Pressure relief calculator

Size the valve. Paste the sheet.

API 520 / 521 orifice sizing with inlet 3% and outlet backpressure piping checks, plus Google Sheets formulas you can paste into A1. Open any unit or Calc dropdown for what the quantity is, which equation uses it, and the live arithmetic behind the number.

API 520 Part I/Critical and subcritical vapor relieving area from mass flow, k, and relieving pressure.

Inputs

Fluid present

Mass flow W

Relieving temperature T

Set pressure

Overpressure

Superimposed backpressure

Atmospheric pressure

Molecular weight M

Ratio of specific heats k

Compressibility Z

Viscosity

Discharge coefficient Kd

Backpressure factor Kb

Combination factor Kc

PSV piping

NPS + schedule look up the inside diameter. ID updates with either control.

Inlet NPS

Inlet schedule

Inlet ID

Outlet NPS

Outlet schedule

Outlet ID

Inlet length

Outlet length

Inlet 90° elbows

Outlet 90° elbows

Valve type

Spring-loaded, no bellows. Total backpressure ≤ 10% of set (API 520 Part I / II).

Case name

Results

Required area

1.0153in²

API 526 J78.892% used

Orifice used78.892%

124.7psia

14.696psia

Regime

Critical

356.06

0.5283

r = P2/P1

0.1179

Rated W

12,676lb/h

Inlet 3% · outlet 10%

Inlet · 3% rule

Pass

2.66% of set

ΔP 2.658 psi · limit 3 (3%)

Outlet · 10% rule

Pass

2.85% of set

Total back 2.85 psig · limit 10 (10%)

Inlet ID / Leq

2.067″ · 5.8ft

Inlet velocity

251.22ft/s · Ma 0.22

Built-up backpressure

2.85psig · 2.9%

Outlet ID / Leq

4.026″ · 25.736ft

Outlet velocity

512.2ft/s · Ma 0.44

Darcy f · Re (inlet)

0.0192 · 2,151,759

Recommended NPS

Current lines pass the 3% and backpressure rules.

Outlet reaction force

116.26lbf

Inlet and outlet losses use the rated capacity of the selected API 526 letter (API 520 Part II).

Google Sheet

Copies a live calculator: highlighted cells are inputs, the rest are formulas. Open a blank Google Sheet, click A1, paste.

ReliefCalc — Gas / vapor (API 520)
Paste into A1 of a blank Google Sheet. Edit INPUT cells in column B — orifice and piping formulas stay live.

INPUTS	Value	Unit	Notes
Fluid present	Air	—	Documentary — MW, k, Z, μ still edit below
Mass flow W	10,000	lb/h	Required relieving rate
Relieving temperature T	100	°F	Stagnation temperature at the inlet
Set pressure	100	psig	PRV set pressure (gauge)
Overpressure	10	%	ASME single-valve non-fire is typically 10%
Superimposed backpressure	0	psig	Constant backpressure at the outlet
Atmospheric pressure	14.696	psia	14.696 psia at sea level
Molecular weight M	28.97	lb/lbmol
Ratio of specific heats k	1.4	—	Cp/Cv
Compressibility Z	1	—	1.0 if unknown and near ideal
Viscosity μ	0.018	cP	For inlet/outlet Reynolds number
Discharge coefficient Kd	0.975	—	0.975 certified vapor PRV (API 520)
Backpressure factor Kb	1	—	1.0 conventional if Pback ≤ 10% of set
Combination factor Kc	1	—	0.9 if a rupture disk is installed upstream

RESULTS	Value	Unit	Notes
Relieving pressure P1	fx124.7	psia	Set × (1+OP/100) + Patm
Absolute backpressure P2	fx14.696	psia
Absolute temperature	fx559.67	°R	T + 459.67
Pressure ratio r	fx0.1179	—	P2 / P1
Critical ratio rc	fx0.5283	—	(2/(k+1))^(k/(k-1))
Flow regime	fxCritical	—	Critical when r ≤ rc
Coefficient C	fx356.06	—	API 520 Eq. 5
Subcritical F2		—	API 520 Eq. 8 (blank if critical)
Required area A	fx1.0153	in²	API 520 Eq. 3 (critical) / Eq. 7 (subcritical)
Required area	fx655.06	mm²
Selected orifice	fxJ	API 526	API 526 effective area — next letter ≥ required A
Letter area	fx1.287	in²
Valve count	fx1	—
Installed area	fx1.287	in²
Rated capacity	fx12,676	lb/h	Capacity of the selected API 526 letter(s)
Orifice used	fx0.789	fraction	1.00 = fully used

PIPING (API 520 Part II)	Value	Unit	Notes
Valve type	conventional	—	conventional \| balanced \| pilot
Backpressure limit	fx0.1	fraction of set	10% conventional · 30% balanced · 50% pilot
Inlet NPS	2	in	Nominal pipe size
Inlet schedule	40	—	Sch. 40
Inlet length	3	ft	Vessel nozzle to PSV
Inlet 90° elbows	1	—	Le/D = 16 each
Outlet NPS	4	in	Tailpipe / header
Outlet schedule	40	—	Sch. 40
Outlet length	15	ft
Outlet 90° elbows	2	—	Le/D = 16 each
Inlet ID	fx2.067	in	ASME B36.10
Outlet ID	fx4.026	in
Inlet Leq	fx5.76	ft	Straight + elbows
Outlet Leq	fx25.736	ft
Darcy f (inlet)	0.0192	—	Copied from ReliefCalc (Swamee–Jain). Weakly depends on Re.
Darcy f (outlet)	0.0169	—	Copied from ReliefCalc (Swamee–Jain).
Piping flow W	fxrated	lb/h	Rated letter capacity (API 520 Part II)
Inlet ΔP	fx2.6577	psi	Isothermal Darcy at P1 = set·(1+OP/100)+Patm (psia). ΔP is psi, not gauge.
Built-up backpressure	fx2.8504	psi	Known downstream: √(Pexit²+kterm)−Pexit. Pexit = superimposed + Patm (psia). Atmosphere is 0 psig.
3% of set	fx3	psig	Inlet non-recoverable limit
Inlet loss	fx0.0266	fraction of set	Must be ≤ 0.03
Inlet 3% rule	fxPASS	—	API 520 Part II
10% of set	fx10	psig	Total backpressure limit for the selected valve type
Total backpressure	fx2.85	psig	Superimposed (gauge) + built-up (differential). Atmosphere is 0 psig, not Patm.
Outlet loss	fx0.0285	fraction of set	Must be ≤ 0.1 for this valve type
Outlet 10% rule	fxPASS	—	Raise valve type or enlarge the tailpipe if FAIL
Outlet reaction force	116.26	lbf	API 520 Part II open-discharge (copied from ReliefCalc). × 4.448 for N.

Methods: API 520 Part I (gas/vapor) and Part II (3% inlet / valve-type outlet). Kd, Kb, Kc from the valve manufacturer. Not a stamped design.