Figure P14.14 shows Superman attempting to drink water...

Figure P14.14 shows Superman attempting to drink water through a very long straw. With his great strength he achieves maximum possible suction. The walls of the tubular straw do not collapse. (a) Find the maximum height through which he can lift the water. (b) What If? Still thirsty, the Man of Steel repeats his attempt on the Moon, which has no atmosphere. Find the difference between the water levels inside and outside the straw.

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity acting on it. In problems involving liquid columns, the weight of the fluid above a given point creates a pressure that increases linearly with depth (or decreases with height when measured from the bottom upward), as described by the relation ?P = ?g?h, where ? is the density, g is the gravitational acceleration, and ?h is the vertical distance. This concept is key when determining how high a fluid can be lifted by a pressure difference.

Atmospheric Pressure

Atmospheric pressure is the force per unit area exerted by the weight of the air above us. It plays a critical role in suction problems since the maximum pressure difference achievable by creating a near perfect vacuum in a straw is limited by the ambient atmospheric pressure. In lifting experiments, such as drinking through a straw, the external atmospheric pressure supports the weight of the fluid column within the straw, determining how high the liquid can rise.

Pressure Differential and Suction

The idea of a pressure differential is central to creating suction. By reducing the pressure at one end of a fluid column (for instance, by sucking to create a near-vacuum inside a straw), a difference in pressure is established between that end and the ambient pressure acting on the fluid outside. This pressure difference provides the necessary force to overcome the gravitational weight of the fluid, thereby lifting it. The maximum height of the liquid column is reached when the pressure difference is exactly balanced by the hydrostatic pressure of the column.

Gravitational Acceleration

Gravitational acceleration is the rate at which objects accelerate due to the force of gravity; on Earth, it is approximately 9.8 m/s², and on other celestial bodies such as the Moon, it is significantly lower. This parameter is crucial in hydrostatic calculations because it directly affects the weight of a fluid column (hence its hydrostatic pressure). Differences in gravitational acceleration explain why the maximum fluid height achievable by suction changes with location.

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