Volume of an horizontal cylinder tank : step by step calculation guide
How to calculate the volume of an horizontal cylindrical tank
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1. Horizontal cylindrical tank
4. STEP 3 : Total volume
5. Excel horizontal tank volume calculator
1. Horizontal cylindrical tank
An horizontal tank is made of cylindrical shell and of 2 ends that can take different standard shapes. Many horizontal vessels are used in process industries, be it just to store water, or to hold chemicals in a road tanker for instance.
With :
D = tank diameter (m)
H = actual height of liquid in the tank (m)
z = tank head height (m)
L = length of the cylindrical shell (m)
The tank heads can have the following shapes :
- Elliptical
- Torispherical
- Hemispheric
This page is explaining how to calculate the volume in the tank as
a function of the level of liquid H.
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2. STEP 1 : Volume of the cylindrical section
2.1 Total volume
The total volume of a cylinder is given by the following formula :
Vcyl_total = π.D2/4*L
2.2 Partial volume horizontal cylinder
The actual volume in the cylinder actually depends on the height of liquid H in the tank. The partial volume filled can be calculated with the following equation :
Vcylpartial = L*D^2/4*(sin-1(2*H/D-1)+π/2+(2*H/D-1)*(2*H/D*(2-2*H/D))0.5)
3. STEP 2 : Volume in the tank ends
3.1 Total volume in tank heads
| Elliptical | V
= π.D3/24 |
| Torispherical | V = 0.1D3 |
| Hemispheric | V = π.D3/12 |
3.2 Partial volume in tank heads
The volume in the tank end depends on the standard shape.
| Elliptical | V
= 0.2618*H^2*(3*D/2-H) |
| Torispherical | V
= 0.2*H^2*(3*D/2-H) |
| Hemispheric | V
= 0.5236*H^2*(3*D/2-H) |
4. STEP 3 : Total volume
Vtotal = Vcylinder + 2*Vhead
(assuming both heads are identical)
5. Excel horizontal tank volume calculator
You can download a calculator to compute the volume of a partially filled horizontal tank : Horizontal Tank volume Excel calculation tool (click here).
Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.
