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01s Handbook rsurement, Proc. ncentration and uid Mechanics II, 30 Chapter 30 in CRC Press' "The MEASUREMENT, INSTRUMENTATION, AND SENSORS HANDBOOK" (c) 1999 by CRC Press LLC Viscosity Measurement VIE Heat Transfer G.E. Leblanc McMaster University 1um, 1977. In, Portugal, 1982, R.A. Secco The University of Western Ontario ) 1993. M. Newtonian and Non-Newtonian Fluids Dimensions and Units of Viscosity Viscometer Types Capillary Viscometers Falling Body Methods Oscillating Method Ultrasonic Methods l l M. Kostic the laser Doppler 30.1 Shear Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... ..... 30-l Northern Illinois University l l l l 3O.1 Shear Viscosity V. Otugen, eds., or enhanced power rner, M. Kawahashi, city measurement by systems, Exp. Fluids, iheory and numerical An important mechanical property of fluids is viscosity. Physical systems and applications as diverse as fluid flow in pipes, the flow of blood, lubrication of engine parts, the dynamics of raindrops, volcanic eruptions, planetary and stellar magnetic field generation, to name just a few, all involve fluid flow and are controlled to some degree by fluid viscosity. Viscosity is defined as the internal friction of a fluid. The microscopic nature of internal friction in a fluid is analogous to the macroscopic concept of mechanical friction in the system of an object moving on a stationary planar surface. Energy must be supplied (1) to overcome the inertial state of the interlocked object and plane caused by surface roughness, and (2) to initiate and sustain motion of the object over the plane. In a fluid, energy must be supplied (1) to create viscous flow units by breaking bonds between atoms and molecules, and (2) to cause the flow units to move relative to one another. The resistance of a fluid to the creation and motion of flow units is due to the viscosity of the fluid, which only manifests itself when motion in the fluid is set up. Since viscosity involves the transport of mass with a certain velocity, the viscous response is called a momentum transport process. The velocity of flow units within the fluid will vary, depending on location. Consider a liquid between two closely spaced parallel plates as shown in Figure 30.1. A force, F, applied to the top plate causes the fluid adjacent to the upper plate to be dragged in the direction of F. The applied force is communicated to neighboring layers of fluid below, each coupled to the driving layer above, but with diminishing magnitude. This results in the progressive decrease in velocity of each fluid layer, as shown by the decreasing velocity vector in Figure 30.1, away from the upper plate. In this system, the applied force is called a shear (when applied over an area it is called a shear stress), and the resulting deformation rate of the fluid, as illustrated by the velocity gradient dUx /dz, is called the shear strain rate, yzx. The mathematical expression describing the viscous response of the system to the shear stress is simply: (30.1) where T:,,, the shear stress, is the force per unit area exerted on the upper plate in the x-direction (and hence is equal to the force per unit area exerted by the fluid on the upper plate in the x-direction under the assumption of a no-slip boundary layer at the fluid-upper plate interface); dU,ldz is the gradient of the x-velocity in the z-direction in the fluid; and η is the coeficient of viscosity. In this case, because one is concerned with a shear force that produces the fluid motion, r\ is more specifically called the shear 0 by CRC Press LLC 30- 1 I .es THE MEASUREMENT, INSTRUMENTATION, AND SENSORS lZrilliams D. Poularikas Jebster HAN DB OOK Editor-in-Chief John G. Webster CRC PRESS Publishedd in Cooperation with IEEE Press