When a person sits erect, increasing the vertical position...

When a person sits erect, increasing the vertical position of their brain by 36.0 $\mathrm{cm}$ , the heart must continue to pump blood to the brain at the same rate. (a) What is the gain in gravitational potential energy for 100 $\mathrm{mL}$ of blood raised 36.0 $\mathrm{cm} ?$ (b) What is the drop in pressure, neglecting any losses due to friction? (c) Discuss how the gain in gravitational potential energy and the decrease in pressure are related.

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Key Concepts

Energy-Pressure Relationship

There is a direct relationship between the gravitational potential energy gained by a volume of fluid and the corresponding drop in hydrostatic pressure. The work done to elevate the fluid (reflected in the gain in potential energy) is equivalent to the energy per unit volume as manifested by a decrease in pressure, linking mechanical energy changes with pressure variations in fluid statics.

Gravitational Potential Energy

This concept involves the energy an object possesses due to its position in a gravitational field. When an object (or fluid) is lifted to a greater height, work is done against the gravitational force, and energy is stored in the form of gravitational potential energy. This energy is calculated by multiplying the mass, gravitational acceleration, and the height change.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. In a fluid column, the pressure difference between two points is a result of the weight of the fluid above, and it is directly proportional to the fluid's density, gravitational acceleration, and the vertical distance between the points.

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