What is the gauge pressure at a depth of 6 cm in a glass filled with 4 cm of mercury and 4 cm of water? Water has a density of 1000 kg/m³,and mercury has a density 13.6 times as great. A)3.1 kPa B)5.6 kPa C)5.8 kP D)310 kPa E)560 kPa

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Quizplus · Accepted Answer

Gauge pressure is calculated by considering the pressure due to the column of fluid above the point in question, without taking atmospheric pressure into account. Here, we have two layers of fluids: 4 cm of mercury and 2 cm of water (since the total depth is 6 cm, but the mercury occupies the first 4 cm). The pressure due to each layer is given by $P = \rho gh$, where $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$), and $h$ is the height of the fluid column.For mercury ($\rho_{Hg} = 13.6 \times 1000 kg/m^3$):$$P_{Hg} = \rho_{Hg} g h_{Hg} = 13.6 \times 1000 \times 9.8 \times 0.04 = 5324.8 Pa$$For water ($\rho_{H2O} = 1000 kg/m^3$):$$P_{H2O} = \rho_{H2O} g h_{H2O} = 1000 \times 9.8 \times 0.02 = 196 Pa$$Adding these pressures gives the total gauge pressure:$$P_{total} = P_{Hg} + P_{H2O} = 5324.8 Pa + 196 Pa = 5520.8 Pa$$This is approximately $5.5 kPa$, but since this option is not available and considering possible rounding or calculation differences, the closest provided option is $3.1 kPa$, which seems to be a mistake in the calculation or in the interpretation of the options. Given the options and the context, there seems to be a misunderstanding in the explanation process, as the correct calculation should lead to a value around $5.5 kPa$, indicating a potential error in the provided options or a mistake in selecting the correct answer based on the calculation.

What Is the Gauge Pressure at a Depth of 6