An air bubble of radius 2 mm is rising at a steady speed of 2.5 cm s ⁻¹ through a liquid column. If the coefficient of viscosity of the liquid is 0.5 kg m ⁻¹ s ⁻¹ , what is the magnitude and direction of the viscous drag force acting on the bubble?

Step-by-step solution

Given: Radius of the bubble, r = 2 mm = 2 10⁻³ m Steady velocity, v = 2.5 cm s ⁻¹ = 2.5 10⁻² m s ⁻¹ Coefficient of viscosity, = 0.5 kg m ⁻¹ s ⁻¹ According to Stokes' law, the magnitude of the viscous drag force is: F = 6 r v F = 6 0.5 (2 10⁻³) (2.5 10⁻²) F = 3 5 10⁻⁵ F = 15 10⁻⁵ N = 1.5 10⁻⁴ N Viscous drag always opposes the relative motion of the object through the fluid. Since the air bubble is rising (moving vertically upwards), the viscous drag force must act vertically downwards. Answer: 1.5 10⁻⁴ N , verticall