Hydrostatic pressure on plane surfaces: Introduction | Fluid Mechanics Lesson 9

Main Ideas

• The lesson introduces hydrostatic pressure on flat, submerged surfaces.

• In a fluid at rest, pressure increases with depth. Gauge pressure varies linearly with vertical depth: [ p = \gamma h ] where (\gamma) is the fluid’s specific weight and (h) is the vertical depth.

• Pressure acts perpendicular to the surface at each point. Because pressure increases with depth, the distribution across a plane surface is generally nonuniform.

• The distributed pressure can be replaced by a single resultant force. For a plane area in a static fluid, its magnitude is: [ F = \gamma h_c A ] where (A) is the area and (h_c) is the vertical depth of its centroid.

• The resultant acts at the center of pressure. This point is generally below the area’s centroid because the deeper parts of the surface experience greater pressure. The center of pressure is distinct from the centroid or center of gravity.

• Locating the center of pressure involves taking moments of the pressure distribution, using first and second moments of area and accounting for the surface’s orientation.

General Method for Analyzing a Submerged Plane

1. Define the geometry and fluid conditions. Identify the surface area and shape, the fluid’s specific weight, the free surface, and the surface’s inclination.
2. Determine pressure by depth. Use the vertical depth below the free surface; pressure varies linearly with depth.
3. Represent the pressure distribution. Show how pressure acts normal to the surface and increases toward its deeper portions.
4. Calculate the resultant force. Integrate pressure over the area or, for a plane surface in a static fluid, multiply the pressure at the centroid by the area.
5. Locate the center of pressure. Take moments of the distributed pressure about a chosen axis and use area-moment properties to determine where the resultant acts.
6. Check the result’s position and direction. The force should act normal to the plane, and its point of application should reflect the greater pressure on the deeper portions.

Speaker or Source

• One instructor/narrator, associated with the Tutor Jack Ph channel. No other identifiable speakers are evident in the subtitles.