## Saturday, July 20, 2024

### 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:

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).

(HP 41C compatible, no modules needed)

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 /

43 ARCL X

44 RTN

45 END

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

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.

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