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Question

Find the velocity of the aerosol solid particles when $t=10\ \mu \mathrm{s}$, if when $t=0$ they leave the can with a horizontal velocity of $30 \mathrm{~m} / \mathrm{s}$. Assume the average diameter of the particles is $0.4\ \mu \mathrm{m}$ and each has a mass of $0.4\left(10^{-12}\right) \mathrm{g}$. The air is at $20^{\circ} \mathrm{C}$. Neglect the vertical component of the velocity. Note: The volume of a sphere is $t=\frac{4}{3} \pi r^3$.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 7**Given:**

- The velocity at $t=0\,\text{s}$: $U_1 = 30\,\frac{\text{m}}{\text{s}}$
- Final time: $t = 10\times10^{-6}\,\text{s}$
- Diameter: $D = 0.4\times10^{-6}\,\text{m}$
- Mass: $m = 0.4\times 10^{-12}\,\text{g} = 0.4\times 10^{-15}\,\text{kg}$
- Density of air: $\rho = 1.202\,\frac{\text{kg}}{\text{m}^3}$
- Dinamic viscosity of air: $\mu = 18.1\times10^{-6}\,\frac{\text{N}\cdot\text{s}}{\text{m}^2}$

**Required:**

- The velocity $U_\text{f}$ at the final time

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