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AE 1350 Lecture Notes #5 WE HAVE LOOKED AT.. • Why should we study properties of atmosphere? • Ideal Gas Law: p = rRT • Variation of Temperature with Altitude • Variation of Pressure with Altitude • Variation of Density with Altitude • Tables of Standard Atmosphere TOPICS TO BE COVERED • Incompressible flow • Streamlines and stream tubes • Conservation of Mass (Continuity) Incompressible Flow • Air is a compressible fluid. • Its density WILL change if temperature changes, or if some external force is applied. – Example: A child squeezing a balloon • A flow is said to be incompressible if there are no changes in density attributable to (or caused by) the velocity or speed of the flow. • Theory and observations in wind tunnels suggest that most flows may be treated as incompressible (I.e. constant density) until the Mach number is sufficiently high (>0.4 or so.) What has flow speed got to do with compressibility? Fluid particles send out signals in the form of acoustic waves to the surrounding fluid, indicating their motion. If there is sufficient time for the sound waves to travel before the fluid particle arrives, the fluid particles downstream will “hear” the message and clear out. Otherwise, there will be a crush (compression), or even a stampede (shock wave). Shocks form when the acoustic waves generated by the air particles in front of the body can not outrun the body. Shocks Streamlines in Steady Flow Inviscid (ideal) flow Viscous flow •Streamlines describe the path the fluid particles will take. •At any point on the streamline, the flow velocity is tangential to the streamline. •Viscosity alters the shape of streamlines around bluff bodies. •Scientists inject smoke particles into streamlines to make them visible to the naked eye. Streamlines over a Cylinder (Low Reynolds Number of 10) Reynolds Number where D Cylinder r VD dia. Streamlines over a Cylinder (High Reynolds Number of 2000) Reynolds Number where D Cylinder r VD dia. Streamlines over an Airfoil at High Angles of Attack Flow Separation Continuity • Consider a stream tube, i.e. a collection of streamlines that form a tube-like shape. • Within this tube mass can not be created or destroyed. • The mass that enters the stream tube from the left (e.g. at the rate of 1 kg/sec) must leave on the right at the same rate (1 kg/sec). Continuity Rate at which mass enters=r1A1V1 Area A1 Density r1 Velocity V1 Rate at which mass leaves=r2A2V2 Area A2 Density r2 Velocity V2 Continuity In compressible flow through a “tube” rAV= constant In incompressible flow, r does not change. Thus, AV = constant Continuity (Continued..) AV = constant If Area between streamlines is high, the velocity is low and vice versa. Low Velocity High Velocity Continuity (Continued..) High Velocity AV = constant If Area between streamlines is high, the velocity is low and vice versa. In regions where the streamlines squeeze together, velocity is high. Low Velocity Venturi Tube is a Device for Measuring Flow Rate we will study later. Low velocity High velocity