Calculate cold differential test pressure (CDTP), set pressure, total back pressure or built-up back pressure for PRVs in psi, bar, kPa, atm or mmHg.
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Cold Differential Test Pressure (CDTP) Formula
For a conventional spring-loaded pressure relief valve, cold differential test pressure adjusts the set pressure for superimposed back pressure. The calculator first finds superimposed back pressure, then uses it to solve for the missing value.
SBP = BP - BUP
CDTP = SP - SBP
CDTP = SP - (BP - BUP)
The calculator can also rearrange the formula to solve for any one missing value:
SP = CDTP + (BP - BUP)
BP = (SP - CDTP) + BUP
BUP = BP - (SP - CDTP)
- CDTP = cold differential test pressure
- SP = set pressure
- BP = total back pressure
- BUP = built-up back pressure
- SBP = superimposed back pressure
To calculate CDTP, enter set pressure, total back pressure, and built-up back pressure. To calculate set pressure, enter CDTP, total back pressure, and built-up back pressure. To calculate total back pressure, enter set pressure, CDTP, and built-up back pressure. To calculate built-up back pressure, enter set pressure, CDTP, and total back pressure.
If you use different pressure units, the calculator converts each input to psi internally, performs the calculation, then converts the missing value back to the unit selected for that field.
Pressure Unit Conversion Factors Used
These factors show how each pressure unit is converted to psi before the formula is applied.
| Unit | Multiply by to convert to psi | Example |
|---|---|---|
| psi | 1 | 100 psi = 100 psi |
| bar | 14.5037738 | 10 bar = 145.0377 psi |
| kPa | 0.1450377377 | 500 kPa = 72.5189 psi |
| atm | 14.6959488 | 2 atm = 29.3919 psi |
| mmHg | 0.0193367747 | 760 mmHg = 14.6959 psi |
Back Pressure Terms in the CDTP Calculation
| Term | Meaning | Role in the formula |
|---|---|---|
| Set pressure, SP | The pressure at which the valve is intended to open under service conditions. | Starting pressure before back pressure adjustment. |
| Total back pressure, BP | The total pressure on the outlet side of the valve. | Used with built-up back pressure to determine superimposed back pressure. |
| Built-up back pressure, BUP | Back pressure generated after the valve opens due to flow through the discharge system. | Subtracted from total back pressure to isolate superimposed back pressure. |
| Superimposed back pressure, SBP | Back pressure present before the valve opens. | Subtracted from set pressure to find CDTP. |
Example Calculations
Example 1: Calculate CDTP
You have a set pressure of 150 psi, a total back pressure of 30 psi, and a built-up back pressure of 10 psi.
SBP = BP - BUP = 30 - 10 = 20 psi
CDTP = SP - SBP = 150 - 20 = 130 psi
The cold differential test pressure is 130 psi.
Example 2: Calculate Set Pressure
You have a CDTP of 180 psi, a total back pressure of 40 psi, and a built-up back pressure of 15 psi.
SBP = BP - BUP = 40 - 15 = 25 psi
SP = CDTP + SBP = 180 + 25 = 205 psi
The set pressure is 205 psi.
FAQ
What does CDTP mean?
CDTP means cold differential test pressure. It is the pressure used when testing a pressure relief valve on a test stand at ambient temperature, adjusted for the effect of superimposed back pressure. For a conventional spring-loaded PRV, the basic relationship is CDTP = set pressure minus superimposed back pressure.
Why is built-up back pressure subtracted from total back pressure?
Total back pressure includes both superimposed back pressure and built-up back pressure. Built-up back pressure is created after the valve opens because of flow through the outlet system. CDTP adjustment uses superimposed back pressure, so the calculator estimates it as total back pressure minus built-up back pressure.
Can CDTP be higher than set pressure?
Yes, but only if the calculated superimposed back pressure is negative. Using the formula CDTP = SP – SBP, a negative SBP increases the CDTP. If that result is unexpected, check the back pressure inputs and make sure total back pressure and built-up back pressure are being entered with the intended definitions and units.