Six lobsters are put in the tank of Question 16.9 and enough...

Six lobsters are put in the tank of Question 16.9 and enough water is removed to keep its depth at $60 \mathrm{~cm}$. The gauge pressure on the tank bottom is now
(a) smaller
(c) greater
(b) the same
(d) any of the above, depending on the mass of the lobsters

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Key Concepts

Gauge Pressure

Gauge pressure is the pressure measured relative to atmospheric pressure. In fluid statics, it is calculated by subtracting atmospheric pressure from the total pressure at a given depth. Because the total pressure is directly proportional to the fluid depth and density, maintaining a constant water depth means the gauge pressure at the bottom of the tank also remains constant.

Fluid Displacement and Buoyancy

When objects are immersed in a fluid, they displace a volume of fluid equivalent to the portion of the object submerged. This displacement is related to Archimedes' principle, which also explains how buoyant forces arise. However, if water is removed to compensate for the volume of the added objects such that the overall fluid depth remains constant, the pressure due to the water column does not change.

Hydrostatic Pressure

Hydrostatic pressure in a fluid is the pressure exerted by the weight of the fluid above a given point. It is determined by the product of the fluid density, gravitational acceleration, and the vertical depth of the fluid column. This concept explains why the pressure at the bottom of a tank depends solely on the height of the water, regardless of the specific contents, as long as the depth remains unchanged.

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