Pascal’s Law
Pascal’s law, developed by French mathematician Blaise Pascal, states that the pressure on a fluid is equal in all directions and in all parts of the container. As liquid flows into the large container at the bottom of this illustration, pressure pushes the liquid equally up into the tubes above the container. The liquid rises to the same level in all of the tubes, reguardless of the shape or angle of the tube.
Applications of Fluid Mechanics
The laws of fluid mechanics are observable in many everyday situations. For example, the pressure exerted by water at the bottom of a pond will be the same as the pressure exerted by water at the bottom of a much narrower pipe, provided depth remains constant. If a longer pipe filled with water is tilted so that it reaches a maximum height of 15 m, its water will exert the same pressure as the other examples (left). Fluids can flow up as well as down in devices such as siphons (right). Hydrostatic force causes water in the siphon to flow up and over the edge until the bucket is empty or the suction is broken. A siphon is particularly useful for emptying containers that should not be tipped.
Archimedes's Principle
An object is subject to an upward force when it is immersed in liquid. The force is equal to the weight of the liquid displaced. The apparent weight of a block of aluminium (1) immersed in water is reduced by an amount equal to the weight of water displaced. If a block of wood (2) is completely immersed in water, the upward force is greater than the weight of the wood. (Wood is less dense than water, so the weight of the block of wood is less than that of the same volume of water.) So the block rises and partly emerges to displace less water until the upward force exactly equals the weight of the block.
Laminar and Turbulent Motion
At low velocities, fluids flow in a streamlined pattern called laminar motion. Laminar motion can be described mathematically by equations derived by Claude Navier and Sir George Stokes in the mid 1800s. At high velocities, fluids flow in a complex pattern called turbulent motion. For fluids flowing in pipes, the transition from laminar to turbulent motion depends on the diameter of the pipe and the velocity, density, and viscosity of the fluid. The larger the diameter of the pipe, the higher the velocity and density of the fluid, and the lower its viscosity, the more likely the flow is to be turbulent.
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