Engineering task and calculation objective
Before commissioning, every pressure vessel must undergo a pressure test — usually a hydrostatic test with water. This module calculates the test pressure for a complete project to DIN EN 13445-5, clause 10.2: for each component, the required test pressure is determined from the maximum allowable pressure PS and the ratio of the material strengths at test and design temperature; the value to be applied at the highest point governs for the apparatus.
The background: when testing with cold water, the material is stronger than at design temperature. The code exploits this and requires the larger value of two criteria — the temperature-corrected approach with the factor 1.25 and the ratio of nominal design stresses fa/fTd, and the flat-rate approach 1.43 · PS. The module evaluates both criteria material by material for all components of the project and delivers the underlying material properties as well.
Optionally, bolts and flanges can be included in or excluded from the assessment — relevant when flange connections would otherwise limit the test pressure. This determines and documents the test pressure to EN 13445 for the entire apparatus in a single step.
Standard and calculation basis: DIN EN 13445-5/10.2: 2021-12
Calculation workflow
- Read in the components and materials of the project: The module takes over all pressure-bearing components of the project with their materials, design temperatures and maximum allowable pressures. An input option controls whether bolts and flanges are considered in the determination.
- Determine nominal design stresses at test and design temperature: For each material, the nominal design stress f_a at test temperature (usually room temperature) and the nominal design stress f_Td at design temperature are determined. The ratio f_a/f_Td reflects the strength reserve that the cold material has compared with the operating condition.
- Calculate the test pressure per component using both criteria: For each component, the test pressure is formed as the maximum of 1.25 · PS · f_a/f_Td and 1.43 · PS. For creep-resistant steels with a significant strength drop at operating temperature, the first criterion usually governs; at low design temperatures, the second.
- Establish the governing test pressure at the highest point: From the component values, the test pressure governing for the apparatus at the highest point of the vessel is determined. During the hydrostatic test, the static head of the water column adds at lower elevations — this must be considered for tall apparatus when assessing the lower shell courses.
- Check the test conditions: Finally, it must be ensured that no component is inadmissibly loaded in the test condition: for the test load case, separate, higher allowable stresses apply (referred to the yield strength at test temperature). The module compiles the material properties of all materials used and makes the assessment traceable.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Select Largest (L) or smallest (S) ratio of strength values | Verhältni | - |
| Consider bolts and flanges (1=No, 0=Yes) | 0=Ja) | - |
| Standard calculation temperature | Ts | °C |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| Druckbehälters | Druckbehälters | - |
| 1 | 1 | - |
| 2 | 2 | - |
| 3 | 3 | - |
| 4 | 4 | - |
| 5 | 5 | - |
| 6 | 6 | - |
| 7 | 7 | - |
| 8 | 8 | - |
| 9 | 9 | - |
| 10 | 10 | - |
| 1 | 1 | mm |
Calculation options
Hydrotest
horizontal · vertical
Worked example
For a vessel made of P265GH with a maximum allowable pressure PS = 16 bar and a design temperature of 200 °C, the test pressure for the hydrostatic test at room temperature is to be determined to DIN EN 13445-5, clause 10.2.3.3.1 — a worked example for calculating the hydrostatic test pressure to EN 13445.
Given values
| Maximum allowable pressure PS | 16 bar |
| Design temperature | 200 °C |
| Test temperature | 20 °C |
| Material | P265GH (Rp0.2/20 °C = 265 MPa; Rp0.2/200 °C = 192 MPa; Rm = 410 MPa) |
Solution
Nominal design stresses at test and design temperature
Nominal design stress at test temperature (20 °C):
fa = min(Rp0.2/20 °C/1.5; Rm/2.4) = min(265/1.5; 410/2.4) = min(176.7; 170.8) = 170.8 MPa
Nominal design stress at design temperature (200 °C):
fTd = min(192/1.5; 410/2.4) = min(128.0; 170.8) = 128.0 MPa
Evaluate both test pressure criteria
Criterion 1 (temperature-corrected):
Pt1 = 1.25 · PS · fa/fTd = 1.25 · 16 · 170.8/128.0 = 26.69 bar
Criterion 2 (flat rate):
Pt2 = 1.43 · PS = 1.43 · 16 = 22.88 bar
Establish the governing test pressure
The maximum of both criteria governs:
Pt = max(26.69; 22.88) = 26.69 bar at the highest point of the vessel.
Because of the strength drop of P265GH between 20 °C and 200 °C (ratio fa/fTd = 1.33), the temperature-corrected criterion is decisive here.
Result
| Nominal design stress f_a (20 °C) | 170.8 MPa |
| Nominal design stress f_Td (200 °C) | 128.0 MPa |
| Test pressure Pt | 26.69 bar (≈ 26.7 bar) |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why does the test pressure formula contain the ratio f_a/f_Td?
The pressure test is meant to load the component at least as severely as the design condition at operating temperature does. Since the material has a higher strength at test temperature (cold) than at design temperature, the test pressure is scaled up by the ratio of the nominal design stresses. Without this correction, a vessel designed for 300 °C would only be incompletely tested to its design level in the cold state.
When does 1.25 · PS · f_a/f_Td govern and when 1.43 · PS?
The first criterion dominates as soon as f_a/f_Td > 1.144 — that is, for materials with a significant strength drop between test and design temperature, typically from design temperatures of about 150–200 °C upwards. For vessels with a low design temperature (f_a ≈ f_Td), the flat-rate factor 1.43 yields the larger and thus governing value. The code always requires the maximum of both criteria.
Why can it make sense to exclude bolts and flanges from the test pressure determination?
Flange connections are frequently the component with the lowest allowable pressure, without their limit reflecting the shell strength — for instance because of gasket properties or bolt utilization. If they determined the test pressure, the apparatus could be tested below its actually required level. The option allows the test pressure to be derived from the pressure-bearing walls and the flange connection to be assessed separately for the test load case.
Must the water column be considered in the hydrostatic test?
Yes. The calculated test pressure applies at the highest point of the vessel. For vertical apparatus, the static head of the filling additionally acts on the lower shell courses — around 2 bar for a 20 m tall column. The lower components must sustain this increased pressure in the test condition; conversely, the pressure gauge at the base must not serve as the reference for the test pressure at the top.