pressure variation with altitude in a static compressible fluid (eg air ：在一个静态的可压缩流体高度压力的变化（如空气.docVIP

Pressure variation with altitude in a static compressible fluid (e.g. air) with constant temperature gradient: ________________________________________________________________________ Basic equation: (1) This equation cannot be integrated since variation of ? with height is not known. Assume air is ideal: (2) From (1) (2): (3) In the troposphere: (4) where ? = temperature lapse rate = 6.5 x 10-3 K/m = 6.5 K/km from (3) (4): (5) Variation of pressure with altitude in a static compressible fluid (e.g. air) at constant temperature Lower stratosphere (): Note: air is still treated as ideal. Temperature lapse rate in the atmosphere under polytropic conditions Static fluid: (1) Polytropic relationship: (n= polytropic index) (2) Assume air is ideal: (3) From (2): (4) From (3): (5) From (4) (5): (6) From (1) (6): Note: (i) for adiabatic conditions: n = k; k: adiabatic index (k = Cp / Cv) (ii) n = 1 in the lower stratosphere Variation of pressure with altitude in the atmosphere under polytropic conditions Basic pressure-height relationship: (1) Assume air to be ideal: (2) Temperature variation with altitude: (3) (1) divided by (2): (4) with (3), (4) becomes (5) Note: the above is valid only in the troposphere. In the lower stratosphere, n = 1; the above will “blow up” Forces due to liquid pressure on plane submerged surfaces: : resultant force due to liquid pressure C: centriod of area P: centre of pressure (i.e. point of application of FR) Note: P is always below C unless the surface is horizontal in which case P = C Need: magnitude of FR direction of FR line of action of FR No shearing stresses in a static fluid; forces will be normal to surface independent of the orientation of the surface (the negative on right-hand side of equation indicates that the direction of is opposite to) Note: positive direction of is the outward drawn normal to the area Resultant force: Pressure-height relationship in a static fluid: (h is positive dow