Molten steel is kept in a ladle. Due in natural convection. mixing occurs inside the melt. A 1cm diameter sphere is held in the centre of the melt where the steel flows upward. so as to measure the force exerted by the melt on the sphere. The force. F exerted by the melt on the sphere is given by $$F = f\left( {\frac{\pi }{8}} \right).\left( {\frac{{{\mu ^2}}}{8}} \right){\left( {\operatorname{Re} } \right)^2}.$$
Data: Density of liquid steels
= 7100 kg. m^-3
Viscosity of liquid steel
= 6.5 × 10^-3 kg. m^-1. s^-1
Reynolds number (Re) of the melt
= 5 × 10³
Friction factor (f) = 0.3
The velocity of melt (m.s^-1) in the central portion of the ladle would be