TI-65 Programs Part II: Reynolds Number/Hydraulic Diameter, Escape Velocity, Speed of Sound/Resonant Frequencies in an Open Pipe

TI-65 Programs Part II:  Reynolds Number/Hydraulic Diameter, Escape Velocity, Speed of Sound/Resonant Frequencies in an Open Pipe

This is the second part of programs for the TI-65 this Fourth of July. 

Click here for Part I:  Digital Root, Complex Number Multiplication, Dew Point

Click here for Part III: Impedance and Phase Angle of a Series RLC Circuit, 2 x 2 Linear System Solution, Prime Factorization

TI-65 Reynolds Number/Hydraulic Diameter

This program utilities the two keyboard labels:

[F1]:  Calculates the Reynolds Number

[F2]:  Calculates the Hydraulic Diameter of a Rectangular Duct

Formula for the Reynolds Number:

Re = (v * DH)/w

v = velocity of the fluid (liquid or gas)

DH = hydraulic diameter

w = kinematic viscosity

The hydraulic diameter of the following ducts:

Tubular pipes:  DH = diameter of the tube

Annulus:  DH = large radius – small radius

Square Duct:  DH = length of one side

Rectangular Duct:  DH = (2*a*b)/(a + b);  a, b are the lengths of the sides

Program:

CODE	STEP	KEY	COMMENT
2nd 53.53	00	LBL F1	Starts F1, have DH on the display (meters)
38	01	*
51	02	R/S	Prompt: velocity of fluid (m/s)
28	03	÷
51	04	R/S	Prompt: kinematic viscosity (m/s)
39	05	=
-15	06	INV EE	Remove Engineering notation
2nd 52	07	RTN	End F1
2nd 53.54	08	LBL F2	Starts F2: have a on display (m)
12.0	09	STO 0
38	10	*
51	11	R/S	Prompt for b
12.1	12	STO 1
38	13	*
2	14	2
28	15	÷
16	16	(
13.0	17	RCL 0
59	18	+
13.1	19	RCL 1
17	20	)
39	21	=	DH of rectangular duct
2nd 52	22	RTN	End F2

TI-65 Reynold’s Number

Input: hydraulic diameter (m) [F1], velocity of the fluid (m/s) [R/S], kinematic viscosity (m/s) [R/S]

Output:  Reynolds number (dimensionless)

Hydraulic Diameter of a Rectangular Duct

Input:  a (m) [F2], b (m) [R/S]

Output:  DH (m)

Test 1:  Tubular Pipe Duct of hydraulic diameter of 3.5 in.  The fluid is water at 68°F (20°C), flowing at 0.5 m/s.  The kinematic viscosity of water of 20°C is 1.004 *10^-6 m/s.

Input:  3.5 [3^rd] [in-cm] [ ÷ ] 100 = [ F1 ], 0.5 [R/S], 1.004 [EE] 6 [+/-] [R/S]

Output:  44,272.90837

Test 2:  Rectangular Duct where a = 1.27 m and b = 0.508 m (50 in x 20 in).  The fluid is air at 60°F (about 15.6°C), flowing at 0.5 m/s.  The kinematic viscosity of air at 15.6°C is 1.58 * 10^-4 m/s.

Input:  1.27 [F2], 0.508 [R/S]

Result:  0.725714286 m  (hydraulic diameter), keep this number in the display

Input:  [F1], 0.5 [R/S], 1.58 [EE] 4 [+/-] [R/S]

Result: 2296.564195  (Reynolds Number)

TI-65 Escape Velocity

The formula for the escape velocity from a planet is:

v = √(2*G*m/r)

v = escape velocity (m/s)

G = University Gravitational Constant = 6.67384 * 10^-11 m^3/(kg*s^2)

m = mass of the planet (kg)

r = radius of the planet (m)

Note that 2*G = 1.334768 * 10^-10 m^3/(kg*s^2)

Program:

CODE	STEP	KEY	COMMENT
2nd 16	00	2nd ENG	Start with mass, set Engineering mode
38	01	*
1	02	1	Enter 2*G
57	03	.	Decimal Point
3	04	3
3	05	3
4	06	4
7	07	7
6	08	6
8	09	8
15	10	EE
1	11	1
0	12	0
58	13	+/-
28	14	÷
51	15	R/S	Prompt for radius
39	16	=
33	17	√
51	18	R/S	Display escape velocity

Input:  mass of the planet (kg) [RST] [R/S], radius of the planet (m) [R/S]

Output:  escape velocity (m/s)

Test 1:  Earth (m = 5.97219 * 10^24 kg, r = 6.378 * 10^6 m)

Input: 5.97219 [EE] 24 [RST] [R/S], 6.378 [EE] 6 [R/S]

Result:  ≈ 11.179E3 (about 11,179 m/s)

Test 2:  Jupiter (m = 1.89796 * 10^27 kg, r = 71.492 * 10^6 m)

Result:  ≈ 59.528E3 (about 59,528 m/s)

 TI-65 Speed of Sound/Resonant Frequencies in an Open Pipe

Formulas:

Speed of Sound (m/s):  v = t*0.6 + 331.4

Where t = temperature (°C)

Resonant Frequencies in an Open Pipe:  fn = n*v/(2*L)

Where fn = frequency (Hz), v = speed of sound (m/s), L = length of pipe (m), n = 1, 2, 3…

If n = 1, then fn is the fundamental frequency

Program:

CODE	STEP	KEY	COMMENT
2nd 53,53	00	LBL F1	Start Label F1
38	01	*
57	02	.	Decimal Point
6	03	6
59	04	+
3	05	3
3	06	3
1	07	1
57	08	.	Decimal point
4	09	4
39	10	=
2nd 52	11	RTN	End F1
2nd 53, 54	12	LBL F2	Start label F2
28	13	÷
13.1	14	RCL 1
28	15	÷
2	16	2
39	17	=
12.0	18	STO 0
1	19	1
12.3	20	STO 3	Counter
2nd 53.0	21	LBL 0	Start loop
13.3	22	RCL 3
2nd 51	23	PAUSE
38	24	*
13.0	25	RCL 0
39	26	=
51	27	R/S	Display fn
1	28	1
12.59	29	STO+
3	30	3	STO+ 3
13.3	31	RCL 3
-3rd 44	32	INV 3rd x>m	x≤m?
2	33	2	x≤R2?
2nd 54.0	34	GTO 0	If x≤R2, GTO LBL 0
13.2	35	RCL 2
2nd 52	36	RTN	End F2

Speed of Sound in Dry Air: 

Input:  Enter temperature in °C [F1]

Result:  Speed of sound (m/s)

Resonant Frequencies:

Store the length of the pipe (m): L [STO] 1

Store the upper limit:  n [STO] 2

Input: speed of sound (m/s) [F2], n flashes before frequency (Hz), press [R/S] to see other frequencies

The program finishes when n is displayed a second time.

Test:

Open pipe of 0.45, where the temperature of the air is 39°C (102.2°F).  Find out the first 3 resonant frequencies.

We’ll need the speed of air, but first, store the required constants:

0.45 [STO] 1, 3 [STO] 2

Next find the speed of air:

Input:  39 [F1]

Result:  354.8 m/s

Find the 3 resonant frequencies:

Input: (with 354.8 in the display) [F2]

Result:  1, 394.2222222 Hz  [R/S]  \\ fundamental frequency

2, 788.4444444 Hz [R/S]  \\ 2^nd frequency

3, 1182.666667 Hz [R/S]  \\ 3^rd frequency

Source:  Browne Ph. D, Michael.  “Schaum’s Outlines:  Physics for Engineering and Science”  2^nd Ed.  McGraw Hill: New York, 2010

This blog is property of Edward Shore, 2016.