Hydrostatics Vs Fluid Dynamics

Fluid statics or what others call hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. It encompasses and includes the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics which is the study of fluids in motion. Hydrostatics are categorized as a part of the fluid statics, which is the study of all fluids, incompressible or not, at rest.

In addition, Fluid Statics and Fluid Dynamics form the two constituents of Fluid Mechanics. Fluid Statics deals with fluids at rest while Fluid Dynamics studies fluids in motion. According to Aerospace, Mechanical and Mechatronic Engg. (2005), “A fluid at rest has no shear stress. Consequently, any force developed is

Fluid statics includes and tackles topics about pressure at a point, equations for pressure field, pressure variation of a fluid at rest which is comprised of incompressible fluids and compressible fluids, standard atmosphere, measurement of pressure, manometry which includes piezometer tube, u-tube manometer, and inclined-tube manometer, mechanical and electronic pressure measuring devices, hydrostatic force on a plane surface, pressure prism, hydrostatic force on a curved surface, buoyancy, flotation, and stability which includes Archimedes’ principle and stability, pressure variation in a fluid with rigid-body motion which also tackles linear motion and rigid-body

The variations of pressure with direction and depth in a fluid will be examined. The term pressure is used to indicate the normal force per unit area at a given point acting on a given plane within the fluid mass of interest. What varies is the orientation of the plane passing through a point.

Figure 2.1 Forces on a wedge shaped element of fluid

Consider a small triangular wedge of fluid taken from an arbitrary location within a fluid mass to determine the variation of pressure with direction. With the absence of shear stresses, the only forces acting on the fluid element are the normal and gravitational forces. Take note that the forces along the x-axis is not shown for the clarity of the explanation. According to Newton’s second law, the forces in the y and z directions can be summed as

y-direction: py ΔxΔz - ps ΔxΔs sinθ = ρ (ΔxΔyΔz/2) ay

z-direction: pz ΔxΔy - ps ΔxΔs cosθ - ρ (ΔxΔyΔz/2) g = ρ (ΔxΔyΔz/2) az Since Δz = Δs sinθ and Δy = Δs cosθ, the above equations reduce