Question

Find the surface tension at critical velocity?

Answer 1

The surface tension at critical velocity can be determined using the following formula: 

γ = (ρv^2) / (2r) 

where: γ is the surface tension of the liquid ρ is the density of the liquid v is the critical velocity of the liquid r is the radius of the tube or capillary The critical velocity is the velocity at which a liquid flowing 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. 

Let's assume that we have a tube of radius r = 0.1 cm, and we want to find the surface tension of a liquid with density ρ = 1000 kg/m^3 at the critical velocity v = 50 cm/s. 

First, we need to convert the units of density and velocity to be consistent with each other.

 We can convert the density to kg/cm^3 by dividing it by 1000, and the velocity to m/s by dividing it by 

100: ρ = 1000 kg/m^3 = 1 kg/cm^3 v = 50 cm/s = 0.5 m/s

Now we can plug these values into the formula: γ = (ρv^2) / (2r) γ = (1 x 0.5^2) / (2 x 0.1) γ = 1.25 N/m 

Therefore, the surface tension at critical velocity is 1.25 N/m.