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Introduction to Fluid Mechanics
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Viscosity
Viscosity is a measure of a fluid's resistance to flow. It quantifies the internal friction in the fluid as layers move past one another. The formula for dynamic viscosity is given by Newton's law of viscosity, , where is the shear stress, is the dynamic viscosity, is the change in velocity across a distance between two fluid layers.
Bernoulli's Equation
Bernoulli's Equation relates the pressure, velocity, and elevation of a fluid in steady, incompressible flow along a streamline. The equation is given as , where is the fluid pressure, is the fluid density, is the fluid velocity, and is the elevation height above a reference plane, with being the acceleration due to gravity.
Reynolds Number
The Reynolds Number is a dimensionless quantity used to predict the flow regime in a fluid. It is calculated using the formula , where is the fluid density, is the velocity of the fluid, is a characteristic linear dimension (like diameter of a pipe), and is the dynamic viscosity. Laminar flow occurs at low Reynolds numbers, while turbulent flow occurs at high Reynolds numbers.
Pressure
Pressure is defined as the force exerted per unit area. In fluid mechanics, pressure at a point in a fluid is isotropic and can be calculated using the formula , where is the pressure, is the normal force, and is the area over which the force is distributed.
Buoyancy
Buoyancy is the upward force exerted by a fluid that opposes the weight of an object immersed in it. It is determined by Archimedes' Principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. The formula for buoyant force () is , where is the fluid density, is the acceleration due to gravity, and is the volume of fluid displaced.
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