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M E 433 Professor John M. Cimbala Lecture 23 Today, we will: • Finish deriving the equation of motion for a particle in air flow • Show how to determine the direction of force (and acceleration) on a particle in air flow • Discuss drag coefficient and use it in the equation of motion for particle trajectories • Discuss the Cunningham correction factor (small particles; free molecular flow effects) → U Example: Direction of drag force Given: A small particle is moving through the air at velocity v as sketched to the right. At the location of the particle, and at a given instant in time, the air velocity is U as also sketched. → v Streamline Particle To do: Which is the correct direction of the drag force on the particle? Text your answer as “a”, “b”, or “c”, without the quotes. → U → U (a) → → U (b) → v v → (c) Fdrag → Fdrag Particle Particle Particle → Fdrag Solution: → v → U → → vr = v - U → → Fdrag Particle Do a vector summation. (a) is the correct answer. → -U → v Example: Direction of drag force → U Given: A small particle is moving through the air at velocity v as sketched to the right. At the location of the particle, and at a given instant in time, the air velocity is U as also sketched. Streamline Particle To do: Which is the correct direction of the drag force on the particle? Text your answer as “a”, “b”, or “c”, without the quotes. → U → U (a) → v → U (b) → (c) Fdrag → Fdrag Particle Particle Particle → Fdrag → → v v Solution: → U → Do a vector summation. (c) is the correct answer. Fdrag Particle → -U → v → → vr = v - U → → v