Fluid Statics

Fluid pressure at one point is the focus of this lesson. It shows that pressure in a fluid is the same in every direction at a single location. This happens because fluid molecules move randomly and collide with nearby molecules in a balanced way.

At a given point, the pressure depends on the surrounding fluid molecules. It is affected by depth and density, not by the shape of the container or the way the fluid is oriented. In a fluid at rest, the pressure acts equally in all directions...

The pressure field equation describes how forces stay balanced inside a small fluid element. In fluid mechanics, this balance helps explain how pressure changes from one place to another within a fluid.

Two main force types act on a fluid segment: surface forces and body forces. Surface forces come from pressure differences across nearby points in the fluid, so they depend on the local pressure gradient, which is the rate of pressure change with position. Body forces are spread through the...

Hydrostatic pressure describes how pressure changes with depth in a fluid at rest. In a stationary fluid, the fluid acceleration is zero, so the forces inside the fluid balance. That means pressure at a point below the surface depends on depth, not on the container’s shape or size.

Only vertical forces affect the pressure change in this situation. These forces come from the weight of the fluid above a point. When pressure is compared at two different levels, the difference in pressure equals...

Fluid pressure is measured with manometers and related gauges. These tools use a liquid column to show pressure differences. The height of the column gives a simple reading of the force the fluid exerts.

A basic manometer is the piezometer. It is a vertical tube that is open at the top and filled with the same fluid being measured. When the tube connects to a container, the fluid height in the tube matches the pressure inside that container.

For more detailed measurements, the U-tube...

Hydrostatic pressure creates force on submerged plane surfaces. The force depends on the fluid pressure and the area of the surface. The way that force acts changes with the surface position.

For a horizontal surface, the depth stays the same across the whole area. That means the pressure is uniform. The resultant force equals the pressure at that depth multiplied by the surface area, and it acts through the centroid of the surface.

For a vertical surface, pressure increases as depth...

Hydrostatic pressure on curved surfaces is an important idea in fluid mechanics. It helps explain how water pushes on curved structures in civil engineering. Examples include reservoirs, dams, and storage tanks. The pressure changes in both size and direction along the curve.

To find the total hydrostatic force on a curved surface, engineers isolate the fluid volume next to that surface. They then study the forces on imaginary horizontal and vertical planes that cut through the volume. The...

Buoyancy and stability explain how submerged and floating bodies behave in a fluid. When a body is fully or partly under water and stays still, the fluid pushes upward on it. That upward push is called the buoyant force.

The buoyant force acts through the center of buoyancy. This is the center of the displaced fluid volume. Archimedes’ principle says the buoyant force equals the weight of the fluid displaced by the body.

Stability describes whether a body can return to its original position...

Archimedes' principle is used to analyze the buoyant force on a wooden block that floats in seawater. The block has a rectangular section, and its dimensions, specific gravity, and the specific weight of seawater are used in the calculation. This setup shows how floating bodies stay in equilibrium.

The first step is to find the weight of the block from its volume and specific gravity. Then Archimedes' principle is applied. The weight of the displaced water must equal the weight of the block.