Submissions:2016/An Engineering Ecosystem

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Developing an Engineering Ecosystem
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Steve Bolman
Equalation LTD Co.
A word about what an Engineering Ecosystem might be built on; a web service providing dimensional analysis based on the unit of measure as metadata attached to scalar data values (float values).

Dimensional analysis is a mathematical device applied in Engineering that facilitates, among other things, the “checking” of calculations by visual inspection without the need to check numeric results. The concept being that most engineering calculations are dimensional, meaning that the arithmetic applied to the ‘numbers’ are also applied to the ‘units’ and if the rules of arithmetic yield a result with the correct unit, then the numeric value of the result is probably also correct.

A simple example of ‘dimensional analysis’ would be as follows;

If I have a glass of water in front of me, and I desire to know the mass of water in the glass, I can measure with a ruler the Inner Diameter (I.D.) of the glass. From this I.D. the cross sectional area may be calculated and the depth of water in the glass measured. With these values and some knowledge of the physical nature of the fluid in the glass (the water) we may determine the mass of water in the glass.

Specific Example;

        1.)    I.D. of Glass (ID)                  = 2.00 in;
        2.)    Cross Sectional Area of Glass (XA)  = ¼π ID²   =   3.14 in²;
        3.)    Depth of water in glass (h)         = 3.00 in;
        4.)    Volume of water in glass (V)        = h * XA = 3.00 in * 3.14 in² = 9.42 in³;
        5.)    Density of water (D)                = 0.036 lbm/in³
        6.)    Mass of water in glass              = V * D = 9.42 in³ * 0.036 lbm/in³ = 0.339 lbm

    • NOTE: this is understood to be a trivial example, deliberately so.

Step 4 illustrates the ‘multiplication of units’ by addition of the exponents in * in² = in³ (no exponent implies the value of ‘1’)

Step 6 shows ‘cancellation units’ in³ * lbm/in³ = lbm

It may be noted that the dimensional metadata is “unit agnostic”, meaning it ignores the unit and ‘sees’ the underlying dimension behind the unit, (see Physical Quantities for discussion what is meant by dimensions). I prefer to use the term dimensionality over dimension to emphasize the broader usage intended, beyond simply…

      a measurement of the size of something in a particular direction, such as the length, width, height, or diameter

The above example displays the utility of dimensional analysis (a checker can see that the inputs to the calculation are length and knows that the function applied to convert diameter to area squares the diameter both the numeric value and unit (in), further knows that density is in units of mass per volume, and I know that the desired result should be in pound mass (lbm). As a checking engineer I can follow the numeric AND unit arithmetic and observe that the result is correct. This is, as noted, a trivial example; it becomes a bit more interesting if considering a Reynolds Number calculation, specifically for flow in a pipe or tube, the Reynolds number may be defined as:

                        (A)              (B)              (C)

Reynolds Number equations per Wikipedia "Reynolds Number"


· DH is the hydraulic diameter of the pipe; its characteristic traveled length, L, (m). · Q is the volumetric flow rate (m3/s) **{length : 3, time : -1} · A is the pipe's cross-sectional area (m2) **{length : 2} · v is the mean velocity of the fluid (m/s) **{length : 1, time : -1} · μ is the dynamic viscosity of the fluid (Pa·s = N·s/m2 = kg/(m·s)) **{length : -1, mass : 1, time : -1} · ν (nu) is the kinematic viscosity (ν = μ/ρ) (m2/s) **{length : 2, time : -1}

· ρ is the density of the fluid (kg/m3) **{length : -3, mass : 1}

    • SI Base units give additional insight into what is meant by dimensionality

The Reynolds number calculation comes in several flavors (A, B, C…), and you select which flavor to use, based on the data you know (the knowns). This decision (A, B or C) is obvious for an engineer; however it is non-trivial for a computer. Here the metadata contributed by the unit of measure gives ‘hints’ to the computer buy attaching dimensionality (via units) as metadata to the known data. By ‘typing’ the data with dimensionality the specific format of the Reynolds number (A, B or C) can be selected, as in example below by matching the pattern present in the dimensionality;

Data Set {scalar : 1.2, length : 3, time : -1} {scalar : 0.67, length : 1} { scalar : 0.89, length : 2, time : -1} { scalar : 0.35, length : 2}

ANSWER = “C” is the equation to use the above data.

Imagine for a moment we don’t know we need a Reynolds Number but we have the above Data Set… and are not sure what to do with it. As will be covered in a moment solving this problem is worth thinking about. In this case we can add to our data set that the desired result is a dimensionless number (without knowing it to be the Reynolds Number), there are ONLY two ways to combine the above data to yield a dimensionless value, the first being a Reynolds Number, and the second being the ‘Inverse of a Reynolds Number’ (which is nonsensical and may be dismissed). In the above case no “Function call” (function = “Reynolds_Number”) is required; it is only required that the Data Set be defined. Given the required data set, the proposed model can provide the Reynolds Number calculation with no function call is required; it may be said to be an eager service.

Pull out a “hydraulic book”, pull out a “Perry’s Handbook of Chemical Engineering” or a “Mark’s Standard Handbook of Mechanical Engineering”, I believe you will be astonished at how frequently the “Function call” is fully defined by the Data Set. Where this condition is not met, we can add that calculations live in a context that includes (per engineering best practice) a narrative description of what is calculated, maybe a sketch and a symbolic and verbose description of the data set. Words and Phrases like “Hydraulic Diameter, Volumetric Flow Rate, Pipe, and viscosity all point to a Fluid Flow problem domain, and these are also fed into the search engine to aid in resolving ambiguous conditions.

By meeting the requirements of an “Eager Service" (the arguments select the function) we can fill a database with functions that represent engineering calculations, that may be queried using the metadata and the domain information gleaned from the calculation notes and user information.

When I talk about an Engineering Ecosystem, I am envisioning a platform where Calculations, Heat and Mass Balances, PFDs, P&IDs, Equipment Data Sheets all reside in a single cloud repository and accessible by teams as required. This then supports online project execution, scheduling, purchasing and logistics.

Many thanks and best regards,

Steve Bolman P.E. Curator of Organism® an Engineering Ecosystem (832) 326-8984

Organism is a registered trademark of Equalation, LLC

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30 min
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  1. Thewellman (talk) 00:28, 27 August 2016 (EDT) I have taught dimensional analysis as a very effective means of giving high-school dropouts the confidence to learn mathematics required for technician certification; and would value an opportunity to compare methods.
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