The settlement velocity of a solid (diameter 0.5 mm, specific gravity 1.75) in water having temperature 10°C, is

ANS:B - 313.5 cm/sec

The settlement velocity of a solid particle in a fluid can be calculated using Stokes' law, which states that the settling velocity (vs​) of a spherical particle in a viscous fluid is given by: vs​=2/9(r^p2​)(Pp​−ρf​)g​ / ​η Where:

• rp​ is the radius of the particle
• ρp​ is the density of the particle
• ρf​ is the density of the fluid
• g is the acceleration due to gravity
• η is the dynamic viscosity of the fluid

Given:

• Diameter of the solid particle (dp​) = 0.5 mm
• Specific gravity of the solid particle (SGp​) = 1.75
• Density of water at 10°C (ρf​) ≈ 999.7 kg/m³
• Dynamic viscosity of water at 10°C (η) ≈ 1.307 × 10⁻³ Pa·s (or kg/(m·s))
• Acceleration due to gravity (g) ≈ 9.81 m/s²

First, we need to convert the diameter (dp​) to radius (rp​): 2=0.5 mm2=0.25 mm=0.25×10−3 mrp​=2dp​​=20.5mm​=0.25mm=0.25×10−3m Now, we can calculate the settling velocity (vs​): =2/9(0.25×10−3)2×(1.75×999.7−999.7)×9.81 / 1.307×10−3​ Vs=2/9(0.25×10−3)2×(0.75×999.7)×9.81/1.307×10−3​ Vs≈2/9×0.252×0.75×999.7×9.81 / 1.307​ Vs≈2/9×0.252×0.75×999.7×9.81 / 1.307 Vs≈2/9×0.0625×0.75×999.7×9.811.307​ Vs≈2/9×4513.08176 /1.307 Vs≈2×4513.081769/1.307​ Vs≈9026.163521/1.763 Vs≈767.72 mm/svs​≈767.72mm/s vs​≈76.772cm/s So, the settlement velocity of the solid particle in water at 10°C is approximately 76.772 cm/s76.772cm/s. However, please double-check the calculations as there could be rounding errors, but the closest option provided in the question is 213.5 cm/sec, which is significantly different from the calculated value. It's possible there was a mistake in the given data or in the calculation.