# SUMMARY OF FLUID MECHANISM

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Density and pressure: Density is mass per unit volume. If a mass m of homogeneous material has volume V, its density r is the ratio m/V. Specific gravity is the ratio of the density of a material to the density of water.

Pressure is normal force per unit area. Pascal’s law states that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid. Absolute pressure is the total pressure in a fluid; gauge pressure is the difference between absolute pressure and atmospheric pressure. The SI unit of pressure is the pascal (Pa): 1 Pa = 1 N/m^{2}

Pressures in a fluid at rest: The pressure difference between points 1 and 2 in a static fluid of uniform density r (an incompressible fluid) is proportional to the difference between the elevations y_{1} and y_{2}. If the pressure at the surface of an incompressible liquid at rest is p_{0}, then the pressure at a depth h is greater by an amount rgh.

Buoyancy: Archimedes’s principle states that when a body is immersed in a fluid, the fluid exerts an upward buoyant force on the body equal to the weight of the fluid that the body displaces.

Fluid flow: An ideal fluid is incompressible and has no viscosity (no internal friction). A flow line is the path of a fluid particle; a streamline is a curve tangent at each point to the velocity vector at that point. A flow tube is a tube bounded at its sides by flow lines. In laminar flow, layers of fluid slide smoothly past each other. In turbulent flow, there is great disorder and a constantly changing flow pattern.

Conservation of mass in an incompressible fluid is expressed by the continuity equation, which relates the flow speeds v_{1} and v_{2} for two cross sections A_{1} and A_{2} in a flow tube. The product Av equals the volume flow rate, dV/dt, the rate at which volume crosses a section of the tube.

Bernoulli’s equation states that a quantity involving the pressure p, flow speed v, and elevation y has the same value anywhere in a flow tube, assuming steady flow in an ideal fluid. This equation can be used to relate the properties of the flow at any two points

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