Thursday, January 1, 2015

TI-84+: Windchill Factor, Boiling Point at Various Elevations, Velocity of Seismic Waves

Happy New Year!  Time flies when we are having fun - we are in 2015 - 15 years into the 21st century.  Here's to making 2015 happy and prosperous for all!

Without further ado, here are the first programs for 2015!

Wind-Chill Factor

The equation, provided by NOA 2011, to determine wind chill is:

W = 35.74 + .6215*T – 35.75*V^.16 + .4275*T*V^.16

Where:
T = air temperature (°F)
V = speed of the wind (mph)

Program WINDCHIL
: Input “AIR TEMP IN °F:”, T
: Input “WIND SPEED (MPH):”, V
: 35.75+.6215*T-35.75*V^.16+.4275*T*V^.16→W
: Disp “WIND CHILL FACTOR:”, W

Example 1:
V = 25 mph, T = 50°F.  Result:  W = 42.75596219
V = 40 mph, T = 20°F.  Result:  W = -.9093161248

Source:  Thomas J. Glover.  “Pocket Ref: 4th Ed” – 2012.  Sequoia Publishing, Inc.:  Littleton, CO




Boiling Point at Various Elevations

Using data   from Pocket Ref, the boiling point of water at certain elevations can be estimated by the following equation:

Y » 211.99262 – (1.94802*10^-3)*X + (7.17273*10^-9)*X^2

X = elevation in feet
Y = boiling point of water in °F

Program BOILH20:
: Input “ELEV. IN FEET:”, X
: 211.99262-(1.94802E-3)*X+(7.17273E-9)*X^2→Y
: Disp “APPROX BAIL PT. (°F):”, Y

Examples:
X = elevation (feet)
Y = boiling point (°F)
250
211.5060633
1000
210.0517727
2750
206.6898088


Source:  Thomas J. Glover.  “Pocket Ref: 4th Ed” – 2012.  Sequoia Publishing, Inc.:  Littleton, CO



Velocity of P-Waves and S-Waves

In measuring seismic waves (earthquakes) of p-waves (primary waves) and s-waves (secondary waves), the following equations can be used:

(I)     First Lamé Parameter:
λ = (v*E)/((1+v)*(1-2*v))

Where: 
v = ratio of soil.  The following parameters are stated from the Foundation Engineering Handbook:

Type of Soil
v =
Clay, above the water table
0.4
Saturated Clay, below the water table
0.5
Wet Sand
0.35
Dry Sand or Rock
0.25

E = elasticity of the soil, measured in thousand-feet per pound

(II)   Shear Modulus (modulus of rigidity)
‘μ = E/(1 + v)

(III) Velocity of the P-Wave (feet/second)
P = √((λ+2μ)*g*1000/w)

w = specific soil weight, in pounds per cubic foot
g = Earth’s gravity constant,  g = 32.1740486 ft/s^2

(IV) Velocity of the S-Wave (feet/second)
S = √(μ*1000*g/w)

Program SEISMIC
: Disp “ELASTICITY (1000 LB/FT)”
: Prompt E
: Disp “SPEC. SOIL WEIGHT”, “(LB/FT^3)”
: Prompt W
: Menu(“SOIL TYPE”, “CLAY”, 1, “BELOW H20 TABLE”, 2, “WET SAND”, 3,
“DRY SAND/ROCK”, 4)
: Lbl 1
: .4→V
: Goto 5
: Lbl 2
: .5→V
: Goto 5
: Lbl 3
: .35→V
: Goto 5
: Lbl 4
: .25→V
: Goto 5
: Lbl 5
: (EV)/((1+V)(1-2V))→L
: E/(2(1+V))→M
: √((L+2M)*32174.0486/W)→P
: √(M*32174.0486/W)→S
: Disp “P-WAVE (FT/S)”,P
: Disp “S-WAVE (FT/S)”,S

Example:
Input: 
E = 3000 pounds per square foot
w = 120 pounds per cubic foot
Type of soil: Clay (v=.4)
Output:
P-Wave Velocity » 1312.863186 ft/s
S-Wave Velocity » 535.9741515 ft/s

Sources: 

Hsai-Yang Fang.  “Foundation Engineering Handbook” Springer Science & Business Media.  1990.

 Indrahil Goswami, Ph.D. P.E. “Civil Engineering PE Breadth and Depth, Exam Guide.  2nd Edition” McGraw Hill. 2014

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This blog is property of Edward Shore. 2015.  




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