Swiss Micros DM41X and Casio fx-CG 50: Minor Head Loss

Swiss Micros DM41X and Casio fx-CG 50: Minor Head Loss

Introduction

When a fluid, such as water, is flowing in a pipe system, energy is lost from the flow due to friction. This loss is known as head loss. The equation presented here is an equation to determine head loss occurring in pipe bends and joints (entrances and exits), which is categorized as minor loss. Minor losses are typically summarized with major losses to determine total head loss.

A formula for minor head loss is stated as:

h = C * v^2 / (2 * g)

where:

h = head loss (m)

C = coefficient

v = velocity of the fluid (m/s)

g = Earth’s gravity = 9.80665 m/s^2 (2 * g = 19.6133 m/s^2)

C = head loss coefficient (see table below)

Type # for C	Value
1. Sharp Exit	1
2. Protruding Entrance	0.8
3. Sharp Entrance	0.5
4. Round Entrance	0.1

If we fit the above table like so:

Type # for C	Value
1	1
2	0.8
3	0.5
4	0.1

Fortunately, the data above (and only the data above) can fit into the quadratic equation:

y = -0.05 * x^2 – 0.05 * x + 1.1 = -0.05 * (x^2 + x) + 1.1

where x is the type number and y is the corresponding coefficient. The assignment of type numbers is arbitrarily.

In the code for the DM41X, I use the polynomial to grab the required coefficient of the user’s choice, mapping choice 1 to C =1 for sharp exit, mapping choice 2 to C = 0.8 for protruding entrance, and so on. I got really lucky because the quadratic equation presented a perfect fit (r^2 = 1). In programming it can serve as alternative way to retrieve coefficient values (but the fit has to be perfect or near perfect with minor adjustments).

Swiss Micros DM41X Code: HEADLOS

(HP 41C compatible, no modules needed)

01 LBL^T HEADLOS

02 LBL 00

03 ^T SHARP EXIT

04 AVIEW

05 PSE

06 PSE

07 ^T PROTRUDING

08 AVIEW

09 PSE

10 PSE

11 ^T 3 SHARP ENT.

12 AVIEW

13 PSE

14 PSE

15 ^T 4 ROUND ENT.

16 AVIEW

17 PSE

18 PSE

19 ^T TYPE?

20 PROMPT

21 INT

22 STO 00 (comparison: reject if the entry is negative or greater than 5)

23 X<=0?

24 GTO 00

25 5

26 X<=Y?

27 GTO 00

28 RCL 00

29 X↑2

30 RCL 00

31 +

32 -20

33 /

34 1.1

35 +

36 ^T VEL. <M/S>?

37 PROMPT

38 X↑2

39 *

40 19.6133

41 /

42 ^T HEAD LOSS=

43 ARCL X

44 RTN

45 END

Casio fx-CG 50 Program HEADLOSS

Menu “TYPE”, “SHARP EXIT”, 1, “PROTRUDING”, 2, “SHARP ENTRANCE”, 3, “ROUND ENTRANCE”, 4

Lbl 1: 1 → C: Goto 5

Lbl 2: 0.8 → C: Goto 5

Lbl 3: 0.5 → C: Goto 5

Lbl 4: 0.1 → C: Goto 5

Lbl 5

“VELOCITY (M _| S)”? → V ( _| is the fraction character [ []/[] ] )

C × V² ÷ 19.6133 → H

“HEAD LOSS:”

H

Example

For the velocity, v = 10.5 ft/s ≈ 3.2004 m/s:

Type	Head Loss (h)
1. Sharp Exit	0.5222
2. Protruding Entrance	0.4178
3. Sharp Entrance	0.2611
4. Round Entrance	0.0522

Sources

Ajmera, Benna. “Engineering Formulas” Quick Study Academic. BarCharts, Inc. 2014

“Minor Losses in Pipes and Ducts“ Ansys. 2020. https://courses.ansys.com/wp-content/uploads/2020/09/Lesson-4-Minor-Losses-in-Pipes-and-Ducts-Handout.pdf Retrieved June 6, 2024.

Until next time,

Eddie

All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Review: Calculated Industries 4090 Sheet Metal/HVAC Pro Review

Review:  Calculated Industries 4090 Sheet Metal/HVAC Pro Review 

Quick Facts

Model: 4090 Sheet Metal/HVAC Pro 

Company: Calculated Industries

Years: approx. 2004 - Present*

Memory Register:  1 independent memory, 3 general memory registers

Battery:  2 x LR44 batteries

Screen:  8 digits with alpha numeric prompts, 12 digit accuracy

Logic:  AOS (Algebraic), Chain 

Price:   retails about $89.95; iOS and Android app available for $29.99; used calculators can be found for less 

Web Page from Calculated Industries:  https://www.calculated.com/mobile/prd722/Sheet-Metal-HVAC-Pro.html

If you purchase it out of the box, either by repackage or retail, both an Armadillo Case and a hard slide cover come with the calculator.  In the box set has a full user's manual, which is really nice and gives an extensive amount of examples and details.  

History

The Sheet Metal/HVAC Pro was exclusive to the International Training Institute (ITI)(https://www.sheetmetal-iti.org/) until 2021, when Calculated Industries made the calculator available to the Public  (7 seconds into this video:  https://www.youtube.com/watch?v=wzmB8UAEjls).

I purchased a used Sheet Metal/HVAC Pro which is why you see the ITI logo in the pictures.  I am very confident both versions have the substantially the same amount of functions.  

Features

* Trigonometry and Right Triangles

* Square, Square Root, Cube, Cube Root

* Fan Laws

* Circle and Arc Calculations

* Column and Cone Calculations

* VP (velocity pressure)/FPM (feet per minute) conversions

* Offset calculations

* Stairs, Hip/Valleys, Jack

* And one of the best known features to come with Calculated Industries industry calculators:  feet-inch-fraction and meter-millimeter calculations. Fractions of inches can be set from 1/2" to 1/64".  I usually work with 1/16".  

I think this is the only calculator from Calculator Industries to have a exponent (10^xx) key (x 10^y), allow for numbers to be entered using scientific notation.  The maximum number is 9.999999 * 10^76.  

Trigonometry

The only angle unit the trigonometric functions work with is degrees.  Two unique features that come with the Sheet Metal/HVAC Pro are the ArcK constant and the Law of Cosines function.  

An ArcK constant, which is equal to π/180 ≈ 0.017453.  This constant is helpful for circle arc calculations.

The Law of Cosines function where given the lengths of three sides A, B, and C, calculate the angle measurements of each of the angle and the area of the triangle using Heron's formula.   This is one of my favorite features of the Sheet Metal/HVAC Pro, as going through the User Guide a lot of pipe work involves determining lengths and angles of triangles.  

There are four keys that deal with right triangles, the multi-purpose [ x (Run) ], [ y (Rise) ],  [ r (Diag) ], and [ θ (Pitch) ] keys.  Enter the given knowns and then just press the remaining keys to solve for the missing parameters.  

Fan Laws

The A and A new (which represent the CFM - cubic feet per minute), and the B and B new registers deal with the three fan laws.  The B and B new parameters change depending on which fan law is used.

Fan Law 1:  B and B new represent RPM (revolutions per minute)

Fan Law 2:  B and B new represent SP (static pressure)

Fan Law 3:  B and B new represent BHP (brake horsepower)

Stairs and Roofs

The Sheet Metal/HVAC Pro has the stair, hip valley, and jack rafter calculations, the same as the construction calculators Construction Pro 5 and the Construction Master Pro.   You can set the default riser height of the stairs, as well as calculate the number of required risers, stairs, the tread width, the stringer length.  The HVAC Pro also works with roofs:  rafter length, pitch, jack rafters including irregular jacks.  

Offset Calculations

The offset calculations on the Sheet Metal/HVAC Pro slightly differ from the offset calculations offered on the Pipe Trades Pro.  The offset deal with sheet metals, and the calculations included are:

*  centerline radius

*  wrapper length

*  throat and heel radius

Verdict

As always, Calculated Industries offers quality calculators that are specific to industrial needs and the Sheet Metal/HVAC Pro is no exception.  The key quality is great, the display has helpful prompts, and the Armadillo cases given solid protection.   I'm happy that this calculator is now available to the public.

Eddie 

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.