Hydrostatic pressure

Definition

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases proportionally with depth in the fluid.

5 Must Know Facts For Your Next Test

1. Hydrostatic pressure can be calculated using the formula $P = \rho gh$, where $\rho$ is the fluid density, $g$ is the acceleration due to gravity, and $h$ is the height of the fluid column.
2. In integration applications, hydrostatic pressure problems often involve calculating forces on submerged surfaces like plates or dams.
3. The integral setup for finding the force on a submerged vertical surface involves integrating pressure over an area: $F = \int_a^b P(y) \, dA$.
4. For non-vertical surfaces, you may need to use parameterizations or different coordinate systems to set up integrals correctly.
5. Understanding how to set up and evaluate these integrals requires knowledge of both single and double integrals in calculus.

Review Questions

• How would you set up an integral to calculate the hydrostatic force on a vertical rectangular plate submerged in water?
• What variables are involved in calculating hydrostatic pressure and how do they affect its value?
• Explain why hydrostatic pressure increases with depth in a fluid.

Related terms

Fluid Density: A measure of mass per unit volume of a fluid, denoted as $\rho$. It affects the calculation of hydrostatic pressure.

Acceleration Due to Gravity: A constant denoted as $g$, approximately equal to $9.8 \text{ m/s}^2$ on Earth's surface. It influences hydrostatic pressure.

Integral:

A fundamental concept in calculus used to calculate areas under curves, volumes, and other quantities. Essential for solving hydrostatic force problems.