Relation Cross Scans

Bulk Pressure Ratio Three-Row Scan

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.

ΔP=KΔVV=12 Pa⋅1 m36 m3=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 ratio scanEqual pressure changes can come from scaled volume ratios.pressurevolume changevolume=6 m^3volumeChange=1 m^3pressureChange=2 Pamodulus=12 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.

ΔP=KΔVV=12 Pa⋅2 m312 m3=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 ratio scanEqual pressure changes can come from scaled volume ratios.pressurevolume changevolume=12 m^3volumeChange=2 m^3pressureChange=2 Pamodulus=12 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.

ΔP=KΔVV=16 Pa⋅1 m38 m3=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}
Bulk pressure ratio scanEqual pressure changes can come from scaled volume ratios.pressurevolume changevolume=8 m^3volumeChange=1 m^3pressureChange=2 Pamodulus=16 Pa