![]() Also, as the triangle shrinks to point B in the fluid, then the product becomes negligible, i.e., the effects of the weight of fluid inside can be neglected. Where is the weight of the fluid per unit length, i.e.,įrom the geometry of the triangle in the figure, then and. Therefore, for horizontal pressure force equilibrium on the fluid per unit length (into the page), thenįor the vertical pressure force equilibrium per unit length, then The pressures acting on the respective faces are in the -direction, in the -direction, and along the diagonal. Schematic used for the proof of Pascal’s Law in two-dimensions it is easily extended to three-dimensions by considering a wedge of fluid. However, the outcome is most easily obtained if the wedge is examined in just one view (or one plane), as shown in the figure below, which appears as a right-angled triangle with horizontal side length, vertical side length, and diagonal length, with the angle. The proof of Pascal’s Law proceeds by considering an infinitesimally small right-angled, three-dimensional fluid wedge at rest. The pressure at a point in a fluid at rest is equal in all directions, so the pressure is referred to as an isotropic scalar quantity that is formally embodied in Pascal’s Law. Use the principles of hydrostatics and the hydrostatic equation to solve some fundamental engineering problems.Understand how to develop and apply the hydrostatic equation.Be able to derive, understand, and use the general equation for a hydrostatic pressure field. ![]() Understand the meaning of a stagnant fluid and the underlying principles of fluid statics.The properties of the atmosphere on Earth or other planets.The pressure and other fluid properties inside containers or vessels, including under the action of body forces or acceleration fields.Design of water retaining structures such as dams and reservoirs.The buoyancy and stability of floating objects, such as ships in the water, and lighter-than-air aircraft, such as balloons and blimps.The measurement of pressure using various types of manometry.The transmission of forces and power using pressurized liquids.Examples of engineering problems that could be analyzed by using hydrostatics and pneumatics include the following: The term pneumatics is used when the principles of fluid statics are applied to gases such as air. However, hydrostatic principles are frequently used to analyze liquids and other predominantly incompressible fluids, i.e., fluids with constant density. Hydrostatic principles apply to all types of fluids, both gases, and liquids. The term hydrostatics often refers to the field of fluid statics in general. Surface forces, e.g., the effects of an external pressure acting over an area.Body forces, e.g., weight, inertial accelerations.Under these conditions, two types of forces on the fluid must be considered: There are no viscous forces on stagnant fluids because there is no relative motion between the fluid elements. In that case, its characteristics or properties (e.g., its pressure, density, etc.) can be described more easily using the physical principles of fluid statics.Ī fluid in static equilibrium can be defined as a state where every fluid particle is either at rest or has no relative motion with respect to the other particles in the fluid. However, suppose the fluid is not moving or stationary, commonly called a stagnant fluid. First, remember that air is just one type of fluid, for which there are many types in the form of gases and liquids. In aerodynamic problem solving, a primary concern is describing and understanding the motion or dynamics of the air. 10 Fluid Statics & the Hydrostatic Equation Introduction
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