Very small objects, such as dust particles, experience a linear drag force, = (bv, direction opposite the motion), where b is a constant. That is, the quadratic model of drag of Equation 6.16 fails for very small particles. For a sphere of radius R, the drag constant can be shown to be b = 6πηR, where η is the viscosity of the gas.
a. Find an expression for the terminal speed vterm of a spherical particle of radius R and mass mfalling through a gas of viscosity η.
b. Suppose a gust of wind has carried a 50-μm-diameter dust particle to a height of 300 m. If the wind suddenly stops, how long will it take the dust particle to settle back to the ground? Dust has a density of 2700 kg/m3, the viscosity of 25°C air is 2.0 × 10−5 N s/m2, and you can assume that the falling dust particle reaches terminal speed almost instantly.
Solution 66 P
Step 1 of 5
We have to find an expression for the terminal speed of a spherical particle of radius and mass falling through a gas of viscosity .
The speed at which the exact balance between the upward drag force and the downward
gravitational force causes an object to fall without acceleration is called the terminal speed