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(Bug?) HP48 Equation Library
02-12-2017, 03:36 PM (This post was last modified: 02-12-2017 04:11 PM by Han.)
Post: #1
(Bug?) HP48 Equation Library
So in the process of creating a data file to replicate the HP48 Equation Library, I noticed that there were possibly bugs in some of the formulas.

In the Advanced User's Guide (for the HP48), Section 4-26 shows a formula that is part of the Flow with Full Pipes system of equations.
\[ \rho \cdot \underbrace{\left(\frac{\pi \cdot D^2}{4}\right) }_\text{Area} \cdot v_\text{avg} \cdot \left( \frac{\Delta P}{\rho} + g \cdot \Delta y + v_\text{avg}^2 \cdot \left( 2 \cdot f \cdot \frac{L}{D} + \frac{\Sigma K}{2} \right) \right) = W \]
The problem is that \( f \) is never defined anywhere. Instead, there is reference to an \( \epsilon \) (roughness) that is defined as a variable, but never used.

I don't know anything about hydraulics, so I have no idea if this formula is correct. But as is, the system cannot solve for all variables (namely \( \epsilon \)). Moreover, many terms may not be solvable because it never sets up the variable \( f \) (because it is not defined for the system). There are a few other systems like this. As another example, Cantilever Moment has the equation
\[ Mx = P \cdot (x-a) + M - \frac{W}{2}\cdot (L^2-2\cdot L \cdot x + x^2) \]
This system defines a variable \( c \) that is never used in this formula. Are there any engineers and/or physicists here who can shed some light on these formulas?

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02-12-2017, 10:35 PM (This post was last modified: 02-12-2017 10:43 PM by SlideRule.)
Post: #2
RE: (Bug?) HP48 Equation Library
(02-12-2017 03:36 PM)Han Wrote:  ... there were possibly bugs in some of the formulas ... for the HP48 ... a variable c that is never used in this formula ...

Often (for better or worse) technical writers assume the reader initiates a topic perusal at an unspecified but assumed beginning. For c, the variable is defined at the beginning of the Chapter (4) on page 4-1 under Columns and Beams (1), Variable Names and Descriptions as c = distance to applied moment (beams).

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02-13-2017, 12:25 AM
Post: #3
RE: (Bug?) HP48 Equation Library
(02-12-2017 10:35 PM)SlideRule Wrote:  
(02-12-2017 03:36 PM)Han Wrote:  ... there were possibly bugs in some of the formulas ... for the HP48 ... a variable c that is never used in this formula ...

Often (for better or worse) technical writers assume the reader initiates a topic perusal at an unspecified but assumed beginning. For c, the variable is defined at the beginning of the Chapter (4) on page 4-1 under Columns and Beams (1), Variable Names and Descriptions as c = distance to applied moment (beams).

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SlideRule

I understood, from reading the AUR, that the variable \(c \) was relevant to the category. However, that variable is completely irrelevant in the second formula above. But because it sets up such a variable, one cannot use the "solve all" and in some cases the result is a bad guess message. Then there is the issue of \( \epsilon \) being clearly explained in the AUR but not appearing the system involving the first formula.

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02-13-2017, 01:14 AM (This post was last modified: 02-13-2017 01:30 AM by Mark Hardman.)
Post: #4
RE: (Bug?) HP48 Equation Library
(02-12-2017 03:36 PM)Han Wrote:  The problem is that \( f \) is never defined anywhere. Instead, there is reference to an \( \epsilon \) (roughness) that is defined as a variable, but never used.

This is the FANNING function which calculates the Fanning friction factor (\(f\)).

From HP 82211A HP Solve Equation Library Application Card Owner's Manual, page 193:

Quote:The FANNING(\(\epsilon\)/D, Re) function calculates the Fanning friction factor \(f\),
a correction factor for the frictional effects of certain fluid flows (constant
temperature, cross-section, velocity, and viscosity-typical pipe flow).
\(\epsilon\)/D is the relative roughness - the ratio of the conduit roughness to its
diameter. Re is the Reynolds number (conduit diameter x average velocity
x fluid density / fluid viscosity). The function uses different computation
routines for laminar flow (Re <= 2100 and turbulent flow (Re > 2100.
\(\epsilon\)/D and Re must be real numbers or unit objects that reduce to
dimensionless numbers. \(\epsilon\)/D and Re must be greater than 0.

FANNING takes \(\epsilon\)/D from level 2 and Re from level 1, and it returns the
Fanning friction factor in level 1.

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02-13-2017, 01:15 AM
Post: #5
RE: (Bug?) HP48 Equation Library
(02-13-2017 12:25 AM)Han Wrote:  I understood, from reading the AUR ... clearly explained in the AUR but not appearing the system involving the first formula.
Han, no insult intended. I am unaware of your level of expertise and simply sought to begin at a simple level and progress to the more complex. I do NOT have my 48 up and running (at the moment they are moth-balled).
Have you used the SUMMATION of FORCES for the individual formulas for a moment at location x from point, uniform and moment applied loads on a cantilever beam? Do you have access to ROARK or other structural formula references? The formula in the 48 manual seems to be just such a simplified summation, agreed?

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02-13-2017, 01:39 AM (This post was last modified: 02-13-2017 02:04 AM by Han.)
Post: #6
RE: (Bug?) HP48 Equation Library
(02-13-2017 01:15 AM)SlideRule Wrote:  
(02-13-2017 12:25 AM)Han Wrote:  I understood, from reading the AUR ... clearly explained in the AUR but not appearing the system involving the first formula.
Han, no insult intended. I am unaware of your level of expertise and simply sought to begin at a simple level and progress to the more complex. I do NOT have my 48 up and running (at the moment they are moth-balled).
Have you used the SUMMATION of FORCES for the individual formulas for a moment at location x from point, uniform and moment applied loads on a cantilever beam? Do you have access to ROARK or other structural formula references? The formula in the 48 manual seems to be just such a simplified summation, agreed?

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SlideRule

No offense taken and I do appreciate any and all help on the formulas. (I was merely explaining what I had quite literally just learned in the AUR.) My level of expertise is below novice when it comes to this formula. However, I am approaching this from the point of view of simply seeing a closed system of equations -- in this case, just one -- for which a variable has been declared but never used. Reading the manual has enabled me to understand what the variables stand for. But for me, this is not an attempt to actually solve anything, or use the formula for anything meaningful. On the contrary, I am merely trying understand why each variable/parameter is necessary and used (or not used) in a formula. In simplest terms, it is as if I declared (and defined the meaning of) the variables x, y, and z and my system is 2x+3y=1 and x-y=7. Anyone would wonder what the purpose of z was given that it does not appear in this closed system.

The "system" in the equation library is literally that one formula. So all on its own, the \( c \) seems extraneous to me.

I confess I know nothing about hydraulics. However, if \( c \) were somehow a value inherent/hidden in the other variables, then this would make sense. Is this perhaps what my deficiency in hydraulics knowledge is preventing me to understand?

Mark Hardman's comment about the Fanning function gives me a good place to do some research. The Fanning function seems to be where the \( \epsilon \) might be involved.

EDIT: Going back to and re-reading the chapter where the first formula, I now see a reference to Fanning -- not sure how I completely missed the large, capital letters Undecided -- but I am still stumped on the \( c \)

EDIT2: Ok, so it looks like the \( f \) in the first formula is FANNING(\(\epsilon / D, Re\) ) where the Reynolds constant is calculated as \( Re = D\cdot v_\text{avg} \cdot \rho / \mu \). The manual says that the Fanning function essentially uses two formulas depending on the whether Re is larger or smaller than 2100. So what are these two formulas?

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02-13-2017, 02:50 AM (This post was last modified: 02-13-2017 02:54 AM by Mark Hardman.)
Post: #7
RE: (Bug?) HP48 Equation Library
(02-13-2017 01:39 AM)Han Wrote:  The "system" in the equation library is literally that one formula. So all on its own, the \( c \) seems extraneous to me.

It would look like the inclusion of c in certain beam equations is superfluous--only being used in Simple Deflection and Simple Slope.

(02-13-2017 01:39 AM)Han Wrote:  EDIT2: Ok, so it looks like the \( f \) in the first formula is FANNING(\(\epsilon / D, Re\) ) where the Reynolds constant is calculated as \( Re = D\cdot v_\text{avg} \cdot \rho / \mu \). The manual says that the Fanning function essentially uses two formulas depending on the whether Re is larger or smaller than 2100. So what are these two formulas?

For non-turbulent flow (Re<=2100), the function returns \(16/Re\). \(\epsilon / D\) is not even considered.

For turbulent flow (Re>2100), it looks like the function is using the equation (implicit in \(f\)) defined in this Wikipedia article: Fanning friction factor.

I lack your obvious skill with Latex, otherwise I would reproduce the formula here. I only tested a few data points (4) but all agreed with the Wikipedia article.

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02-13-2017, 02:59 AM
Post: #8
RE: (Bug?) HP48 Equation Library
Thanks, Mark! This helps greatly. It makes me wonder if the \( c \) in the other equation is similarly imbedded in another parameter/variable/function.

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02-13-2017, 03:10 AM
Post: #9
RE: (Bug?) HP48 Equation Library
(02-13-2017 02:59 AM)Han Wrote:  Thanks, Mark! This helps greatly. It makes me wonder if the \( c \) in the other equation is similarly imbedded in another parameter/variable/function.

Using the example solution on page 59 of the HP Solve Equation Library manual, I get the same result for \( Mx \) regardless of the value specified for \( c \).

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02-13-2017, 05:11 AM
Post: #10
RE: (Bug?) HP48 Equation Library
(02-13-2017 02:50 AM)Mark Hardman Wrote:  Fanning friction factor.

Just to be extremely sure, you're referring to the bottom-most formula involving A and B, yes? I wonder why they chose to have the term \( (2.457 \ln( \text{blah}^{-1}))^{16} \) when it would just simplify to \( ( 2.457 \ln(\text{blah}))^{16} \) using the properties of logarithms.

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02-13-2017, 04:03 PM (This post was last modified: 02-13-2017 04:28 PM by Vtile.)
Post: #11
RE: (Bug?) HP48 Equation Library
(02-13-2017 05:11 AM)Han Wrote:  
(02-13-2017 02:50 AM)Mark Hardman Wrote:  Fanning friction factor.

Just to be extremely sure, you're referring to the bottom-most formula involving A and B, yes? I wonder why they chose to have the term \( (2.457 \ln( \text{blah}^{-1}))^{16} \) when it would just simplify to \( ( 2.457 \ln(\text{blah}))^{16} \) using the properties of logarithms.

It might be typically written in the format as it is in equation library, that would be the simplest answer. Engineers aren't necessary mathematicians and do not run after extreme "simplification" in formulas if this means that its "readapility" (aka ability to mirror in practice) suffers. Some fields of engineering are also extremely conservative, what comes how things are done and what formulas are used.

Simple examples are Pi*D and (Pi*D^2)/4 which are in some areas of engineering much more usefull in that format than writing with r as in mathematic is customory. That comes directly from the fact we usually measure diameter and not radius ie. with micrometer.

I myself do not know (pretty much) nothing about hydraulics.
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02-13-2017, 05:31 PM
Post: #12
RE: (Bug?) HP48 Equation Library
(02-13-2017 03:10 AM)Mark Hardman Wrote:  Using the example solution on page 59 of the HP Solve Equation Library manual, I get the same result for \( Mx \) regardless of the value specified for \( c \).

Han
The value of c is most definitely used to calculate and plot the TOTAL MOMENT at point x on cantilever beam of length L. The value of c in relation to x indicates WHEN the moment at c contributes to the total moment at the point under consideration, x.
I've attached a PDF output for a cantilever beam analysis to facilitate this discussion. The discontinuity in the MOMENT CURVE at point 4 stems from the moment applied at point 4. However, if the moment is applied at point 1, the discontinuity will shift to point 1. and the value of the moment at point 2 will be reduced (or increased depending on the SIGN of the applied MOMENT) accordingly.
I'm uncertain HOW the HP-48 queries for the position value of an applied moment since my 48's are currently in storage so I can NOT address this line of discussion. The given equation seems to omit the relevance of the position (c) of an applied moment but ... the correlation of the actual algorithm and the equation is implied for civil, mechanical, structural etc. engineers.

.pdf  BeamAnal.pdf (Size: 39.65 KB / Downloads: 13)

Again, not knowing your expertise nor the frequency of exposure to Statics, I hope this is helpful and furthers useful discussion.

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02-13-2017, 06:08 PM
Post: #13
RE: (Bug?) HP48 Equation Library
(02-13-2017 05:31 PM)SlideRule Wrote:  
(02-13-2017 03:10 AM)Mark Hardman Wrote:  Using the example solution on page 59 of the HP Solve Equation Library manual, I get the same result for \( Mx \) regardless of the value specified for \( c \).

Han
The value of c is most definitely used to calculate and plot the TOTAL MOMENT at point x on cantilever beam of length L. The value of c in relation to x indicates WHEN the moment at c contributes to the total moment at the point under consideration, x.
I've attached a PDF output for a cantilever beam analysis to facilitate this discussion. The discontinuity in the MOMENT CURVE at point 4 stems from the moment applied at point 4. However, if the moment is applied at point 1, the discontinuity will shift to point 1. and the value of the moment at point 2 will be reduced (or increased depending on the SIGN of the applied MOMENT) accordingly.
I'm uncertain HOW the HP-48 queries for the position value of an applied moment since my 48's are currently in storage so I can NOT address this line of discussion. The given equation seems to omit the relevance of the position (c) of an applied moment but ... the correlation of the actual algorithm and the equation is implied for civil, mechanical, structural etc. engineers.


Again, not knowing your expertise nor the frequency of exposure to Statics, I hope this is helpful and furthers useful discussion.

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SlideRule

This is definitely helpful. I am also currently reviewing these formulas here: http://www.awc.org/pdf/codes-standards/p...s-0710.pdf

It's been a while since I've done statics so I have a lot of brushing up to do.

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02-13-2017, 11:29 PM
Post: #14
RE: (Bug?) HP48 Equation Library
(02-12-2017 03:36 PM)Han Wrote:  There are a few other systems like this. As another example, Cantilever Moment has the equation
\[ Mx = P \cdot (x-a) + M - \frac{W}{2}\cdot (L^2-2\cdot L \cdot x + x^2) \]
This system defines a variable \( c \) that is never used in this formula. Are there any engineers and/or physicists here who can shed some light on these formulas?


This equation might be better understood if the AUR authors had used a subscript for Mx, and had also called it "bending moment" rather than "internal moment". It looks like they mean M*x, but they do not. Mx is the bending moment at any point along the beam. It is the sum of the external forces and moments acting on the beam on one side of the section. The variable "c" is not needed for this equation because wherever the applied moment "M" acts, the effect on the internal bending moment on that side of the beam is the same.

The rest of the terms are just summing the moments resulting from external point loads \[ P \cdot (x-a) \] and the internal weight distribution \[ \frac{W}{2}\cdot (L-x)^2 \]
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02-14-2017, 12:13 AM
Post: #15
RE: (Bug?) HP48 Equation Library
(02-13-2017 11:29 PM)Brad Barton Wrote:  This equation might be better understood if ... "c" is not needed for this equation ... The rest of the terms are just summing the moments resulting from external point loads \[ P \cdot (x-a) \] and the internal weight distribution \[ \frac{W}{2}\cdot (L-x)^2 \]

Problem is, the authors DO provide a value for c and then provide an equivalency for a total MOMENT at point x as a SUM of applied point, distributed AND moment LOADS.
Still, there are differing possible interpretations.

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02-14-2017, 12:45 AM (This post was last modified: 02-14-2017 12:52 AM by Brad Barton.)
Post: #16
RE: (Bug?) HP48 Equation Library
(02-14-2017 12:13 AM)SlideRule Wrote:  Problem is, the authors DO provide a value for c and then provide an equivalency for a total MOMENT at point x as a SUM of applied point, distributed AND moment LOADS.
Still, there are differing possible interpretations.

This is only semantics, but I don't see a VALUE for c anywhere; only a definition of the variable and a graphic representation. Perhaps the authors only intended to show that the location of the applied moment's action is immaterial since it appears in none of the equations.

I won't pretend to know their intentions, so this is only a guess.

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02-14-2017, 01:30 AM
Post: #17
RE: (Bug?) HP48 Equation Library
(02-14-2017 12:45 AM)Brad Barton Wrote:  ... I don't see a VALUE for c anywhere; only a definition of the variable and a graphic representation...
My apologies - see attached PDF for the source of this discussion and the subsequent references to variables and assigned values. This should have been included earlier in the discussion for those who might not have access to the 48 Advanced User Reference Manual.
.pdf  HP48 AURM Page 4-8 Equation Reference.pdf (Size: 142.38 KB / Downloads: 7)
The yellow highlights are the items of interest. I am in complete agreement with respect to 'knowing' the authors intent; beyond my skills as well. Your interpretation is as valid as any.

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02-14-2017, 02:20 AM (This post was last modified: 02-14-2017 02:29 AM by Brad Barton.)
Post: #18
RE: (Bug?) HP48 Equation Library
Ah, I see your point regarding c being given a value. I was only looking at the variable and equation list in the 48 itself.

The confusion may be rooted in the difference between external (applied) moments and internal bending (reaction) moments. In the beam analysis print outs that you provided, you were able to produce a change in the external moment distribution by changing the value for c.

Note however that the graph of the shear values inside the beam did not change. Since shear is dM/dx, it is apparent from the shear plot that the internal or bending moments inside the beam did not change even though the the location of the applied external moment did.

The cantilever beam equations provided in the equation library calculate deflection, slope, (internal) moments, and shear; none of which appear to be influenced by the the position of an applied (external) moment.
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02-14-2017, 02:41 AM
Post: #19
RE: (Bug?) HP48 Equation Library
Han

Does this help?

Brad-thanks for the exchange & joining in. For what my small opinion is worth, I concur.

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02-14-2017, 03:09 AM
Post: #20
RE: (Bug?) HP48 Equation Library
(02-14-2017 01:30 AM)SlideRule Wrote:  My apologies - see attached PDF for the source of this discussion and the subsequent references to variables and assigned values. This should have been included earlier in the discussion for those who might not have access to the 48 Advanced User Reference Manual.
The yellow highlights are the items of interest. I am in complete agreement with respect to 'knowing' the authors intent; beyond my skills as well. Your interpretation is as valid as any.

c is defined on page 4-1 as the Distance (from the 'wall') to the applied Moment (M), whereas Mx is the Bending Moment at distance x along the beam.

Authors could have chosen less confusing symbology.

c does matter to understand the externally applied Moment although it is not used in the core Bending Moment calculation. Basically, if c is less than x or greater than x determines the role of the applied moment in the overall calculation. In the example, try plugging-in different values of c while holding all other variables constant and you will see the resulting Mx changes when c exceeds x.

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