Consequence Analysis 1.2

Mechanical Energy Balance

Flow of Liquid Through a Hole let then

Discharge Coefficient For sharp-edged orifices and for Re greater than 30000, Co approaches the value of 0.61. For a well-rounded nozzle, it approaches unity. For a short section of pipe attached to a vessel (with L/D not less than 3), it is approximately 0.81. For cases where it is unknown or uncertain, use a value of 1.0.

Flow of Liquid Through a Hole in a Tank

Empty Time

Empty Time

Liquid Discharge Discharge of pure non-flashing liquid through an orifice

Flow of Vapor Through Holes (Isentropic Expansion)

Flow of Vapor Through Holes (Isentropic Expansion) For ideal gas

Choked Pressure The choked pressure is the maximum downstream/upstream pressure ratio resulting in maximum flow through the hole, i.e.

Critical Pressure Ratio Typical value of specific heat ratio range from 1.1 to 1.67, which gives the critical values of 1.71 to 2.05. Thus for releases of most diatomic gases (1.4) to atmosphere, upstream pressures over 1.9 bar abs. will result in sonic flow.

Critical Pressure Ratio For pressure ratio larger than r_crit, The velocity of fluid at the throat of the leak is the velocity of sound; The velocity and mass flow rate cannot be increased further by reducing the downstream pressure and/or increasing the upstream pressure. This type of flow is called choked, critical, or sonic flow.

Gas Discharge Rate

Flow Factor For subsonic flows For sonic (choked) flows

Flashing Liquid Excess energy in superheated liquid Mass of liquid vaporized Fraction of liquid vaporized The implied assumption is constant physical property.

Flashing Liquid Without the assumption

Flow of Flashing Liquid If the flow path length is very short, nonequilibrium condition exists, the liquid flash external to the hole. The equations describing incompressible fluid flow through hole apply. If the flow path length is greater than 10 cm, equilibrium flashing conditions are achieved and the flow is choked. A good approximation is to assume a choked pressure equal to the saturation vapor pressure of the flashing liquid. The result will be applicable for liquids stored at higher pressure.

Flow of Flashing Liquid Stored at Higher Pressure

Flow of Flashing Liquid Stored at Saturation Vapor Pressure

Flow of Flashing Liquid Stored at Saturation Vapor Pressure

Two-Phase Discharge (1) The discharge of subcooled or saturated liquids The effect of subcooling is accounted for by

Two-Phase Discharge (2) For saturated liquids, equilibrium is reached if the discharge pipe size is greater than 0.1 m (length greater than 10 diameter). The discharge rate is

Two-Phase Discharge (3) For discharge pipe less than 0.1 m, the flashing flow increases strongly with decreasing length, approaching all liquid flow as the pipe length approaches zero. The discharge rate of flashing liquids from sharp-edged orifice at vessels can be estimated as though there were no flashing.