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 linearity.

For terminal linearity, there is no flexibility allowed in the placement of the straight line in order to minimize the deviations. The straight line must be located such that each of its end-points coincides with the device's actual upper and lower range values. This means that the non-linearity measured by this definition will typically be larger than that measured by the independent, or the zero-based linearity definitions. This definition of linearity is often associated with ADCs, DACs and various sensors.

A fourth linearity definition, absolute linearity, is sometimes also encountered. Absolute linearity is a variation of terminal linearity, in that it allows no flexibility in the placement of the straight line, however in this case the gain and offset errors of the actual device are included in the linearity measurement, making this the most difficult measure of a device's performance. For absolute linearity the end points of the straight line are defined by the ideal upper and lower range values for the device, rather than the actual values. The linearity error in this instance is the maximum deviation of the actual device's performance from ideal.

I. Modeling Elasticity

b. Young's Modulus of Elasticity

numerical constant, named for the 18th-century English physician and physicist Thomas Young, that describes the elastic properties of a solid undergoing tension or compression in only one direction, as in the case of a metal rod that after being stretched or compressed lengthwise returns to its original length. Young's modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression. Sometimes referred to as the modulus of elasticity, Young's modulus is equal to the longitudinal stress divided by the strain. Stress and strain may be described