Science Elasticity

TERM PAPER

IN

SCIENCE IV

_Mr. Michael Edar_ _Reynaldo B. Castro Jr._

Teacher Student

Fourth Year Section Seven

Elasticity

I. Modeling Elasticity

a. Linear Elasticity

b. Young’s Modulus of Elasticity

c. Approximation

d. Elasticity Tenser

II. Transition to Inelasticity

a. Stress-Strain Curves

b. Non-Newtonian Fluids

c. Viscoelastic Fluids

d. Viscosity

III. Fluids Physics

a. Newtonian Fluid

b. Velocity Gradient

c. The Centinuum Hypothesis

d. Molecules

e. Statistical Mechanics

f. Knudsen Number

g. Mean Free

h. Unity

IV. Navier Stokes Equation

a. Momentum

b. Acceleration

c. Friction

d. Computational Fluid Dynamics

V. Newtonian vs. Non-Newtonian Fluids

a. Newtonian Fluids

b. Perpendicular

c. Velocity Gradient

d. Non-Newtonian Fluid

e. Fluid Appears Thinners

I. Modeling Elasticity

a. Linear Elasticity

There are three basic definitions for integral linearity in common use: independent linearity, zero-based linearity, and terminal, or end-point, linearity. In each case, linearity defines how well the device's actual performance across a specified operating range approximates a straight line. Linearity is usually measured in terms of a deviation, or non-linearity, from an ideal straight line and it is typically expressed in terms of percent of full scale, or in ppm (parts per million) of full scale. Typically, the straight line is obtained by performing a least-squares fit of the data. The three definitions vary in the manner in which the straight line is positioned relative to the actual device's performance. Also, all three of these definitions ignore any gain, or offset errors that may be present in the actual device's performance characteristics.

Many times a device's specifications will simply refer to linearity, with no other explanation as to which type of linearity is intended. In cases where a specification is expressed simply as linearity, it is assumed to imply independent linearity.

Independent linearity is probably the most commonly-used linearity definition and is often found in the specifications for DMMs and ADCs, as well as devices like potentiometers. Independent linearity is defined as the maximum deviation of actual performance relative to a straight line, located such that it minimizes the maximum deviation. In that case there are no constraints placed upon the positioning of the straight line and it may be wherever necessary to minimize the deviations between it and the device's actual performance characteristic.

Zero-based linearity forces the lower range value of the straight line to be equal to the actual lower range value of the device's characteristic, but it does allow the line to be rotated to minimize the maximum deviation. In this case, since the positioning of the straight line is constrained by the requirement that the lower range values of the line and the device's characteristic be coincident, the non-linearity based on this definition will generally be larger than for independent