Engineering task and calculation objective
Before even a single wall thickness can be sized, the design pressure and test pressure of a pressure vessel must be established. The design pressure is the pressure with which all strength verifications of the AD 2000 B series are carried out; the test pressure is the pressure of the hydrostatic test before commissioning. Module B0 determines both quantities for vessels under internal pressure to AD 2000-Merkblatt B0 and HP 30 of the German AD 2000 pressure vessel code.
The starting point is the maximum allowable operating pressure. To this are added any additional margin on the operating pressure (for example to cover control and set-point differentials of the overpressure protection) and — often underestimated — the hydrostatic pressure of the liquid column: from the vessel diameter, the maximum operating liquid level and the density of the operating medium, the module obtains the calculated operating pressure at the lowest point of the vessel. For the pressure test, the calculation correspondingly uses the maximum filling height and the density of the test medium (usually water).
The module additionally offers the option of holding a 10 % stress reserve in the shell (cf. AD 2000 S3/6) and, if desired, raising the test pressure accordingly. Determining the design pressure and test pressure correctly is the foundation of every pressure vessel calculation — errors at this stage propagate into all wall thickness verifications.
Standard and calculation basis: AD 2000 B0: 2014-11; HP 30: 2016-05
Calculation workflow
- Define the allowable operating pressure and additions: The starting quantity is the maximum allowable operating gauge pressure PS of the vessel. An addition to the operating pressure can also be specified, for example to cover pressure fluctuations in operation or the blowdown of the safety valve.
- Determine the hydrostatic component in operation: From the maximum operating liquid level and the density or specific weight of the operating medium, the static pressure of the liquid column is calculated. It is added to the operating gauge pressure and yields the calculated operating pressure at the lowest point — the governing quantity for the verification of the low-lying components.
- Select the stress reserve options: Optionally, an additional 10 % stress reserve in the shell can be specified (see AD 2000 S3/6, 1st scope). The module then asks whether the reserve should also be applied to the addition to the operating pressure and to the test pressure.
- Determine the test pressure to HP 30: The test pressure of the hydrostatic test is derived from the design pressure to AD 2000 HP 30; for equipment within the scope of the Pressure Equipment Directive, the directive's minimum test pressure (Annex I, 7.4) must also be observed. For the test condition, the maximum filling height and the density of the test medium are taken into account, since the water column additionally loads the bottom during the pressure test.
- Pass the results to the follow-on modules: The design pressure and test pressure are then available as input quantities for the wall thickness verifications of modules B1 to B13 and for the verification of the test condition.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Allowable operating pressure | p | bar |
| Diameter of vessel (inside) | Di | m |
| Max. liquid level, test (= vessel height) | H | m |
| Max. liquid level, operation | HF | m |
| Density of the operation medium | ρF | kg/m³ |
| Density of the test medium | ρP | kg/m³ |
| Content during test | 1. | – |
| Testing under condition described in 4.19.1? (under safe conditions) (Y/N) | _Prüfbedingungen | – |
| Vessel clad with material sensitive to strain or pressure as described in 4.18.2? (Y/N) | ausgekleidet | – |
| Test performed | 2. | – |
| Coefficient for test pressure (4.17 - 4.19) | Fp | – |
| , for pressure test acc. 4.10. | Pp | bar |
| Spec. weight (operation medium) | γF | dN/dm³ |
| Spec. weight (test medium) | γP | dN/dm³ |
| Pressure for design strength value | pmat | bar |
| Permit additional 10% strength in the shell (see also AD-S3/6, 1. Scope)? (Y/N) | Spannungsreserven | – |
| Druckbehälters | 1 | – |
| Max. operating temperature | T | °C |
| Druckbehälters | 2 | – |
| Druckbehälters | 3 | – |
| Druckbehälters | 4 | – |
| Druckbehälters | 5 | – |
| Druckbehälters | 6 | – |
| Druckbehälters | 7 | – |
Calculation options
Content during test
liquid · gas
Test performed
with put-up vessel (Calculation acc. to 4.10.1) · once with layed-down vessel (acc. to 4.10.2) · only with layed-down vessel (acc. to 4.10.3)
Worked example
A vertical storage vessel (water, ρ = 1,000 kg/m³) has a maximum allowable operating gauge pressure of 10 bar. The maximum operating liquid level is 8 m. Find the calculated operating pressure at the lowest point and the minimum test pressure under the Pressure Equipment Directive (design temperature 20 °C, strength ratio test/design temperature = 1) — a worked example of determining design pressure and test pressure.
Given values
| Maximum allowable operating gauge pressure PS | 10 bar |
| Maximum operating liquid level H | 8 m |
| Density of the operating medium ρ | 1,000 kg/m³ |
| Gravitational acceleration g | 9.81 m/s² |
Solution
Hydrostatic pressure of the liquid column
pstat = ρ · g · H = 1,000 · 9.81 · 8 = 78,480 Pa ≈ 0.785 bar
Calculated operating pressure at the lowest point
p = PS + pstat = 10 + 0.7848 = 10.78 bar
The low-lying components (lower course, bottom head) must be verified with this pressure.
Minimum test pressure to PED Annex I, 7.4
pT = max(1.25 · PS · ftest/fdesign; 1.43 · PS) = max(1.25 · 10 · 1; 1.43 · 10) = max(12.5; 14.3) = 14.3 bar
During the pressure test, the static head of the test water is additionally applied at the lowest point (approx. 0.98 bar at a filling height of 10 m), which must be taken into account when verifying the test condition.
Result
| Calculated operating pressure at the lowest point | 10.78 bar |
| Minimum test pressure pT | 14.3 bar |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
What is the difference between operating pressure, design pressure and maximum allowable pressure PS?
The operating pressure is the pressure actually occurring in normal operation. PS is the maximum allowable pressure specified by the manufacturer, at which the overpressure protection is set. The design pressure is the pressure with which the strength verifications are carried out — it is at least equal to PS and additionally includes the hydrostatic component at the point considered as well as any additions.
When must the hydrostatic pressure be taken into account?
Whenever it is not negligibly small compared with the operating gauge pressure. As a rule of thumb: from about 5 % of the operating gauge pressure onwards, the liquid column should be included. For tall, slender vessels with heavy media (e.g. columns) and at low operating pressures, the static component is frequently design-governing for the lower courses and the bottom head.
How high is the test pressure for the hydrostatic test?
Under the Pressure Equipment Directive (Annex I, 7.4), the test pressure is at least the greater of 1.25 · PS · (strength value at test temperature / strength value at design temperature) and 1.43 · PS. AD 2000 HP 30 specifies how the test is carried out. For design temperatures close to room temperature, the value 1.43 · PS is usually governing.
What is the purpose of the 10 % stress reserve in the shell?
The option under AD 2000 S3/6 holds a calculational reserve of 10 % in the shell, which creates margin for example under cyclic loading or for later changes of service. It leads to somewhat greater wall thicknesses; whether it is also applied to the operating pressure addition and to the test pressure is a project-specific decision and can be set in the module.