Vertical Cylinder + Torispherical Heads — Level-based Volume & Weight
Heads approximated as spherical caps: crown radius Rc = D, head depth Hh = k·D (default k = 0.193 for Standard F&D). Enter level h from 0 to Htot=Hcyl+2·Hh.
Head Depth Hh–
Total Height Htot=Hcyl+2·Hh–
One Head Volume (m³)–
Cylinder Volume (m³)–
Total Vessel Volume (m³)–
Liquid Volume at level h (m³)–
Fluid Weight at level h (kg)–
Fluid Weight at level h (t)–
Method & formulae
- Depth: \(H_h = k\,D\) (default \(k=0.193\), Standard F&D).
- Head volume (per head): spherical cap with sphere radius \(R_c=D\): \(V_{cap}(y) = \frac{\pi y^2 (3R_c – y)}{3}\), so \(V_{head}=V_{cap}(H_h)\).
- Cylinder volume: with vessel radius \(R=D/2\), \(V_{cyl}=\pi R^2 H_{cyl}\).
- Total volume: \(V_{tot}=V_{cyl}+2V_{head}\).
- Level-based liquid volume (fill height \(h\)): piecewise
- \(0\le h\le H_h:\; V=V_{cap}(h)\)
- \(H_h<h\le H_h+H_{cyl}:\; V=V_{head}+A_{cyl}(h-H_h)\), with \(A_{cyl}=\pi R^2\)
- \(H_h+H_{cyl}<h\le H_{tot}:\; V=V_{head}+A_{cyl}H_{cyl}+V_{cap}(h-(H_h+H_{cyl}))\)
- Weight: \(W=\rho\,V\) (ρ in kg/m³).
- Note: This spherical-cap model is a practical estimate (≈1–3% for Standard F&D). For code work, use vendor head profiles.