Vertical Cylinder + Ellipsoidal Heads — Level-based Volume & Weight
Default is 2:1 ellipsoidal heads (depth ratio k = Hh/D = 0.25). Enter filled height 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
- Ellipsoidal head: \(H_h = kD\) (default \(k=0.25\)). Semi-axes \(a=H_h\), \(b=D/2\).
- Head volume (per head): half prolate spheroid \(V_\text{head}=\frac{2}{3}\pi a b^2=\frac{2}{3}\pi H_h (D/2)^2\).
- Cylinder volume: \(R=D/2\), \(V_{cyl}=\pi R^2 H_{cyl}\).
- Total volume: \(V_{tot}=V_{cyl}+2V_\text{head}\).
- Level-based volume (vertical): piecewise with **scaled sphere-cap fraction** \(f(y)=\dfrac{\pi y^2(3R-y)/3}{(2/3)\pi R^3}\) for head fill depth \(y\).
- \(0\le h\le H_h:\; V=V_\text{head}\,f(h)\)
- \(H_h<h\le H_h+H_{cyl}:\; V=V_\text{head}+\pi R^2(h-H_h)\)
- \(H_h+H_{cyl}<h\le H_{tot}:\; V=V_\text{head}+\pi R^2H_{cyl}+V_\text{head}\,f(h-(H_h+H_{cyl}))\)
- Weight: \(W=\rho\,V\) (ρ in kg/m³).
- Note: This preserves exact full capacities with simple closed forms; for code work, integrate the exact ellipsoidal profile.