What is the terminal velocity (msec-1) of a sand size particle (2 mm in diameter) with a density of 2600 kg m-3. Assume water has a density of 1000.0 kg m-3 and a viscosity of 10-3 Pa s? Use 2 significant figures in your answer.

Question

What is the terminal velocity (msec-1) of a sand size particle (2 mm in diameter) with a density of 2600 kg m-3. Assume water has a density of 1000.0 kg m-3 and a viscosity of 10-3 Pa s?  Use 2 significant figures in your answer.

BlackTom AI · Accepted Answer

The question asks for the terminal velocity of a sand-sized particle in water, given diameter 2 mm, particle density 2600 kg/m^3, water density 1000 kg/m^3, and dynamic viscosity 1.0×10^-3 Pa·s. First, note that for small spherical particles in a viscous fluid, the terminal velocity is described by Stokes’ law: v_t = [ (2/9) (ρ_p − ρ_f) g R^2 ] / μ, where ρ_p is particle density, ρ_f is fluid density, g is gravitational acceleration, R is particle radius, and μ is dynamic viscosity. Here: R = d/2 = 0.002 m / 2 = 0.001 m. The density difference is ρ_p − ρ_f = 2600 − 1000 = 1600 kg/m^3. Use g ≈ 9.81 m/s^2 and μ = 1.0×10^-3 Pa·s. Compute R^2 = (0.001 m)^2 = 1.0×10^-6 m^2.

Plug into the formula: v_t = (2/9) × (1600) × (9.81) × (1.0×10^-6) / (1.0×10^-3).
Calculate step by step: 1600 × 9.81 ≈ 15696; multiply by 1.0×10^-6 gives ≈ 0.015696; multiply by (2/9) ≈ 0.222... gives ≈ 0.003488; then divide by 1.0×10^-3 to account for μ, giving ≈ 3.488 m/s.
Rounding to two significant figures as requested, v_t ≈ 3.5 m/s.

Notes:
- This result assumes laminar (Stokes) regime, which is typically valid for small particles and low Reynolds numbers; if the particle were larger or the fluid velocity higher, a non-Stokes drag model might be required.
- Since no answer options were provided, there is no need to compare choices. The calculated value matches the expected order of magnitude for a 2 mm particle in water under these conditions.

EAS1600 Sediment_HeatPump_inclass_0428_2025

What is the terminal velocity (msec-1) of a sand size particle (2 mm in diameter) with a density of 2600 kg m-3. Assume water has a density of 1000.0 kg m-3 and a viscosity of 10-3 Pa s? Use 2 significant figures in your answer.

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