How is the volume of a partially filled horizontal cylindrical tank calculated?

The calculation involves two main parts: the volume of the partially filled cylindrical section and the volume of the liquid in the tank heads. The cylindrical section's volume is derived from the geometry of a circular segment, while the head volume depends on its specific shape (elliptical, torispherical, hemispheric) and the liquid level.

What are common types of tank heads for horizontal vessels?

Common tank head shapes for horizontal cylindrical vessels include elliptical heads, torispherical heads, and hemispherical heads. Each shape has distinct geometric properties that affect the total and partial volume calculations.

Why is it important to accurately calculate tank volume at different liquid levels?

Accurate tank volume calculation at varying liquid levels is crucial for inventory management, process control, safety (preventing overfilling or running dry), and ensuring product quality. It helps operators and engineers understand the actual quantity of material stored in the vessel at any given time.

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

2. STEP 1 : Volume of the cylindrical section

3. STEP 2 : Volume in the tank ends
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.

⚠️ ENGINEERING NOTICE & EDUCATIONAL DISCLAIMER: This interactive calculator is provided exclusively for preliminary estimation and educational purposes. It is not intended for detailed design or equipment procurement without certified vendor rating. No warranty, expressed or implied, is provided, and no liability is assumed.

Horizontal Tank Volume Calculator

Shell inner diameter (D) m

Actual height of liquid (H) m

Length of cylindrical shell (L) m

Tank Head Type

Calculation Results

Total Cylindrical Volume: m³

Partial Cylindrical Volume: m³

Total Head Volume (2 heads): m³

Partial Head Volume (2 heads): m³

Total Tank Volume (Full): m³

Total Tank Volume (Filled): m³

2. STEP 1 : Volume of the cylindrical section

2.1 Total volume

The total volume of a cylinder is given by the following formula :

\[V_{cyl\_total} = \pi \cdot \frac{D^2}{4} \times L\]

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 :

\[V_{cylpartial} = L \cdot \frac{D^2}{4} \left( \sin^{-1}\left(2\frac{H}{D}-1\right)+\frac{\pi}{2}+\left(2\frac{H}{D}-1\right)\sqrt{2\frac{H}{D}\left(2-2\frac{H}{D}\right)} \right)\] Formula partial volume of horizontal cylinder

Formula partial volume of horizontal cylinder

3. STEP 2 : Volume in the tank ends

3.1 Total volume in tank heads

Elliptical	\[V = \pi \cdot \frac{D^3}{24}\]
Torispherical	\[V = 0.1 \cdot D^3\]
Hemispheric	\[V = \pi \cdot \frac{D^3}{12}\]

3.2 Partial volume in tank heads

The volume in the tank end depends on the standard shape.

Elliptical	\[V = 0.2618 \cdot H^2 \cdot \left(\frac{3D}{2}-H\right)\]
Torispherical	\[V = 0.2 \cdot H^2 \cdot \left(\frac{3D}{2}-H\right)\]
Hemispheric	\[V = 0.5236 \cdot H^2 \cdot \left(\frac{3D}{2}-H\right)\]

Practical Plant Engineering Rules of Thumb & Safety Limits

Level Measurement Accuracy: For precise inventory control, ensure level transmitters are regularly calibrated. The accuracy of the calculated volume heavily relies on the accuracy of the liquid height (H) measurement.
Tank Strapping & Calibration: For commercial transactions or custody transfer, tanks are typically 'strapped' or calibrated to create a precise volume table. This calculator provides theoretical values and should not replace certified strapping tables.
Overfill Protection: Always design with high-level alarms and trips to prevent overfilling, which can lead to spills, environmental damage, and safety hazards. Consider a minimum ullage (vapor space) even for 'full' conditions.
Minimum Operating Level: For pumps connected to the tank, ensure a minimum liquid level (NPSH available) is maintained to prevent cavitation and damage to the pump.
Vent Sizing: Tanks must be adequately vented to prevent over-pressurization or vacuum formation during filling/emptying and thermal breathing. The tank volume plays a role in vent sizing.
Structural Integrity: Be mindful of the weight of the liquid. The design should account for the maximum liquid density and volume to ensure the tank structure and supports are adequate.

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.