05-30-2014, 07:55 PM

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)

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)