Bulk Pressure Ratio Three-Row Scan - Elasticity and Nonlinear Dynamics Step by Step

A bulk-pressure-ratio scan varies volume change, volume, and modulus together across three rows, checking that the product delta-P = K * delta-V / V stays constant row by row. The arithmetic is exact only for the stated pressures, volume changes, volumes, and modulus values in the ideal linear-elastic bulk model. Real materials add nonlinearity, hysteresis, geometry tolerances, temperature effects, load-cell/length calibration, finite precision, and measurement uncertainty.

Bulk pressure change follows modulus times volume-change ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Bulk pressure follows modulus times volume-change ratio

Volume change 1 cubic meter over volume 6 cubic meters with modulus 12 Pa gives pressure change 2 Pa.

\Delta P=K\frac{\Delta V}{V}=12\ \text{Pa}\cdot\frac{1\ \text{m}^{3}}{6\ \text{m}^{3}}=2\ \text{Pa}

Bulk pressure follows modulus times volume-change ratio

Volume change 2 cubic meters over volume 12 cubic meters with modulus 12 Pa gives pressure change 2 Pa.

\Delta P=K\frac{\Delta V}{V}=12\ \text{Pa}\cdot\frac{2\ \text{m}^{3}}{12\ \text{m}^{3}}=2\ \text{Pa}

Bulk pressure follows modulus times volume-change ratio

Volume change 1 cubic meter over volume 8 cubic meters with modulus 16 Pa gives pressure change 2 Pa.

\Delta P=K\frac{\Delta V}{V}=16\ \text{Pa}\cdot\frac{1\ \text{m}^{3}}{8\ \text{m}^{3}}=2\ \text{Pa}