Partial Volume in a Vertical Cylindrical Tank with Hemispherical Heads - Feet

Calculate the volume of a partial filled vertical cylindrical tank or container with hemispherical heads, a vertical capsule.
The vertical capsule tank is a cylinder with hemispherical heads on top and bottom. This calculator uses feet for measurements.

Approximate weight of Fuel or Water

one US gallon of water = 8.34 pounds.
one US gallon of diesel fuel = 7.1 pounds
one US gallon of gas = 6 pounds 

Calculator

1. enter the diameter of the vertical capsule tank in feet and or inches
2. the height of the tank in feet and or inches
3. the depth of the liquid inside the tank in feet and or inches
4. the weight of the liquid in pounds per US gallons

Results

1. the volume of the tank in cubic feet
2. the volume of the tank in cubic inches
3. the volume of the tank in cubic metres
4. the total amount of liquid the tank can hold in US gallons
5. amount of liquid the tank can hold in litres
6. the amount of liquid inside the tank in cubic feet
7. the amount of liquid inside the tank in US gallons
8. the amount of liquid inside the tank in Imperial gallons
9. the amount of liquid inside the tank in litres
10. the amount of liquid inside the tank in hectolitres
11. the weight of the liquid inside the tank based on lbs/gal US
12. the amount of liquid it will take to fill this tank in US gallons

Formula

Vt = 𝝅/12(3D²d-4d³)
Vc = 𝝅(D/2)²d
Vb = 𝝅/6(3Dd²-2d³)
where Vt is the partial volume in the upper head
Vc partial volume of the cylinder
Vb the partial volume in the lower head
D tank diameter
d the fill height of the liquid

Conversions

one cubic foot (ft³) = 1728 cubic inches (in³)
one cubic foot (ft³) = 28316846.592 cubic millimetres (mm³)
one cubic foot (ft³) = 0.028316846592 cubic metres (m³)
one cubic foot (ft³) = 7.48051948051947 gallons (gal) US
one cubic foot (ft³) = 6.22883545904283 gallons (gal) Imperial
one square foot (ft²) = 144 square inches (in²)
one square foot (ft²) = 92903.04 square millimetres (mm²)
one square foot (ft²) = 0.09290304 square metres (m²)