At 2735 m (8973 ft) below sea level, the Kidd mine reportedly has the deepest non-marine point of the Earth's surface (since the Kola borehole is sealed). I wonder what the pressure down there is, as compared to 14.696 psi (1013.25 hPa) at sea level and 15.45 psi (1065 hPa) on the shore of the Dead Sea (413 m = 1355 ft below sea level standard).
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$\begingroup$ link $\endgroup$– David García BodegoCommented Dec 19, 2022 at 3:56
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$\begingroup$ @DavidGarcíaBodego Your link writes that it's 4 km (2.5 mi) below ground level. The Kidd mine has the deepest point below sea level. $\endgroup$– GiovanniCommented Dec 19, 2022 at 13:07
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$\begingroup$ @Gionanni, Mine is 600 meters above sea level and depth is 4000 meters, so it is 3400 meters below sea level. I think that this is more than 2735 meters b.s.l. $\endgroup$– David García BodegoCommented Jan 29, 2023 at 8:38
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1 Answer
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From the book Environmental Engineering in South African Mines, The Mine Ventilation Society of South Africa, 1989, pp 451-455.
The equation required is:
$P \ = \ P_{atm}\cdot e^{\frac{-gMh}{1000R\cdot (273.15+t_{dry})}}$
Where:
- $P_{atm}$ = Atmospheric air pressure
- $t_{dry}$ = Dry bulb temperature
- $g$ = acceleration due to gravity, 9.8 m/s2
- $M$ = Molar mass of air on Earth, 28.9644 g/mol
- $h$ = The difference in elevation, -2735 m
- $R$ = The universal gas constant, 8.3144622 J/mol$\cdot$K
Current data is being taken from the Canadian government weather service website. The nearest town to Kidd Creek is Timmins, Ontario, approximately 25 km south.
For 14 December 2022, the dry bulb temperature on the surface is -12.6 °C and the sea level adjusted atmospheric pressure is 1032 hPa (103 200 Pa). Given the depth of the mine and heating of the air due to both auto compression, the geothermal gradient and any diesel powered equipment in the mine, the temperature of the air at the bottom of the exhaust ventilation shaft will most likely be around 30 °C.
The atmospheric pressure at a depth of 2735 m is,
$P \ = \ 103\ 200\cdot e^{\frac{-9.8(28.9644)(-2735)}{1000(8.31446) (273.15+30)}}$ = $140\ 400\ Pa = 1404\ hPa = 20.37 \ psi$
