BIZOMAT MAKEOS · Strength
Tank Wall Panel under Liquid Pressure (Force, Plate Stress, Deflection)
What liquid pressure and force act on this flat tank wall, and is a panel between stiffeners thick enough in stress and deflection?
Check of a flat-walled (rectangular) tank: pressure at the bottom, the resultant force on the wall and its centre of pressure (as the hydrostatic force tool), and a rectangular panel between stiffeners treated as simply supported under the bottom pressure (conservative), with its bending stress and centre deflection (as the rectangular plate tool), the thickness needed for the allowable stress, and checks against the allowable stress and deflection limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Liquid depth | m | Depth of liquid above the tank floor. |
| Liquid density | kg/m³ | Density of the liquid. |
| Wall width | m | Width of the wall. |
| Gas pressure above the liquid | kPa | Gas or vapour pressure above the liquid (0 for an open tank). |
| Panel long side (between stiffeners) | mm | Longer side of the panel between stiffeners. |
| Panel short side | mm | Shorter side of the panel. |
| Plate thickness | mm | Plate thickness (after corrosion allowance). |
| Elastic modulus | GPa | Elastic modulus of the plate. |
| Allowable bending stress | MPa | Allowable bending stress in the plate (your design value). |
| Largest panel deflection | mm | Largest deflection you accept at the panel centre. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Liquid depth
- What it is
- The depth of liquid from its free surface down to the tank floor.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 50 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Floor pressure rises in proportion; the total wall force rises with the square of depth.
- Get it right
- Metres, while the panel sizes are in millimetres.
What this means: Liquid density
- What it is
- The density of the liquid held in the tank, which sets the hydrostatic pressure.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 100 kg/m³ to 3000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Wall width
- What it is
- The horizontal width of the tank wall holding the liquid, used for the total force on the wall.
- Units and format
- Enter a number in m: metres. The form accepts 0.000001 m to 200 m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Gas pressure above the liquid
- What it is
- Any gas or vapour pressure above the liquid surface, added to the liquid pressure on the wall.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 0 kPa to 1000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- 0 = open tank; enter gauge pressure.
What this means: Panel long side (between stiffeners)
- What it is
- The longer side of one flat plate panel between neighbouring stiffeners or wall edges.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Panel short side
- What it is
- The shorter side of the plate panel between stiffeners.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must not exceed the long side.
What this means: Plate thickness
- What it is
- The thickness of the wall plate, after deducting any corrosion allowance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress falls with the square of thickness and deflection with the cube.
What this means: Elastic modulus
- What it is
- Young’s modulus of the plate material, from the material data. It is used only for the panel deflection.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 400 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in GPa, not MPa: 1 GPa = 1000 MPa, so divide a data-sheet value given in MPa by 1000.
What this means: Allowable bending stress
- What it is
- The largest bending stress you accept in the plate, from the material strength and your design code.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 160 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Largest panel deflection
- What it is
- The largest deflection you accept at the panel centre, for appearance, linings, coatings or fittings.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Bottom pressure p = p_s + ρ g h; wall force = ρ g w h² ÷ 2 + p_s w h; centre of pressure from the floor (as the hydrostatic force tool).
- Simply supported rectangular panel under uniform pressure p: σ = 0.75 W ÷ [t² (L ÷ l + 1.61 l² ÷ L²)]; deflection = 0.1422 W ÷ [E t³ (L ÷ l³ + 2.21 ÷ L²)], W = p L l (as the rectangular plate tool).
- Thickness for the allowable: t = √{0.75 W ÷ [σ_allow (L ÷ l + 1.61 l² ÷ L²)]}.
- Example: 2 m of liquid gives 19.613 kPa at the floor; a 1000 × 600 mm panel of 7 mm plate runs at 80.187 MPa and deflects 3.5665 mm.
Limitations
- The bottom pressure is applied to the whole panel (conservative for upper panels).
- Stiffeners, corners and floor joints need their own design.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the plate of a rectangular water or chemical tank
- Choose stiffener spacing for a tank wall
- Check an existing tank for a heavier liquid
Who it is for
- Structural engineers
- Fabrication supervisors
- Plant engineers
What you get
- Bottom pressure, wall force and centre of pressure
- Panel stress and deflection
- Thickness needed and checks
Interpreting the result
- Halving the short side of the panel cuts the stress roughly four times: closer stiffeners save plate.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3024–3027, 288–290. Topic reference; no source tables or recommended settings are reproduced.
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Open the Tank Wall Panel under Liquid Pressure (Force, Plate Stress, Deflection) calculator