A dam retains a lake 6 m deep, as shown in Fig. P1.97. To construct a gate in the dam, we need

step 1 So we want to find what the net force on the gate of this dam is. So what we're first going to d

A dam retains a lake 6 m deep, as shown in Fig. P1.97. To...

A dam retains a lake $6 \mathrm{~m}$ deep, as shown in Fig. P1.97. To construct a gate in the dam, we need to know the net horizontal force on a $5-\mathrm{m}$ -wide, $6-\mathrm{m}$ -tall port section that then replaces a $5-\mathrm{m}$ section of the dam. Find the net horizontal force from the water on one side and air on the other side of the port.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases linearly with depth because the weight of the fluid above a given point contributes to the pressure at that point. In problems involving dams or submerged surfaces, understanding how pressure changes with depth is crucial for calculating forces on the structures.

Integration Over a Submerged Surface

Calculating the force exerted by a fluid on a submerged surface involves integrating the pressure distribution over the entire surface area. Since pressure varies with depth, the integration accounts for the changing pressure, typically by summing the infinitesimal forces over differential elements of the surface area. This is essential in determining the net horizontal force on vertical structures such as dam gates.

Center of Pressure

The center of pressure is the point on a submerged surface where the total hydrostatic force is considered to act. It is located below the centroid of the area because fluid pressure increases with depth. Understanding the center of pressure is important in the design of structures to ensure that they can resist the moments and forces created by the water pressure distribution.

Transcript

Please give Ace some feedback