(50g) Civil Engineering

[Eddie W. Shore]

Mohr's Circle

σ: ALPHA, Right-Shift, S
τ: ALPHA, Right-Shift, U
SQ: x^2

Program MOHR
<< "Shear Stress σx" PROMPT
"Shear Stress σy" PROMPT
"Normal Stress τ" PROMPT
→ X Y T
<< X Y - 2 / SQ T SQ + √
"Radius" →TAG
X Y + 2 / (0,0) +
"Center" →TAG
T 2 * X Y - / ATAN 2 /
"View Angle" →TAG >> >>

Example:
σx = 100
σy = -220
τ = 80

Results:
R ≈ 178.88544
S = -60 (center (-60,0))
θ ≈ 13.28253° ≈ .23183 radians

Horizontal Pipe Discharge

Variables:
X, Y, and D (diameter of the pipe) are in inches. Flow (Q) is calculated in GPM (gallons per minute).

Q ≈ .25974 * π * D^2/4 * X * √( g /(2 * Y))

Where
g = 9.80665 m/s^2 ≈ 386.08858 in/s^2
1 in^3/s ≈ .25974 gal/min

Source:

Gary P. Markey. Lecture 14: Flow Measurement in Pipes. BIE 5300/6300 Lectures
Utah State University - Open Courseware

http://ocw.usu.edu/Biological_and_Irriga...nPipes.pdf

Program HPD
<< "Hose Diameter (in)" PROMPT
"X (in)" PROMPT
"Y (in)" PROMPT
→ D X Y
<< π D SQ * X * 4 / →NUM
386.08858 2 Y * / √ *
.25974 * "Flow (GPM)" →TAG >> >>

Example:
D = 2.5 in
X = 8 in
Y = 4 in

Result:
Flow ≈ 70.85936 Gallons per Minute

Internal Pressure in a Vessel

I = inner radius of the vessel
O = outer radius of the vessel
P = pressure of the water flow
σh = hoop stress

σh = P * (O^2 + I^2)/(O^2 - I^2)

Source: Goswami, Indramil Ph.D. P.E. "All In One Civil Engineering PE Breadth and Depth Exam Guide" 2nd Edition. McGraw Hill: 2012

Program VESSEL
<< "Inner Radius" PROMPT
"Outer Radius" PROMPT
"Pressure" PROMPT
→ I O P
<< O SQ I SQ DUP2
+ UNROT - / P * →NUM
"σh" →TAG >> >>

Example:
O = 3/8 in = .375 in
I = 3/32 in = .09375 in
P = 10 lb/(s*in^2)

Result:
σh ≈ 11.3333 lb/(s*in^2)