Horizontal Cylinder + Ellipsoidal Heads — Level-based Volume & Weight
Default is 2:1 ellipsoidal heads (depth ratio k = Hh/D = 0.25). Enter fill height 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
- 2:1 Ellipsoidal head: \(H_h = kD\) (default \(k=0.25\)). Semi-axes \(a=H_h\) (axial), \(b=D/2\) (radial).
- Head volume (per head): half prolate spheroid \(V_\text{head}=\frac{2}{3}\pi a b^2=\frac{\pi k D^3}{6}\).
- Cylinder volume: \(R=D/2\), \(V_{cyl}=\pi R^2 L_{cyl}\).
- Total volume: \(V_{tot}=V_{cyl}+2V_\text{head}\).
- Level-based volume (horizontal):
- Cylinder segment area \(A(h)=R^2\cos^{-1}\!\big(\tfrac{R-h}{R}\big)-(R-h)\sqrt{2Rh-h^2}\);\; cylinder part \(=A(h)L_{cyl}\).
- Heads: use **scaled sphere-segment fraction** \(f(h)=\dfrac{\pi h^2(3R-h)/3}{\tfrac{4}{3}\pi R^3}\); head part \(=2\,V_\text{head}\,f(h)\).
- Weight: \(W=\rho\,V\) with \(\rho\) in kg/m³.
- Note: Level behavior for ellipsoidal heads is approximated (good for design/sizing). For code work, integrate the exact profile.