When a sphere of radius `r_1=1.2mm` moves in glycerin, the laminar flow is observed if the velocity of the sphere does not exceed `v_1=23cm//s`. At what minimum velocity `v_2` of a sphere of radius `r_2=5.5cm` will the flow in water become turbulent? The viscosities of glycerin and water are equal to `eta_1=13.9P` and `n_2=0.011P` respectively.

Explanation

We know that Reynold's number for turbulent flow is greater than that on laminar flow.
Now, `(R_e)_l=(rhovd)/(eta)=(2rho_1v_1r_1)/(eta_1)` and `(R_e)_t=(2rho_2v_2r_2)/(eta)`
But, `(R_e)_tge(R_e)_l`
so `v_(2_(min))=(rho_1v_1r_1eta_2)/(rho_2r_2eta_1)=5mu m//s` on putting the values.