Boundary Depth Scans

curvature-pressure-ceiling-three-row-scan

Radius is scanned through a pressure ceiling. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Radius is scanned against a pressure ceiling

Gamma and curvature factor stay fixed. Radius is 2 m so the checked pressure jump is 6 Pa. This row is above boundary relative to the 4 Pa ceiling.

ΔP=kγ/R=2×6 N/m/2 m=6 PaPmax⁡=4 Pa\Delta P=k\gamma/R=2\times6\ \text{N/m}/2\ \text{m}=6\ \text{Pa}\qquad P_{\max}=4\ \text{Pa}
Curvature-pressure boundary rowA wider radius lowers the checked pressure jump.radiuspressureabove boundary

Radius is scanned against a pressure ceiling

Gamma and curvature factor stay fixed. Radius is 3 m so the checked pressure jump is 4 Pa. This row is on boundary relative to the 4 Pa ceiling.

ΔP=kγ/R=2×6 N/m/3 m=4 PaPmax⁡=4 Pa\Delta P=k\gamma/R=2\times6\ \text{N/m}/3\ \text{m}=4\ \text{Pa}\qquad P_{\max}=4\ \text{Pa}
Curvature-pressure boundary rowA wider radius lowers the checked pressure jump.radiuspressureon boundary

Radius is scanned against a pressure ceiling

Gamma and curvature factor stay fixed. Radius is 6 m so the checked pressure jump is 2 Pa. This row is below boundary relative to the 4 Pa ceiling.

ΔP=kγ/R=2×6 N/m/6 m=2 PaPmax⁡=4 Pa\Delta P=k\gamma/R=2\times6\ \text{N/m}/6\ \text{m}=2\ \text{Pa}\qquad P_{\max}=4\ \text{Pa}
Curvature-pressure boundary rowA wider radius lowers the checked pressure jump.radiuspressurebelow boundary