Horizontal 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 D (vessel diameter).
Head Depth 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).
- Full head volume (per head): spherical cap (sphere radius \(R_c=D\)): \(V_\text{head}=\dfrac{\pi H_h^2 (3R_c – H_h)}{3}\).
- Cylinder volume: radius \(R=D/2\), \(V_{cyl}=\pi R^2 L_{cyl}\).
- Total volume: \(V_{tot}=V_{cyl}+2V_\text{head}\).
- Horizontal level-based liquid volume:
- Cylinder area segment \(A(h)=R^2\cos^{-1}\!\big(\tfrac{R-h}{R}\big) – (R-h)\sqrt{2Rh-h^2}\), \(0\le h\le 2R\); cylinder part \(=A(h)\,L_{cyl}\).
- Heads (both): use **scaled sphere segment** \(V_{seg}(h) = \dfrac{\pi h^2(3R – h)}{3}\) and \(f(h)=V_{seg}(h)\big/\big(\tfrac{4}{3}\pi R^3\big)\), then head contribution \(=2\,V_\text{head}\,f(h)\). This preserves each head’s true full volume while giving realistic h-dependence.
- Weight: \(W=\rho\,V\) (ρ in kg/m³).
- Note: This is a practical estimate. For code compliance, use vendor profiles or numerical integration of the exact torispherical shape.