Fundamental Equations and Solutions

Abstract

Every other day one may observe puzzling fluid mechanics phenomena. Such counter-intuitive examples include: (a) Keeping the tailgate of a pick-up truck up reduces aerodynamic drag (why?) and hence saves gasoline; although, most drivers intentionally keep it down and even install “airflow” nets to retain cargo when accelerating. (b) Under otherwise identical conditions, it is easy to blow out a candle but nearly impossible to suck it out. Why? (c) Very high (horizontal) winds can lift pitched roofs off houses. How? (d) When bringing a spoon near a jet, e.g., faucet stream, it gets sucked into the stream. Try it out and explain! (e) Chunks of metal are torn out from ship propellers at high speeds after a long period of time in operation. Why? (f) The long hair of a girl driving a convertible is being pushed into her face rather than swept back. How come? (g) A snowstorm leaves a cavity in front of a pole or tree and deposits snow behind the “vertical cylinder.” Impossible? (h) Three-dimensional effects in river bends create unusual (axial) velocity profiles right after the bend and subsequently, lateral material transport results in shifting riverbeds. Explain! (i) Certain non-Newtonian fluids when stirred in an open container climb up the rotating rod, rather than forming a depressed, parabolic free surface. Weird! (j) Airplanes flying through microbursts (or high up in the blue sky) may crash. What is happening during these two very different weather types? (k) Racecar (and motorcycle) tires are hardly threaded but passenger cars are. Why? (l) Consider a tsunami (Japanese for “great harbor wave”) hitting either a very shallow shore or a deep sea near the shoreline. Describe cause-and-effect for these two scenarios. (m) Wildfires spread rapidly because of their own local weather pattern they create. Describe the underlying convection system, and how “back-fires” work. (n) A very small amount of carbon nanotubes added to a liquid increases measurably the apparent (or effective) thermal conductivity, k, of the dilute mixture (called a nanofluid) when compared to k [W/(m K)] of the pure base fluid. Why? (o) Gas flow in microchannels may exhibit significantly higher flow rates than predicted by conventional theory. What’s happening?