## Sunday, April 23, 2017

### HP Prime and TI-84 Plus CE: Shallow Wave Analysis

HP Prime and TI-84 Plus CE:  Shallow Wave Analysis

Introduction

The program H2OWAVES calculates wave speed, impedance, and wave flux for shallow ocean waves.  The following are assumed:

1. The criteria of λ < D/20 is assumed where λ is the length of the wave.
2. The water assumed to be 0°C, where the density (ρ) is 1,000 kg/m.
3. SI units are used.  For gravity, g = 9.80665 m/s^2 is used.

Formulas Used

Wave Speed (m/s):  v = √(g * D)
Wave Impedance (Mks):  Z = ρ * v
Wave Energy Flux (W/m):  I = (ρ * g * H)^2/(2 * Z)
Maximum Possible Length (m):  λ = 20 * D

HP Prime Program H2OWAVES

EXPORT H2OWAVES()
BEGIN
// EWS 2017-04-21
// Shallow Wave Analysis
// for D/L<1/20
// SI Units

LOCAL D,H;
LOCAL v,Z,I;

INPUT({D,H},
"Wave Analysis",
{"D: ","H: "},
{"Depth (m)","Wave Height (m)"});

v:=√(9.80665*D);
Z:=1000*v;
I:=(9806.65*H)^2/(2*Z);

PRINT();
PRINT("Wave speed (m/s): "+v);
PRINT("Impedance (Mks): "+Z);
PRINT("Wave Flux (W/m): "+I);

RETURN {v,Z,I};

END;

TI-84 Plus CE Program H2OWAVES

"EWS 2017-04-23"
"SHALLOW WAVES"
"D<F/20"
Disp "SHALLOW WAVES"
Input "DEPTH (M): ",D
Input "HEIGHT (M): ",H
√(9.80665*D)→V
1000*V→Z
(9806.65*H)^2/(2*Z)→I
Disp "WAVE SPEED (M/S):",V
Disp "IMPEDANCE (WKS):",Z
Disp "WAVE FLUX (W/M):",I

Example

Input:
Depth:  3.2 m
Height:  0.49 m

Output:
Wave Speed: 5.601899678 m/s
Impedance:  5601.899678 Wks
Wave Flux:  2060.953478 W/m

Source:

Ingard, K.U. Fundamental of Waves and Oscillations Cambridge University Press:  New York 1988.  IBSN 0 521 32734

Surf’s up!  Eddie

This blog is property of Edward Shore, 2017.