Fluid Drag: Quadratic Resistance, Terminal Speed, and Linear-Drag Motion

All flashcards

What is the quadratic drag equation?

For many large objects moving through air, $F_D = \frac{1}{2}C\rho A v^2$, where $C$ is the drag coefficient, $\rho$ is fluid density, $A$ is frontal area, and $v$ is speed.

What is terminal speed under quadratic drag?

When drag balances weight and buoyancy is neglected, $v_T = \sqrt{\frac{2mg}{\rho C A}}$.

How does a falling object's velocity change under linear drag?

From rest, with downward positive, $v(t)=\frac{mg}{b}(1-e^{-bt/m})$; the velocity approaches $v_T=mg/b$.

What is Stokes' law for a sphere?

In the low-speed viscous regime, the drag magnitude is $F_S=6\pi r\eta v$, where $r$ is radius and $\eta$ is viscosity.

What limiting distance does a coasting boat approach under linear drag?

For initial speed $v_0$, mass $m$, and drag coefficient $b$, the additional distance approaches $x_{\max}=\frac{mv_0}{b}$.

Quiz questions

1. In which direction does drag act on an object moving relative to a fluid?Answer: Opposite the object's velocity relative to the fluid.
2. Which expression gives quadratic drag for many large objects moving through air?Answer: $F_D=\frac{1}{2}C\rho A v^2$
3. For a falling object at terminal speed, with buoyancy neglected, what is the force balance?Answer: Upward drag equals downward weight.
4. A boat coasts from initial speed $v_0$ under linear drag with coefficient $b$. What limiting distance does it travel if its mass is $m$?Answer: $\frac{mv_0}{b}$
5. For a falling object with downward positive and linear drag $-bv$, what is its terminal speed?Answer: $\frac{mg}{b}$