A holding tank at sea level (atmospheric pressure 1.01 x 105 Pa) containing water has a pressure of 2 x 105 Pa at 10 m depth. What is the pressure in an equivalent holding tank containing mercury (specific gravity = 13) at 1 m depth in Denver, CO (atmospheric pressure 8.4 x 104 Pa)?
a) 2 x 105 Pa
b) 1 x 105 Pa
c) 1.4 x 106 Pa
d) 8.4 x 104 Pa
Formula for hydrostatic pressure in a fluid:
Ptot = P0 + ρgh
Here, we can simply plug in the values provided:
Ptot = (8.4 x 104) + (13,000 kg/m3 x 10m/s2 x 1m) = 2.14 x 105 Pa
a) 2 x 105 Pa correct, matches our calculation
b) 1 x 105 Pa, incorrect, this is the same pressure at sea level for 10m of water, ignores fluid change and atmospheric pressure change
c) 1.4 x 106 Pa, incorrect, this answer fails to change the fluid depth to 1m for the mercury rather than the 10m depth used for water
d) 8.4 x 104 Pa, incorrect, this answer ignores the fluid contribution to pressure and only uses the atmospheric contribution
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