Enter the desired set pressure (SP), total back pressure (BP), and built-up back pressure (BUP) into the calculator to determine the cold differential test pressure (CDTP) (sometimes informally called “cold differential set pressure”). Use consistent units and the same pressure basis for all inputs (all gauge or all absolute).

Cold Differential Test Pressure (CDTP) Calculator

Enter any 3 values to calculate the missing variable (for conventional spring-loaded PRVs, CDTP = SP − SBP, where SBP = BP − BUP).

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Cold Differential Test Pressure (CDTP) Formula

The following relationship is commonly used for conventional spring-loaded pressure relief valves to set the cold differential test pressure (bench setting) based on back pressure components. The key correction to set pressure is based on superimposed back pressure (the back pressure present before the valve opens). Balanced bellows and pilot-operated valves may require different treatment; consult the applicable code/standard and the valve manufacturer.

CDTP = SP - (BP - BUP)

Variables:

  • CDTP is the Cold Differential Test Pressure (the bench test setting at ambient/cold conditions).
  • SP is the Set Pressure (the desired in-service opening pressure).
  • BP is the Total Back Pressure (BP = SBP + BUP).
  • BUP is the Built-up Back Pressure (the portion created by flow through the discharge system after the valve opens). The superimposed back pressure is SBP = BP − BUP.

To calculate CDTP, first find the superimposed back pressure (SBP) as SBP = BP − BUP, then subtract SBP from the set pressure: CDTP = SP − SBP.

What is Cold Differential Test Pressure?

Cold Differential Test Pressure (CDTP) is a pressure relief valve term used for bench testing a valve at ambient (“cold”) conditions. It is the test stand pressure at which the valve is adjusted to start opening so that, when installed in service (where superimposed back pressure and other conditions may exist), the valve will open at the desired set pressure. In many references, CDTP may also include corrections for temperature and other effects; this calculator focuses on the back pressure component shown above.

How to Calculate Cold Differential Test Pressure?

The following steps outline how to calculate the Cold Differential Test Pressure (CDTP) using back pressure components.

  1. Determine the desired set pressure (SP) for the protected equipment.
  2. Determine the total back pressure (BP) expected at the valve outlet during relieving.
  3. Determine the built-up back pressure (BUP) (the portion of back pressure that develops due to flow after the valve opens).
  4. Compute superimposed back pressure: SBP = BP − BUP.
  5. Calculate CDTP using CDTP = SP − SBP (equivalently CDTP = SP − (BP − BUP)).
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Set Pressure (SP) = 100 psi

Total Back Pressure (BP) = 10 psi

Built-up Back Pressure (BUP) = 5 psi (so SBP = BP − BUP = 5 psi, and CDTP = SP − SBP = 95 psi)