An open vessel contains a 40 cm deep layer of water above a 20 cm deep layer of mercury. The densities of water and mercury are 1000 kg/m³ and 13600 kg/m³, respectively. Taking g = 10 m/s², what is the gauge pressure at the bottom of the vessel?
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Question

An open vessel contains a 40 cm deep layer of water above a 20 cm deep layer of mercury. The densities of water and mercury are 1000 kg/m³ and 13600 kg/m³, respectively. Taking g = 10 m/s², what is the gauge pressure at the bottom of the vessel?

Options

G1 Physics · Accepted Answer

The gauge pressure at the bottom is the sum of the pressure contributions of both liquid layers. For the water layer, P(water) = ρ(water)gh(water) = 1000×10×0.40 = 4000 Pa. For the mercury layer, P(Hg) = ρ(Hg)gh(Hg) = 13600×10×0.20 = 27200 Pa. Therefore, P(gauge) = P(water)+P(Hg) = 4000+27200 = 31200 Pa = 31.2 kPa. Correct option: B.