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f02_fall - Fluids Lecture 2 Notes 1 Hydrostatic Equation 2...

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Fluids – Lecture 2 Notes 1. Hydrostatic Equation 2. Manometer 3. Buoyancy Force Reading: Anderson 1.9 Hydrostatic Equation Consider a fluid element in a pressure gradient in the vertical y direction. Gravity is also present. y dp dy g dy dx dz x z If the fluid element is at rest, the net force on it must be zero. For the vertical y -force in particular, we have Pressure force + Gravity force = 0 dp p dA p + dy dA ρ g d V = 0 dy dp dy dA ρ g d V = 0 dy The area on which the pressures act is dA = dx dz , and the volume is d V = dx dy dz , so that dp dx dy dz ρ g dx dy dz = 0 dy dp = ρg dy (1) which is the differential form of the Hydrostatic Equation . If we make the further assumption that the density is constant, this equation can be integrated to the equivalent integral form. p ( y ) = p 0 ρgy (2) The constant of integration p 0 is the pressure at the particular location y = 0. Note that this integral form is valid provided the density is constant within the region of interest .
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