1. Consequence Analysis 1.2

3. Mechanical Energy Balance

5. Flow of Liquid Through a Hole
let
then

6. 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.

8. Flow of Liquid Through a Hole in a Tank

9. Empty Time

10. Empty Time

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

13. Flow of Vapor Through Holes (Isentropic Expansion)

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

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

16. 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 Thus for releases of most diatomic
gases (1.4) to atmosphere, upstream pressures over 1.9 bar abs. will
result in sonic flow.

17. 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.

19. Gas Discharge Rate

20. Flow Factor
For subsonic flows
For sonic (choked) flows

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

22. Flashing Liquid
Without the assumption

23. 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.

24. Flow of Flashing Liquid Stored at Higher Pressure

25. Flow of Flashing Liquid Stored at Saturation Vapor Pressure

26. Flow of Flashing Liquid Stored at Saturation Vapor Pressure

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

28. 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

29. 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.