# Find the cooldown rate and the suppression pool temperature in Problem 23 for a case that the relief

Find the cooldown rate and the suppression pool temperature
in Problem 23 for a case that the relief valve has stuck open for five minutes.
The valve flow area is 0.1 ft2 (_ 0.01 m2).

Problem 23

The steam line in a BWR is equipped with a relief valve to
discharge steam to the pressure suppression pool during an emergency. The valve
opens upon the closure of the isolation valve. To prevent overcooling of the
reactor pressure vessel, the discharge of steam through the valve must not
result in a cooldown rate in excess of 100 F/h. Use the data and the associated
simplifying assumptions to
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Find the cooldown rate and the suppression pool temperature
in Problem 23 for a case that the relief valve has stuck open for five minutes.
The valve flow area is 0.1 ft2 (_ 0.01 m2).

Problem 23

The steam line in a BWR is equipped with a relief valve to
discharge steam to the pressure suppression pool during an emergency. The valve
opens upon the closure of the isolation valve. To prevent overcooling of the
reactor pressure vessel, the discharge of steam through the valve must not
result in a cooldown rate in excess of 100 F/h. Use the data and the associated
simplifying assumptions to find pressure in the reactor pressure vessel (RPV)
and temperature in the suppression pool as functions of time for a discharge
period of 10 minutes.

RPV initial condition:

Pressure: 1015 psia (7 MPa),

water volume: 14,583 ft3 (413 m3),

steam volume: 8370 ft3  (237 m3),

RPV injection data:

feedwater flow rate: 1,252,000 lbm/h (32 kg/s), feedwater
enthalpy: 335 Btu/lbm (780 kJ/kg),

RPV power addition data: rate of heat deposition to the
mixture from the RPV internal structure: 950 Btu/s

(§ 1 MW), rate of heat deposition to the mixture from
radioisotope decay: 1% of the reactor nominal power of 3434 MWth,

Suppression pool initial condition:

Water mass: 7.6E6 lbm (3,447 kg), water temperature: 90 F
(32 C), pressure: 14.7psia (1 atm)

RPV assumptions:

a) water and steam are completely mixed and remain in
thermodynamic equilibrium throughout the discharge period,

b) only saturated steam leaves the RPV,

c) the rate of heat deposition to the RPV from both sources
remain constant throughout the discharge period.

Suppression pool assumptions:

a) water in the suppression pool remains subcooled at
atmospheric pressure throughout the event, and

b) no residual heat removal system is activated for the
suppression pool as long as the pool temperature remains below 110 F (43 C).

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