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en/4.5.12.md
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| + | ### Statement | ||
| + | |||
| + | $4.5.12.$ [Insert the problem statement] | ||
| + | |||
| + | ### Solution | ||
| + | |||
| + | The sum of the forces acting on the volume of liquid highlighted in the figure is zero,so let's write force balance to the $x$ axis: | ||
| + | |||
| + | \begin{equation} | ||
| + | \sigma L-\sigma L\sin\theta=P_{avg}Lh | ||
| + | \end{equation} | ||
| + | |||
| + | where $P_{avg}$ is an average pressure of the liquid.As pressure linearly increasing with depth we get: | ||
| + | |||
| + | |||
| + | \begin{equation} | ||
| + | P_{avg}=\frac{1}{2}\rho gh | ||
| + | \end{equation} | ||
| + | |||
| + | |||
| + | |||
| + | Plugging eq(2) into eq(1) we get rise height of the liquid: | ||
| + | |||
| + | |||
| + | \begin{equation} | ||
| + | h=\sqrt{\frac{2\sigma(1-\sin\theta)}{\rho g}} | ||
| + | \end{equation} | ||
| + | |||
| + | |||
| + | In the case of complete wetting, the contact angle is zero,so: | ||
| + | |||
| + | |||
| + | \begin{equation} | ||
| + | h=\sqrt{\frac{2\sigma}{\rho g}} | ||
| + | \end{equation} | ||
| + | |||
| + | |||
| + | For the water $\sigma=0.073 \frac{N}{m}$,$\rho=1000\frac{kg}{m^3}$ and $g=9.8\frac{m}{s^2}$,so: | ||
| + | |||
| + | |||
| + | |||
| + | \begin{equation} | ||
| + | h \approx 3.9mm | ||
| + | \end{equation} | ||
| + | |||
| + | |||
| + | #### Answer | ||
| + | |||
| + | [Insert a concise answer or boxed result] | ||
| @@ -0,0 +1,49 @@ | |||
| ### Statement | |||
| $4.5.12.$ [Insert the problem statement] | |||
| ### Solution | |||
| The sum of the forces acting on the volume of liquid highlighted in the figure is zero,so let's write force balance to the $x$ axis: | |||
| \begin{equation} | |||
| \sigma L-\sigma L\sin\theta=P_{avg}Lh | |||
| \end{equation} | |||
| where $P_{avg}$ is an average pressure of the liquid.As pressure linearly increasing with depth we get: | |||
| \begin{equation} | |||
| P_{avg}=\frac{1}{2}\rho gh | |||
| \end{equation} | |||
| Plugging eq(2) into eq(1) we get rise height of the liquid: | |||
| \begin{equation} | |||
| h=\sqrt{\frac{2\sigma(1-\sin\theta)}{\rho g}} | |||
| \end{equation} | |||
| In the case of complete wetting, the contact angle is zero,so: | |||
| \begin{equation} | |||
| h=\sqrt{\frac{2\sigma}{\rho g}} | |||
| \end{equation} | |||
| For the water $\sigma=0.073 \frac{N}{m}$,$\rho=1000\frac{kg}{m^3}$ and $g=9.8\frac{m}{s^2}$,so: | |||
| \begin{equation} | |||
| h \approx 3.9mm | |||
| \end{equation} | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||