-viscosity felsic magma will create a tall, steep stratovolcano, because it cannot flow far before it cools, while low-viscosity mafic lava will create a wide, shallow-sloped shield volcano. Viscosity is defined as the measure of fluid resistance to the flow of one layer of fluid over adjacent layer. 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. Viscosity describes a fluids internal resistance to flow and may be thought of as a measure of fluid friction. 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 introduction of viscous forces requires a model to obtain a set of conditions on the flow field to express the viscous stress tensor, ij dPdx2RR2w. The first fluid exhibits a laminar flow (sometimes described as a steady flow), represented by smooth, parallel streamlines. The diagrams in Figure use streamlines to illustrate two examples of fluids moving through a pipe. ![]() It is the constant in this formula that we know as the dynamic viscosity of the. The velocity is always tangential to the streamline. good basic knowledge of fluid mechanics equivalent to the Engineering. This force is a very complicated force that depends on both the properties of the object and the properties of the fluid. A streamline represents the path of a small volume of fluid as it flows. When a solid object moves through a fluid it will experience a resistive force, called the drag force, opposing its motion. Before we can define viscosity, then, we need to define laminar flow and turbulent flow. The colors represent the relative vorticity, a measure of turning or spinning of the air.Īnother method for representing fluid motion is a streamline. The precise definition of viscosity is based on laminar, or nonturbulent, flow. ![]() Notice the circulation of the wind around the eye of the hurricane. Figure 14.24 The velocity vectors show the flow of wind in Hurricane Arthur. ![]()
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