The characteristic time τ:

Greek Letter = Function

ככל שמשהו גדול יותר, כך הוא זז יותר לאט

רשום זמן אז נבחר גודל

טאו (τ) = כמה מהר חלקיק מגיב לשינוי בזרימה והוא תלוי בגודל שלו! חלקיק גדול = מגיב לאט

מישהו מבין למה 1 ולא 2?

יש טעות, לםי ההרצאה ונוסחת טאו. התשובה הנכונה הינה B. הסבר:The correct answer is B: τ is the reaction time for a particle to adjust when the flow velocity changes. ⸻ Why τ ≠ “just particle size” (and why B is the real star) 1. Definition of τ In fluid mechanics, the characteristic time (also called the relaxation time) is how long it takes for a particle’s velocity to “catch up” to a suddenly altered fluid velocity. Mathematically: τ = \frac{m_p}{6\pi\,μ\,R} = \frac{ρ_p \, R^2}{9\,μ} where • m_p = particle mass (∝ ρ_p\,R^3), • R = particle radius, • μ = fluid viscosity, • ρ_p = particle density. 2. Dependence on multiple factors • Particle size (R) appears, but squared—not the whole story (so A is over-simplified). • Fluid viscosity (μ) sits proudly in the denominator—more viscous fluid = slower response (so D is outright false). • Particle density (ρ_p) also ramps τ up or down, so heavy particles take longer to adapt (directly contradicting C). 3. Physical interpretation • Imagine plowing a bowling ball vs. a ping-pong ball through honey. The bowling ball (large, dense) resists changes in your push and lags far behind. Its τ is huge. • The ping-pong ball (tiny, light) flits along almost instantly—its τ is minuscule. • τ thus quantifies the “inertia vs. drag” battle and tells you exactly how long particles need to resign themselves to the new flow regime.

דמות ראשית characteristic mainly