A 30% (by volume) suspension of spherical sand particles in a viscous oil has a hindered settling velocity of 4.44 μm/s. If the Richardson Zaki hindered settling index is 4.5, then the terminal velocity of a sand grain is

Answer: Option B

The Richardson-Zaki equation relates the hindered settling velocity (V_h) to the terminal settling velocity (V_t) through the expression:

V_h = V_t × (1 - φ)ⁿ

where φ is the volume fraction of solids (here, φ = 0.30) and n is the Richardson-Zaki index (given as 4.5).

First calculate (1 - φ):

1 - 0.30 = 0.70

Then raise it to the power of n:

(0.70)^4.5 ≈ 0.2008

Rearranging the equation for terminal velocity gives:

V_t = V_h / (1 - φ)ⁿ

Substituting the values:

V_t = 4.44 μm/s / 0.2008 ≈ 22.1 μm/s

Therefore, the terminal velocity of a sand grain is 22.1 μm/s.