Question

Problem #3 At very low Reynolds numbers a ball viscometer can be used to measure fluid viscosity by dropping a spherical ball in the fluid and measuring its terminal velocity. Consider a solid ball of radius a = 1cm and density Ps = 2,500 kg/m falling in liquid glycerin with density P = 1,250 kg/m3. The measured terminal velocity of the ball is U = 0.15 m/s. Calculate the viscosity of the liquid.

Answer 1

Radius of ball (a)=1 cm 110) density of ball = 2500 kg/m3 Se density of liquid = 1,250 kg/m² terminal velocity = 0.15 m/ - (VA) at equilibrium weight = boxs buoyancy + Drag force a Fd+ Fb Juevolume) 7 Dog = ve g + 37 u V₂ (29) » ug (80-8e) = (6 Vera). M M= 4 na? (sor P2 Xg 6л V - а 4 na? (So- Sl) g 67 Vt

x (0.01)2 x(2500 - 1250) *9.81 = 1-816 Nis m2