Tank Force Inputs
Enter internal tank measurements and liquid properties in SI units.
Formula Used
This calculator treats the tank as an upright circular cylinder with a horizontal free liquid surface.
Pressure at the base
pb = ρgh
ρ is liquid density, g is gravity, and h is liquid depth.
Base force
Fbase = pbAbase
Abase = πD² / 4
The base force equals the liquid weight when the tank is upright.
Wall values
Awall = πDh
Fnormal,sum = (ρgh / 2)(πDh)
This is a sum of radial force magnitudes around the wall.
Half-wall resultant
Fhalf = ρgDh² / 2
It acts horizontally on one semicircular half of the wall.
Center of pressure
ycp = 2h / 3
It is measured below the liquid free surface for the half-wall projection.
Optional hoop stress
σh ≈ pbD / (2t)
Use this thin-wall screening estimate only when its assumptions are appropriate.
How to Use This Calculator
- Measure the tank inside diameter, not its outside diameter.
- Enter the actual liquid depth at the operating condition.
- Use a density matching the liquid temperature and composition.
- Keep standard gravity unless your application requires another value.
- Enter a safety factor for a preliminary factored base-load comparison.
- Add wall thickness only for the optional thin-wall screening result.
- Select calculate. Review results above the form before using them.
Example Data
These sample inputs match the prefilled calculator values.
| Quantity | Example value | Unit | Meaning |
|---|---|---|---|
| Liquid density | 1000 | kg/m³ | Fresh water approximation |
| Gravity | 9.80665 | m/s² | Standard Earth gravity |
| Inside diameter | 2.00 | m | Internal circular width |
| Liquid depth | 3.00 | m | Free surface to base |
| Safety factor | 1.50 | — | Preliminary load multiplier |
Understanding Cylindrical Tank Hydrostatic Loads
Hydrostatic loading comes from the weight of stationary liquid. Pressure grows with depth. It does not depend on the tank diameter at one chosen depth. A deeper liquid column produces higher pressure at the base. A denser liquid also produces higher pressure. These relationships make depth and density critical design inputs.
Pressure Changes Down the Wall
At the free surface, gauge pressure is zero. Pressure rises linearly as the liquid moves downward. The bottom pressure is density multiplied by gravity and liquid depth. This is the greatest pressure inside an open upright tank. The pressure distribution forms a triangle when drawn on a vertical wall section. That triangular pattern controls wall loading and the center of pressure.
Base Force Equals Liquid Weight
The tank base carries the downward hydrostatic force. For an upright cylinder, base pressure multiplied by base area gives that force. The result also equals the liquid weight. This equality provides a useful check. Increase the tank diameter and the base area grows quickly. Increase the liquid depth and both pressure and volume grow. Base loading therefore rises rapidly with larger dimensions.
Curved Wall Forces Need Care
Pressure acts perpendicular to every small wall area. On a cylindrical wall, those local directions point radially outward. They do not all point in one direction. The full cylinder has no single net horizontal force from internal liquid pressure. Opposite portions balance. However, the shell still experiences important local pressure and hoop action. The integrated wall normal load shown here sums force magnitudes. It is useful for understanding total local loading, not external support reaction.
Half-Wall Resultant and Its Location
Engineers sometimes isolate one semicircular half of the shell. Its horizontal hydrostatic resultant can then be calculated from the vertical projected area. The resultant acts at two-thirds of the liquid depth below the free surface. This is the center of pressure. It lies below the centroid because lower regions carry more pressure. The half-wall value can assist with conceptual shell splits, restraints, and inspection of load paths.
Using the Safety Factor
The displayed factored base force is the calculated base force multiplied by your selected safety factor. It is a planning value. It does not establish compliance with any tank code. A proper design can require load combinations, allowable stresses, buckling checks, weld efficiency, corrosion allowance, anchors, foundation behavior, wind, seismic effects, and internal vacuum cases. Use the calculator to organize preliminary quantities. Then verify the final tank design through suitable engineering standards.
Important Measurement Choices
Use internal diameter. Use current liquid depth, including possible operating maximum. Choose density at realistic temperature and concentration. Avoid assuming water density for chemicals, brines, oils, or slurries. Confirm whether pressure should be gauge or absolute. This calculator reports gauge pressure from the liquid alone. Add gas pressure above the liquid separately when a closed or pressurized vessel is involved.
Frequently Asked Questions
1. What does hydrostatic force mean?
Hydrostatic force is the force created by a liquid at rest. It results from pressure acting over an area. Pressure increases with liquid depth, so lower tank surfaces carry greater load.
2. Does tank diameter change bottom pressure?
No. Bottom pressure depends on liquid density, gravity, and depth. Diameter changes the base area. Therefore, diameter changes total base force and stored liquid volume.
3. Why is the base force equal to liquid weight?
For an upright tank with a horizontal base, the liquid weight acts downward. The hydrostatic pressure force on the base provides the matching upward support. Their magnitudes are equal in static equilibrium.
4. What is gauge pressure in this calculator?
Gauge pressure is pressure above surrounding atmospheric pressure. The calculator starts at zero gauge pressure at the free surface. It does not include extra gas pressure in a sealed vessel.
5. Can I use this calculator for a pressurized tank?
Use it only for the liquid-head portion. Add the uniform internal gas pressure separately to relevant surface-pressure calculations. A pressurized vessel requires additional design checks beyond this preliminary tool.
6. What is the integrated wall normal load?
It is the sum of local force magnitudes acting normal to the wetted cylindrical wall. Because directions vary around the circumference, it is not a single net horizontal force on the complete tank.
7. Why is the center of pressure below mid-depth?
Lower wall regions have greater liquid pressure. This shifts the resultant below the projected-area centroid. For the triangular pressure pattern, the location is two-thirds of the depth below the free surface.
8. Is the hoop stress result a complete wall design?
No. It is a thin-wall estimate at maximum liquid pressure. It excludes weld details, material properties, corrosion, buckling, openings, supports, design standards, and many other required checks.
9. Which density should I enter for salt water?
Enter the measured or specified density for your actual salt-water concentration and temperature. Do not automatically use fresh-water density. Small density changes directly change pressure and force.
10. Can this model analyze a horizontal cylinder?
No. This model assumes an upright cylinder with a circular horizontal base. A horizontal tank has changing submerged geometry and needs a different volume and force analysis.
11. What safety factor should I choose?
Use the value required by your project, material, operating conditions, and governing standard. The default is a demonstration value only. It does not replace a code-based load combination or design review.