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Unformatted text preview: 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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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05