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Transcript
Fluid Properties • Density, r – The measure of the mass per unit volume M r Lim V 0 – Mathematically: – Units: slugs/ft3 (British) V kg/m3 (SI) • Specific volume, u – The term “specific” implies “per unit mass”. – Thus, “specific volume” = “volume per unit mass” – u = 1/r – Specific volume is primarily used when dealing with thermodynamics - density is preferred in most aerodynamics! AE 301 Aerodynamics I 5 5/22/2017 Fluid Properties (continued) • Pressure, p – The measure of the average momentum exchanged per unit area between a gas and a solid surface. – Closely related to the average momentum due to the random motion in a gas or liquid. – The force due to pressure always acts normal to the surface. F A F p Lim A0 – Mathematically: A – Units: lbf/ft2 (British) N/m2=Pascal – Alternate units: AE 301 Aerodynamics I (SI) lbf/in2, atm, bar, mmhg, mmH20, inH20, ... 6 5/22/2017 Fluid Properties (continued) • Temperature, T – The measure of the average random kinetic energy per unit mass in a gas or liquid – Units: oR – Alternate units: (British) oK (SI) oF, oC • Learn conversions! 0oF=460oR 0oC=273oK • Equation of State – Equation expressing the relationship between r, p, and T – For a perfect gas: p = rRT – R is the specific gas constant. For air at standard conditions: • R = 1716 ft2/sec2/oR = 287 m2/sec2/oK AE 301 Aerodynamics I 7 5/22/2017 Fluid Properties (continued) • Velocity, V – A vector describing the direction and magnitude (speed) of motion – In Cartesean coordinates: V ui vj wk • Viscosity, m – A measure of the resistance a fluid offers to a shearing velocity gradient. – On surfaces, a shearing gradient is created by the no slip condition – The resulting shearing stress, t, due to viscosity always acts tangent to the surface – Units: slug/ft/sec (British) AE 301 Aerodynamics I kg/m/sec (SI) 8 5/22/2017 Flowfields • Dependencies of Properties – When dealing with large volumes (like the atmosphere) or flowing fluids, the fluid properties are different at different locations in the fluid. I.e.: • Air temperature, density, and pressure vary with altitude • Sitting in the bed of a truck is much more pleasant then sitting on the hood at 60 mph. – Fluid properties may also vary with time. I.e.: • Air temperature heat up during the day, cools at night. • A wind sock fills up and drops back in a gusting wind – Thus: r(x,y,z,t) p(x,y,z,t) V(x,y,z,t) m(x,y,z,t) AE 301 Aerodynamics I T(x,y,z,t) 9 5/22/2017 Flowfields (continued) • Streaklines – The path a fluid packet makes as it moves through a flowfield is called a streakline – Streaklines can be visualized with smoke, bubbles, ink (in liquids) – Mathematically, streaklines can be found by integrating the velocity or tracing the velocity vector • Streamlines – In many situations of interest, the fluid properties are not changing with time and is called steady – If a flowfield is steady streaklines are repeatable from one instance to another. – These repeatable streaklines are called streamlines AE 301 Aerodynamics I 10 5/22/2017 Aerodynamic Forces • There are only two sources of aerodynamic forces: – Pressure forces which act normal and into the surface. p – Viscous forces which act tangent and in the direction of local fluid flow t – The total force is found by finding and then integrating these forces, p and t, over the surface area. AE 301 Aerodynamics I 11 5/22/2017