Chapter 8 Introduction and Basic Fluid Properties

Fluid Mechanics Fluid Mechanics is concerned with the behavior of fluids at rest and in motion Distinction between solids and fluids: -A solid is “hard” and not easily deformed. -A fluid is “soft” and deforms easily. -Fluid is a substance that alters its shape in response to any force however small, that tends to flow or to conform to the outline of its container, and that includes gases and liquids and mixtures of solids and liquids capable of flow. -A fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude. - A shearing stress is created whenever a tangential force acts on a surface.

Fluid and Solid When a constant shear force is applied: Solid deforms or bends (ie can resists a shear stress) Fluid continuously deforms (can not resists shear stress)

Simple Flows Flow between a fixed and a moving plate Fluid in contact with the plate has the same velocity as the plate u = x-direction component of velocity u=U Moving plate Fixed plate y x U u=0 b Fluid

Simple Flows Flow through a long straight pipe, fluid in contact with the pipe wall has the same velocity as the wall u = x-direction component of velocity r x R U Fluid

Fluidity of Fluid When the force F is applied to the upper plate, it will move continuously with a velocity U. The fluid “sticks” to the solid boundaries and is referred to as the NON-SLIP conditions. The fluid between the two plates moves with velocity u=u(y) that would be assumed to vary linearly, u=Uy/b. In such case, the velocity gradient is du / dy = U / b. F

Fluidity of Fluid If the shearing stress is increased by F, the rate of shearing strain is increased in direct proportion, The common fluids such as water, oil, gasoline, and air, the shearing stress and rate of shearing strain can be related with a relationship

Shear in Different Fluids Shear-stress relations for different types of fluids Newtonian fluids: linear relationship Slope of line (coefficient of proportionality) is “viscosity”

Viscosity Newton’s Law of Viscosity Viscosity Units Water (@ 20oC) m = 1x10-3 N-s/m2 Air (@ 20oC) m = 1.8x10-5 N-s/m2 Kinematic viscosity

Kinematic Viscosity Defining kinematic viscosity The dimensions of kinematic viscosity are L2/t. The units of kinematic viscosity in BG system are ft2/s and SI system are m2/s. In the CGS system, the kinematic viscosity has the units is called a stoke, abbreviated St. It is sometimes expressed in terms of centiStokes (cSt). 1 St = 1 cm2·s−1 = 10−4 m2·s−1. 1 cSt = 1 mm2·s−1 = 10−6m2·s−1. Water at 20 °C has a kinematic viscosity of about 1 cSt.

Example Newtonian Fluid Shear Stress 1/3

Example Newtonian Fluid Shear Stress 2/3

Example Newtonian Fluid Shear Stress 3/3

Dimension and Unit of Viscosity The dimension of μ : Ft/L2 (FT/L2) or M/Lt. The unit of μ: In BG : lbf . s/ft2 or slug/(ft.s) In SI : kg/(m . s) or N . s/m2 or Pa . s In the Absolute Metric: poise=1g/(cm . s) The primary parameter correlating the viscous behavior of all Newtonian fluids is the dimensionless Reynolds number (Re) ρuD uD Re=---------= -------- μ υ u is the average velocity, D is the diameter and υ is the Kinematic viscosity

Generally, the first thing a fluids engineer should do is estimate the Reynolds number range of the flow under study. Very low Re indicates viscous creeping motion, where inertia effects are negligible. Moderate Re implies a smoothly varying laminar flow. High Re probably spells turbulent flow, which is slowly varying in the time-mean but has superimposed strong random high-frequency fluctuations.. For a given value of u and D in a flow, these fluids exhibit a spread of four orders of magnitude in the Reynolds number

Example Viscosity and Dimensionless Quantities

Example Viscosity and Dimensionless Quantities