If the pressure difference measured at two depths of a tank of mercury is 130,000 Pa, what is the height difference between the two depths? (Use specific gravity of mercury = 13 and gravity = 10m/sec^{2})

a) 10cm

b) 1m

c) 10m

d) 1000m

**Explanation**

In a column of fluid, the pressure difference between two depths is given by the formula ΔP = (SG)ρ_{water}gh, where ΔP is the pressure difference, SG is the specific gravity of the fluid, and ρ_{water}gh is the product of water density, gravity, and height difference. Remember that specific gravity, SG, is the ratio of fluid density to water density. Water density is 1g/cm^{3} or 1000kg/m^{3}.

130,000Pa = 13* 1,000kg/m^{3} * 10 m/sec^{2 }* h, h = 1m.

a) 10cm, incorrect.

b) 1m, correct.

c) 10m, incorrect, This answer neglects the contribution from gravity.

d) 1000m, incorrect, This answer uses 1kg/m^{3} for the density of water rather than the correct value of 1000kg/m^{3}.