Casio fx-991 CW: Scientific Constants in Calculations

 Casio fx-991 CW: Scientific Constants in Calculations

Obtaining the Scientific Constants

I believe we can do this in every mode.

1. Press the [ CATALOG ] button.

2. Scroll to the Sci Constants submenu. It’s faster to scroll up in this case.

3. Press the right button [ → ] to get to the categories.

4. Select the category and press the right button again.

5. Select the constant and press [ OK ].

We can select the back button, the one with the curved arrow, to go back to the previous menu.

I wish the fx-991CW had a custom menu where we could store constants and other commands so we could reduce the number of keystrokes for common constants and commands.

Table of Common Scientific Constants

All scientific constants in the fx-991CW use SI units (meters, kilograms, seconds, Kelvin/Celsius, etc.). I believe the 2018 CODATA values are used, at least with the calculator I bought three years ago in 2022.

Name	Symbol	Category	Value (Norm 1)
Vacuum Permeability (Magnetic Constant)	μ₀	Universal	1.256637062 × 10^(-6) N/A² Exact: (4π × 10^(-7))
Universal Gravitational Constant	G	Universal	6.6743 × 10^(-11) N m²/kg²
Vacuum Permittivity (Electric Constant)	ε₀	Universal	8.854187813 × 10^(-12) F/m
Speed of Light (in a vacuum)	c	Universal	299,792,458 m/s
Planck’s Constant	h	Universal	6.62607015 × 10^(-34) J s
Earth’s Gravity Constant	gₙ (note the n subscript)	Adopted Values	9.80665 m/s²
Universal Gas Constant	R	Physico-Chem	8.314462618 J/(mol K)
Avogadro Constant	Nₐ (the a is capitalized)	Physico-Chem	6.02214076 × 10^23 mol⁻¹
Boltzmann Constant	k	Physico-Chem	1.380649 × 10^(-23) J/K
Stefan-Boltzmann Constant (Constant of Proportionality)	σ	Physico-Chem	5.670374419 × 10^(-8) W/(m² K⁴)
Elementary Charge	e	Electromagnetic	1.602176634 × 10^(-19) C
Mass of an Electron	me	Atomic&Nuclear	9.109383702 × 10^(-31) kg
Volume of a Mole at 0° C	Vm	Physico-Chem	0.02271095464 m³/mol
Atomic Mass Constant (1/12 of mass of a neutral carbon-12 atom)	m_u (the u is a subscript, classically marked u)	Physico-Chem	1.660539067 × 10^(-27) kg

A full list of the 47 constants can be found here:

https://support.casio.com/global/en/calc/manual/fx-570CW_991CW_en/advanced_calculations/scientific_constants.html

Note the manual only lists the symbol.

Examples

Scientific Constants are highlighted in dark blue.

Lorenz Factor

γ = 1 / √(1 – v^2/c^2) (Universal)

γ = time dilation factor

v = 150 × 10^6 m/s, put the entire quantity in parenthesis like this (150×10^6)

γ ≈ 1.154967184

Escape Velocity

v = √(2 * G * m / r) (Universal)

v = velocity required to escape the planet

Radius: r = 7.2 × 10^6 m, again with the ×10^ button, put the entire number in parenthesis (7.2×10^6)

Mass: m = 5.9 × 10^24 kg

v ≈ 10458.69787 m/s

Coulomb’s Law

F = (q1 * q2) / (4 * π * ε₀ * r^2) (Universal)

F = force between two charges

Charge # 1: q1 = 4 × 10^(-5) C

Charge # 2: q2 = 3.3 × 10^(-5) C

Radius: r = 0.24 m (24 cm)

F = 205.9647286 N

Source: Casio fx-1000F/fx-5000F Manual

Solenoid Inductance

L = μ₀ × μr × n^2 × A × h (Universal)

L = inductance in micro henrys (mH)

Relative Permeability: μr = 2.5 (unit-less)

Number of Turns: n = 30/cm

Area: A = 0.2 cm^2

Length: h = 3.5 cm (note the symbol)

L = 0.00197920337 mH

Source: HP 50/49g+/48gII graphing calculator: advanced user’s reference manual

Simple Pendulum

F = -(m * gₙ * x) / l (Adopted Values)

F = force of a pendulum at point x

Position to be analyzed: x = 1 m

Length: l = 1.5 m

Mass: m = 10 lb ≈ 4.535924 kg

F = -29.65481273 N

Source: Casio fx-1000F/fx-5000F Manual

I hope you find this useful, and enjoy the physical constants library of the fx-991CW. Until next time,

Eddie

All original content copyright, © 2011-2025. 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.

HP 20S - Normal Distribution, Direction Cosine, Fire Friction Loss

HP 20S - Normal Distribution, Direction Cosine, Fire Friction Loss

HP 20S Normal Distribution

Goal: To estimate the area of the normal curve

∫( e^(-x^2 / 2) dx, a, b) / √(2 * π)

Steps:

1. Enter the programming editor: [ <| ] [ R/S ] {PRGM}

2. Load the integration program: [ <| ] [ ← ] {LOAD} [ e^x ] { B }. The screen shows “int”.

3. Go one up one step to get to Step 58: [ <| ] [ 8 ] { ↑ }

4. Enter the program after 58: 61, 41, F (LBL F)

51, 11	x^2
45	÷
2	2
74	=
32	±
12	e^x
45	÷
33	(
2	2
55	×
61, 22	π
34	)
11	√
74	=

5. Store the lower limit in register 5: a [ STO ] [ 5 ]

6. Store the upper limit in register 6: b [ STO ] [ 6 ]

7. Enter the number of intervals, it must be an even integer, and execute label A: n [ XEQ ] [ √ ] { A }

Example

At n = 20 intervals, estimate areas (ALL setting)

a = 0, b = 3; area ≈ 0.498649878

a = -3, b = 3; area ≈ 0.997293118

a = -1, b = 2; area ≈ 0.818595675

HP 20S: Direction Cosines

The direction cosines of 3D vector v = [x, y, z] are:

a = arccos(x / norm(v))

b = arccos(y / norm(v))

c = arccos(z / norm(v))

where norm(v) = √( x^2 + y^2 + z^2 )

The following program sets the angle mode to degrees, however, a change in the second step will allow the user to use radians or grads instead. The program uses the rectangular to polar conversion to obtain the norm.

Math note:

Find the magnitude of (√(x^2 + y^2), z).

magnitude

= √( [√(x^2 + y^2)]^2 + z^2 )

= √( x^2 + y^2 + z^2)

= norm(v)

Executing the →P command gives the angle first. Obtaining the magnitude requires a swap. ( [ <| ] [ INPUT ] {SWAP} ).

61, 41, b	LBL B
61, 23	DEG (61, 24 for RAD, 61, 25 for GRD)
22, 1	RCL 1
31	INPUT
22, 2	RCL 2
51, 21	→ P
51, 31	SWAP
31	INPUT
22, 3	RCL 3
51, 21	→ P
51, 31	SWAP
21, 4	STO 4
22, 1	RCL 1
41, C	XEQ C
26	R/S
22, 2	RCL 2
41, C	XEQ C
26	R/S
22, 3	RCL 3
41, C	XEQ C
61, 26	RTN
61, 41, C	LBL C (subroutine)
45	÷
22, 4	RCL 4
74	=
51, 24	ACOS
61, 26	RTN

Store x in register 1, y in register 2, and z in register 3. The angles are shown in order

Examples (FIX 4):

x = 4, y = 8, z = 5

Direction Cosines: a ≈ 67.0231°, b ≈ 38.6734°, c ≈ 60.7941°

x = -3, y = 8, z = 6

Direction Cosines: a ≈ 106.6992°, b ≈ 39.9807°, c ≈ 54.9217°

Source:

“Direction Cosine” Wikipedia. Accessed November 5, 2024. https://en.wikipedia.org/wiki/Direction_cosine

HP 20S: Determining the Coefficient for Friction Loss

When fighting fires, the friction loss of a hose lay can be determined by the formula:

FL = C * (flow rate/100)^2 * (hose length/100)

where:

C = coefficient

flow rate = the rate of water in GPM (gallons per minute)

hose length = length of the hose in ft (feet)

FL = friction loss in PSI (pounds per square inch)

This formula assumes a single line is used.

Solving for C:

C = FL / ((flow rate/100)^2 * (hose length/100))

The friction loss was determined by using various flow rates and hose lengths by using the FireCalc Pocket Calculator. You can see my spotlight on the FireCalc Pocket Calculator here: https://edspi31415.blogspot.com/2024/11/spotlight-akron-brass-firecalc-pocket.html

Friction Loss Table:

1” Hose Size

GPM ↓ / Length →	100 ft	150 ft	200 ft
100	150	225	300
150	338	506	675
200	600	900	1200

1.5” Hose Size

GPM ↓ / Length →	100 ft	150 ft	200 ft
100	24	36	48
150	54	81	108
200	96	144	192

2” Hose Size

GPM ↓ / Length →	100 ft	150 ft	200 ft
100	8	12	16
150	18	27	36
200	32	48	64

The coefficient is built in to the FireCalc. I used the HP 20S to extract the coefficient by the following program:

61, 41, A	LBL A
33	(
22, 2	RCL 2
45	÷
1	1
0	0
0	0
34	)
51, 11	x^2
55	×
33	(
22, 3	RCL 3
45	÷
1	1
0	0
0	0
34	)
74	‘=
15	1/x
55	×
22, 1	RCL 1
74	=
61, 26	RTN

Values are stored in the following registers:

Register 1 = friction loss (PSI)

Register 2 = flow rate (GPM)

Register 3 = hose length (ft)

Fortunately, running the program with various data points above, I obtain the coefficient as:

1” Hose Size: coefficient = 150

1.5” Hose Size: coefficient = 24

2” Hose Size: coefficient = 8

Source:

Task Force Tips. “Hydraulic Calculations Every Firefighting Needs to Know” Firefighter Trending Report. 2024. Retrieved November 10, 2024. https://tft.com/hydraulic-calculations-every-firefighter-needs-to-know/

Enjoy!

Eddie

All original content copyright, © 2011-2025. 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.