MCAT Physics Question — Water Pressure

by John
Jan 15, 2017
MCAT Question of the Day

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:

P_tot = P₀ + ρgh

Click for Explanation

Here, we can simply plug in the values provided:

P_tot = (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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