Hydraulic-Acoustic System: Governing Equations and Material Properties
GOVERNING EQUATIONS FOR THE GIZA HYDRAULIC-ACOUSTIC SYSTEM
All equations are textbook physics used in standard engineering.
EQUATION 1 — HYDRAULIC POWER (conservation of energy): P = rho g Q * h
g = 9.81m/s^2
Q = volumetric flow rate (m^3/s)
h = height drop (m)
EQUATION 2 — WATER HAMMER (Joukowsky, 1898):
delta_p = rho c delta_v
delta_v = change in flow velocity (m/s)
Yields pressure in pascals. Valid for rigid pipe (stone).
EQUATION 3 — HELMHOLTZ RESONANCE:
f = (c / 2pi) sqrt(A / (V * L_eff))
V = cavity volume (m^3)
L_eff = effective neck length with end correction (m)
EQUATION 4 — ACOUSTIC IMPEDANCE TRANSMISSION:
T = 4 * Z1 * Z2 / (Z1 + Z2)^2
EQUATION 5 — SABINE ROOM ACOUSTICS:
p^2 = 4 rho c P / (alpha S)
S = total surface area (m^2)
EQUATION 6 — PIEZOELECTRIC VOLTAGE:
V = g sigma t
sigma = stress (Pa)
t = thickness (m)
MATERIAL PROPERTIES (published, measured):
Limestone: rho=2500 kg/m^3, c=3500m/s, Z=8.75e6 Pa*s/m
Granite: rho=2700 kg/m^3, c=5000m/s, Z=1.35e7 Pa*s/m
Air: rho=1.2 kg/m^3, c=343m/s, Z=411.6 Pa*s/m
Calcite d_11 = 2.3 pC/N (piezoelectric coefficient)
Quartz d_11 = 2.3 pC/N
Quartz g_11 = 50e-3 V*m/N (voltage coefficient)
Limestone absorption alpha (<100Hz) = 0.01-0.02
Limestone attenuation (<100Hz) = 0.01-0.1dB/m
Limestone Young's modulus = 30-50 GPa
Granite compressive strength = 130-280 MPa
Limestone compressive strength = 20-170 MPa
MEASURED DIMENSIONS (Petrie 1883, published archaeology):
Area = 1.24m^2, Angle = 26d 31m 23s (26.52 deg)
Entrance ~17m above base, Subterranean Ch. ~30m below base
Total vertical drop = 47m
Subterranean Chamber: 14.08m x 8.36m x 3.48m = ~410m^3
Dead-end south passage: ~16m long, 0.74m x 0.84m
Floor pit: ~1.8m deep
King's Chamber: 10.47m x 5.23m x 5.82m = ~319m^3
Granite walls, ceiling, floor. 5 relieving chambers above.
~43 granite beams total, each ~1-2m thick
Grand Gallery: L=46.7m, H=8.6m (corbelled)
Well Shaft: connects Grand Gallery to Subterranean area
These dimensions and properties are the complete input set. Every calculation that follows is arithmetic from these numbers.
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