Looking for classes? Ksquare Career Institute, Bengaluru →
Mechanical Properties of Fluids
Capillary rise and angle of contact
1 question from 1 paper, each with its answer.
- question
- 1
- paper
- 1
- of Mechanical Properties of Fluids
- 2.94%
Concepts tested
- capillary-rise-contact-angle
All Questions
2016 Phase II 1 question
-
Three liquids of densities $\rho_1$, $\rho_2$ and $\rho_3$ (with $\rho_1 > \rho_2 > \rho_3$), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $\theta_1$, $\theta_2$ and $\theta_3$ obey:
Equal rise needs $\cos\theta \propto \rho$.
$h = \frac{2T\cos\theta}{\rho gr}$; as r, h and T are the same, $\frac{\cos\theta}{\rho}$ = constant
$\frac{\cos\theta_1}{\rho_1} = \frac{\cos\theta_2}{\rho_2} = \frac{\cos\theta_3}{\rho_3}$
As $\rho_1 > \rho_2 > \rho_3$: $\cos\theta_1 > \cos\theta_2 > \cos\theta_3 \Rightarrow \theta_1 < \theta_2 < \theta_3$
As the liquid rises, θ must be acute, so $0 \le \theta_1 < \theta_2 < \theta_3 < \frac{\pi}{2}$
