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Introduction to Fluid Mechanics Chapter 2 Fundamental Concepts © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald Main Topics پیوستگی سیال میدان سرعت میدان تنش ویسکوزیته تنش سطحی دسته بندی حرکت سیال © Fox, Pritchard, & McDonald Fluid as a Continuum © Fox, Pritchard, & McDonald Velocity Field چگالی نسبی وزن مخصوص © Fox, Pritchard, & McDonald Velocity Field Consider also Steady and Unsteady Flows 1D, 2D, and 3D Flows Timelines, Pathlines, and Streaklines © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald :جریان خط © Fox, Pritchard, & McDonald خط مسیر © Fox, Pritchard, & McDonald رگه © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald خط مسیر را برای میدان سرعت داده شده بیابید. © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald Stress Field © Fox, Pritchard, & McDonald Viscosity Newtonian Fluids • Most of the common fluids (water, air, oil, etc.) • “Linear” fluids © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald Viscosity Non-Newtonian Fluids • Special fluids (e.g., most biological fluids, toothpaste, some paints, etc.) • “Non-linear” fluids © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald Viscosity Non-Newtonian Fluids © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald Surface Tension © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald Description and Classification of Fluid Motions © Fox, Pritchard, & McDonald Viscous torque is produced by the annular gap around the inner cylinder. Additional viscous torque is produced by the flat bottom of the inner cylinder as it rotates above the flat bottom of the stationary outer cylinder. Obtain an algebraic expression for the viscous torque due to flow in the annular gap of width a. Obtain an algebraic expression for the viscous torque due to flow in the bottom clearance gap of height b. © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald A viscometer is built from a conical pointed shaft that turns in a conical bearing, as shown. The gap between shaft and bearing is filled with a sample of the test oil. Obtain an algebraic expression for the viscosity μ of the oil as a function of viscometer geometry (H, a, and θ), turning speed ω, and applied torque T. For the data given, find by referring to Figure A.2 in Appendix A, the type of oil for which the applied torque is 0.325 N m. The oil is at 20C. Hint: First obtain an expression for the shear stress on the surface of the conical shaft as a function of z. © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald © Fox, Pritchard, & McDonald
