Question

Find the surface tension at critical velocity?

Answer 1

Given formula for surface tension at critical velocity:

The formula for surface tension at the critical velocity is given by:

\[ \gamma = \frac{\rho v^2}{2r} \] where:

• \(\gamma\) is the surface tension of the liquid,
• \(\rho\) is the density of the liquid,
• \(v\) is the critical velocity of the liquid,
• \(r\) is the radius of the tube or capillary.

 

Critical velocity:
The critical velocity is the velocity at which the flow of a liquid through a tube or capillary changes from laminar flow to turbulent flow. At this velocity, the surface tension of the liquid is balanced by the inertial forces of the flowing liquid.

Given values:
- \( r = 0.1 \, \text{cm} \) (radius of the tube),
- \( \rho = 1000 \, \text{kg/m}^3 \) (density of the liquid),
- \( v = 50 \, \text{cm/s} \) (critical velocity).

Step 1: Convert the units to be consistent:
We need to convert the density and velocity into compatible units, such as kg/cm³ for density and m/s for velocity.

• Convert the density: \( \rho = 1000 \, \text{kg/m}^3 = 1 \, \text{kg/cm}^3 \),
• Convert the velocity: \( v = 50 \, \text{cm/s} = 0.5 \, \text{m/s} \).