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Introduction to Fluid Mechanics

Chapter 2

Fundamental Concepts

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© Fox, Pritchard, & McDonald

Main Topics

سیال پیوستگی سرعت میدان تنش میدانویسکوزیته سطحی تنش سیال حرکت بندی دسته

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Fluid as a Continuum

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Velocity Field

نسبی چگالی

مخصوص وزن

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Velocity Field

Consider alsoSteady and Unsteady Flows1D, 2D, and 3D FlowsTimelines, Pathlines, and

Streaklines

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خط :جریان

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مسیر خط

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رگه

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© Fox, Pritchard, & McDonald

داده سرعت میدان برای را مسیر خطبیابید .شده

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© Fox, Pritchard, & McDonald

© Fox, Pritchard, & McDonald

Stress Field

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ViscosityNewtonian Fluids

• Most of the common fluids (water, air, oil, etc.)• “Linear” fluids

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© Fox, Pritchard, & McDonald

ViscosityNon-Newtonian Fluids

• Special fluids (e.g., most biological fluids, toothpaste, some paints, etc.)• “Non-linear” fluids

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© Fox, Pritchard, & McDonald

Viscosity

Non-Newtonian Fluids

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Surface Tension

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Description and Classification of Fluid Motions

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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 annulargap of width a. Obtain an algebraic expression for the viscous torque due to flow in the bottom clearance gap of height b.

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© Fox, Pritchard, & McDonald

A viscometer is built from a conical pointed shaft thatturns in a conical bearing, as shown. The gap between shaftand bearing is filled with a sample of the test oil. Obtain analgebraic expression for the viscosity μ of the oil as a functionof viscometer geometry (H, a, and θ), turning speed ω,and applied torque T. For the data given, find by referring toFigure A.2 in Appendix A, the type of oil for which theapplied torque is 0.325 N m. The oil is at 20C. Hint: Firstobtain an expression for the shear stress on the surface of theconical shaft as a function of z.

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© Fox, Pritchard, & McDonald

© Fox, Pritchard, & McDonald