Complex Unit Converter and Expression Evaluator






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MikeVV@AnalysisChamp.com

5/14/2009, 7/17/2009, 3/12/2010, 8/26/2011, 1/18/2012, 1/4/2013, 11/17/2013, 7/22/2014

AnalysisChamp.com Expression Evaluator


Description

Convert complex expressions with units properly handled. Enter the value expression and its unit string as formulas. Also enter the desired output unit expression string. The Complex Converter will calculate the value, define the conversion factors for the unit expressions and verify that the desired output unit expression is proper.

The names for all units are provided in AnalysisChamp.com/EEx/AllUnitNames.htm and a shorter list of more common unit names is located in AnalysisChamp.com/EEx/FavUnitNames.htm. Select Examples to jump to a list of sample problems that can be inserted into the input fields. You can type over the inserted text to perform new calculations.

This site can also process all MS VBScript functions. See Microsoft MSDN VBScript Reference and Microsoft Derived Math Functions for specific information.

Check our blog at: AnalysisChamp.com/Wordpress.

A Spreadsheet with added functions can be downloaded from: FreeStyle.xls.


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Expression Builder

The expressions used for calculations can be built using the following menu box selections. Select the INSERT NUMBER link to copy and paste the expression into the converter number field, select INPUT UNITS to copy and paste into the converter unit input field and select OUTPUT UNITS to copy and paste into the converter output unit field.


Unit Selection Links:

Length, Time, Mass, Time, Temperature, Quantity, Luminesence, ElectoMag, Constant, Multiplier, Angle, Area, Energy, Force, Power, Pressure, Velocity, Viscosity, and Volume.

Length Time
Mass Temperature
Quantity Luminesence
ElectoMag Constant
Multiplier Angle
Area Energy
Force Power
Pressure Velocity
Viscosity Volume

Complex Converter - Example Strings (See also: FreeStyle.xls)
MikeVV@AnalysisChamp.com 5/14/2009, 8/26/2011, 1/18/2012, 11/17/2013, 7/22/2014

Examples are given using short function callout versions
(turn word wrap off before copying strings and pasting into expression evaluator)
Each expression string can be copied from the web page by selecting the text and pressing ctrl^C then inserting into the evaluation field and pressing ctrl^V.
The precision of returned values is not more accurate than 6 significant digits.

Example 01 - Temperature Calculations
[Enter Example 01]
What is the absolute temperature, degrees Kelvin, at 32 degrees farenheight (F)?
------
32, DEGF, DEGK
= 273.15

Example 02.01 - Length Conversions
[Enter Example 02.01]
What is the length, in feet, of 200 rods?
------
200, ROD, FT
= 3300 ft

Example 02.02 - Circle Perimeter
[Enter Example 02.02]
What is the length, in feet, of the perimeter of a circle 12 inches in diameter?
------
12, PI*IN, FT
= 3.14158637 ft

Example 02.03 - Circle Area
[Enter Example 02.03]
What is the area, in square feet, of a circle whose diameter is 24 inches?
------
1/4*24^2, PI*IN^2, FT^2
= 3.14158 ft^2

Example 03 - Speed, Torque and Power Calculations
[Enter Example 03]
What is the torque, in pound-feet, of a shaft driving a 10 horsepower load at 3600 revolutions per minute?
Power = torque * speed so torque = power / speed
------
10/3600, HP/RPM, FT*LBF
= 14.6 ft*lbf

Example 04 - Gas Law Calculations
[Enter Example 04]
What is the volume per mole of an ideal gas (like air) at 0 degC (273.15 degK) and atmoshperic pressure?
p*V = n*R*T so V/n = R*T/p
------
Temperature is a biased measurement unit. In this case, if the temperature in degrees Centigrade was used directly it would give erroneous results. First, convert temperature into DEGK...
0, DEGC, DEGK = 273.15, then:
1*273.15/1, RGC*DEGK/ATM, L/MOL
= 22.4 L/Mole

Example 05 - Air Density Calculations
[Enter Example 05]
What is the density of air, in pounds per cubic foot, at 15 degC (288 degK) and
atmospheric pressure of 30.10 inches-mercury?
p*V = n*R*T and mass = moles * grams per mole (gpm) so n/V = p/(R*T) and density = n*gpm/V = p * gpm / (R*T)
------
The temperature needs to be in an absolute measurement system for proper evaluation...
15, DEGC, DEGK = 273.15, then:
30.1*28.8/(1*288), IN[HG]*(GM/MOL)/(RGC*DEGK), LBM/FT^3
= .0763 lbm/ft^3

Example 06 - Propeller Tip Speed Calculations
[Enter Example 06]
What is the tip speed, mach at standard sea level atmosphere, of a 72 inch diameter propeller spinning at 2400 RPM?
V = diameter / 2 * rotational speed
------
72/2*2400, IN*RPM, MACH[S]
= .675 mach

Example 07 - Hydraulic Power Calculations
[Enter Example 07]
What is the hydraulic pressure of a 200 horsepower system with 400 gallons per minute flow rate?
power = pressure * flow rate so pressure = power / flow rate
------
200/400, HP/(GAL/MIN), PSI
= 857 psi

Example 08 - Dynamic Pressure Calculation
[Enter Example 08]
What is the dynamic pressure, in pascals, of an air-stream at 150 knots? Air density is .0775 pounds per cubic foot.
q = 1/2 * rho * V^2
------
1/2*.0775*150^2,(LBM/FT^3)*KNOT^2, PA
= 3696 Pa

Example 09 - Shaft Load with Sheave
[Enter Example 09]
What is the side load on a shaft, in Newtons, with a 200 cm diameter sheave if it carries 30 kW power at 55 Hz?
F = p/(n*r)
------
30/(55*(200/2)), KW/(HZ*CM), N
= 86.8 Newton

Example 10 - Radiated Power
[Enter Example 10]
What is the ideal radiated power per unit area of a body at 3000 degrees R in watts?
q = sigma * T^4
------
The temperature is expressed in absolute units and can be used without a primary conversion (see Example 5):
1*3000^4, SIGMA*DEGR^4, W/M^2
= 4.38E5 W/M^2

Example 11 - Chemical Equivalent - Pounds(mass) to Moles
[Enter Example 11]
How many pounds of caffeine does a 1.35 mole sample weigh? The chemical formula for caffeine is C8-H10-N4-O2.
The formula weight of caffeine is 8*12.01115 + 10*1.00797 + 4*14.0067 + 2*15.9994
------
Addition and subtraction of units must be done carefully because they cannont be mixed within a sum or difference calculation. Checks on the units for each term in such a calculation must be made.
1.35*(8*12.01115+10*1.00797+4*14.0067+2*15.9994), MOL*(GM/MOL), LBM
= .578 lbm

Example 12 - Area of a Circle
[Enter Example 12]
What is the area of a circle, in square feet, if it has a diameter of 2 meter?
Area = pi/4 * Diameter^2
1/4*2^2, PI*M^2, FT^2
= 33.8157 ft^2

Example 13 - Temperature of One Billion Standard Cubic Feet of Ideal Gas at one Atmosphere Pressure
[Enter Example 13]
What is the temperature, in degrees Farenheight, of 1 billion standard cubic feet of an ideal gas at one atmosphere pressure?
Ideal gas law:
p*V = m * RGC * T; solving for T:
T = (m * RGC)/(p * V)
where:
T = temperature, m = quantity (billion standard cubic feet), RGC = universal gas constant, p = pressure and V = volume.
------
The temperature can be returned in biased units (DEGC or DEGF) because the result is converted after evaluation.
(1E9*1)/(1*1), (FT^3*ATM)/(BCF*RGC), DEGF
= 60 degF

Example 14 - Molecular weights with English and Metric Units
[Enter Example 14]
What is the weight, in pico*grains, of a 1/4 inch long string of carbon atoms if each averages 1.5E-08 centimeters in diameter?
Carbon has an atomic weight of 12.01115 grams per mole.
total weight = total length * Weight/Atom * number of Atoms/length
where the weight/atom = formula weight / Avogadro's number
------
.25*(12.01115/1)*(1/1.50E-8), IN*((GM/MOL)/NA)*(1/CM), PICO*GRAIN
= .013 pico*grain

Example 15 - Percent Chemical Composition of a Compound
[Enter Example 15]
What is the percent composition of chlorine in FeCl3? Iron (Fe) weighs 55.847 grams per mole and chlorine (Cl) weighs 35.453 grams per mole based on atomic weight.
Molecule Weight = Fe*1+Cl*3 = (1*(55.847)+3*(35.453)) MOL*(GM/MOL)
Chlorine weight per molecule = (35.453)*3
Cl Percentage = (chlorine weight per molecule)/(molecule weight)
------
3*35.453/(1*55.847+3*35.453), (GM/MOL)/(GM/MOL), CENTI
= 65.6 percent (centi) (centi)

Example 16 - Centrifugal Force
[Enter Example 16]
What is the centrifugal force of a mass of 3.31 lbm rotating at 3000 revolutions per minute (rpm) at a radius of 18 inches?
Centrifugal Force = mass * radius * rotation speed ^ 2
------
3.31*18*3000^2, LBM*IN*RPM^2, LBF
= 15230 lbf

Example 17 - Linear Interpolator
[Enter Example 17]
What is the interpolated estimate for y where y=f(x) at x=.25 when y1=2.5 at x1=1.0 and y2=7.5 at x2=1.5?
The linear interpolation formula is: y = (x-x1)*(y2-y1)/(x2-x1)+y1
------
(.25-1.0)*(7.5-2.5)/(1.5-1.0)+2.5, item, item
= -5.0

Example 18 - Heat Conduction thru Wall
[Enter Example 18]
How much energy (in watts) is transferred through a concrete wall 8 feet tall x 12 feet wide x 8 inches thick when the temperature difference is 25 degrees F? The coefficient of thermal conductivity for concrete is .5 BTU*ft/(hr*ft^2*degR)
Heat flow Rate = (Coefficient of Thermal Conductivity * Area * Temperature difference)/thickness
------
(.5*(8*12)*25)/8, ((BTU*ft/(hr*ft^2*degR))*(ft*ft)*degR)/in, W
= 527.5 W

Example 19 - Moment of Inertia (MoInertia) Calculation
[Enter Example 19]
What is the moment of inertia (MoInertia) of a rectangular cross section 12 inch tall x 3.5 inch wide?
MoInertia = 1/12 * base * height^3 = 1/12 * 3.5 in * 12^3 in^3
------
1/12*3.5*12^3, IN*IN^3, IN^4
= 504 IN^4

Example 20 - Bending Stress Calculation
[Enter Example 20]
What is the bending stress at the extreme edge of a beam of rectangular cross section 12 inch tall x 3.5 inch wide?
Stress = Moment * Extreme Fiber / (MoInertia)
Moment = 250 lbf * 8 ft
Extreme Fiber = 12 in / 2
MoInertia = 1/12 * base * height^3 = 1/12 * 3.5 in * 12^3 in^3
------
(250*8)*(12/2)/(1/12*3.5*12^3), (LBF*FT)*IN/(IN*IN^3), W
= 285.7 PSI

Example 21 - I-Beam Moment of Inertia (MoInertia) Calculation
[Enter Example 21]
What is the moment of inertia (MoInertia) of a W14x30 steel I-Beam with 13.86 inch height, 6.73 inch wide flanges, .27 inch thick web and .38 inch thick flanges?
MoInertia = 1/12*((base*height^3)-((base-tw)*(height-2*tf)^3))
= 1/12*((6.73*13.86^3)-((6.73-.27)*(13.86-2*.38)^3))
------
(250*8)*(12/2)/(1/12*3.5*12^3), (LBF*FT)*IN/(IN*IN^3), W
= 289.0 IN^4

Example 22 - Radius of Gyration Calculation
[Enter Example 22]
What is the radius of gyration of a W14x30 steel I-Beam with 13.86 inch height, 6.73 inch wide flanges, .27 inch thick web and .38 inch thick flanges?
Radius of Gyration, k = (MoInertia/Area)^(1/2)
Area = (13.86-2*.38)*.27+2*(6.73*.38)
= 8.652 in^2 MoInertia = 1/12*((base*height^3)-((base-tw)*(height-2*tf)^3))
= 1/12*((6.73*13.86^3)-((6.73-.27)*(13.86-2*.38)^3))
= 289.0 in^4
------
(289.0/8.652)^(1/2), (IN^4/IN^2)^(1/2), IN
= 5.78 IN

Example 23 - Column Euler Stress Calculation
[Enter Example 23]
What is the Euler buckling stress, SigmaE, in a steel W14x30 I-Beam column 10 feet tall? (See previous example for radius of gyration, k = 5.78 IN.) The modulus of elasticity, E, is 2.9E7 PSI.
SigmaE = (PI^2 * E) / (Length / k)^2
------
((3.14159^2)*2.9E7)/((10/5.78)^2), (PSI)/((FT/IN)^2), PSI
= 664031 IN^2

Example 24 - ArcCos Calculation
What is the inverse cosine (ArcCos) of (.25*1000)/(36000*8.65-1000)?
The ArcCos function is derived from VBScript Atn() and Sqr() functions. It is found at the Microsoft MSDN VBScript Reference - Derived Math Functions website.
[Enter X]
------
(.25*1000)/(36000*8.65-1000), ITEM, ITEM
X = (.25*1000)/(36000*8.65-1000) = 8.0541234E-04

Then, the Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1),
Substituting in gives:
[Enter ArcCos(X)]
Arccos(X) = Atn(-(8.0541234E-04) / Sqr(-(8.0541234E-04) * (8.0541234E-04)+1)) + 2*Atn(1)
------
Atn(-(8.0541234E-04)/Sqr(-(8.0541234E-04)*((8.0541234E-04)+1)))+2*Atn(1), ITEM, ITEM
= 1.5700

MikeVV@AnalysisChamp.com