The Seetru safety valve capacity determination expressions below are based on BS 6759: Part 2: 1984. They apply to critical flow conditions, which occur when

where

For air, k = 1.4, and r becomes

Hence critical flow for air occurs broadly above 1 bar gauge set pressure, when discharging to atmosphere.

The mass flow of gas, q_mg, being discharged by the safety valve is then given by

where

where

Any departure of the value Z from 1 is a measure of the departure of the vapour properties from that of a gas. Z can be calculated from vapour tables, but may be taken as approximately 1 for significantly susuperheated vapours. BS 6759 provides curves of Z as a function of vapour conditions.

By substituting (3) in (2) a modified expression is obtained

which can be convenient if the specific volume, v, of a vapour is known.

For air M = 29, C = 2.7, Z = 1. Thus from (2) the mass flow of air, q_ma, is given by

For standard rating flow temperature of 15°C and a valve seat bore diameter of d_o mm

This is the mass flow given on the Seetru safety valve data sheets.

To convert a critical mass flow of air q_ma at 15°C for a given valve to that of another gas of molecular mass M, value Z_gas, and flowing at t°C, this follows as

where

The factor F is tabulated for a range of gases see table

(6) can be transposed

This form is useful to give the mass flow of air equivalent to a known mass flow of gas. It will allow a safety valve sizing to be checked against tabulation of air mass flow in kg/hr

from (5) and (6), for a given mass flow q_mg of a gas, the required safety bore d_o can be found using

taking Z_gas=1

As an alternative, the rated flow of gases is often given in standard litres per second, which is the volume occupied by the mass per second at 1 atmosphere pressure (1.013 bar absolute) and 15°C.

The general expression according to the gas laws for the volume V litres of a mass W kg of gas of molecular mass M at pressure P bar absolute and temperature T °K absolute is

For standard litres T=288°K,P=1.013 bar

It may be noted that for European standards the standard litre is defined at 0°C, and hence it must be reduced in the ratio

Multiplied by 3.6, this standard litre per second converts to European normal cubic metre per hour: N m³/hr.

Hence a mass flow of q_mg kg/hr is equivalent to

where Q_gas = Volumetric flow at standard conditions

By substituting from (2)

For air flowing at t=15°C

In terms of flow diameter d_o

Hence to convert to Q_gas std. litres/s flowing at t°C from tabulated values of Q_air (e.g. In Seetru datasheets)

where

is also shown from the gas properties table that (14) can also be transposed;

This form is useful to give the air flow in std. litres/sec equivalent to a known gas flow in std. litres/s. It will allow a safety valve sizing to be checked against tabulation of standard volumetric air flow.

Using (12) and (14), for a given flow of gas Q_gas Std. litres/s, the required safety valve d_o can be found;

For Z_gas=1;

If for a given range of safety valves the value of the coefficient of discharge is not uniform, then by putting the lowest value into (16), the minimum safe seat diameter will be obtained.