If a 1 cm diameter sphere drops through castor oil (kinematic viscosity 10 stokes) at a terminal velocity of 1.5 cm/sec, what is the drag coefficient on the sphere________________?
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Answer: C. 160
Explanation
Combining terminal velocity, sphere diameter, and kinematic viscosity via Stokes law yields one sixty. Drag coefficient normalizes fluid resistance forces against dynamic pressure and cross-sectional area. Kinematic viscosity of ten stokes represents high fluid resistance encountered by the dropping sphere. Stokes law describes the drag force experienced by spherical objects moving through viscous fluids. Terminal velocity is reached when gravitational forces perfectly balance opposing viscous drag forces. Viscous drag calculations require careful conversion between stokes and square meters per second.
Falling sphere viscometers use these exact equations to measure fluid viscosity in industrial laboratories. Sedimentation processes in wastewater treatment plants rely on settling velocity and drag principles. Chemical engineers calculate particle drag coefficients to design efficient slurry transport pipelines. A drag coefficient less than one occurs only at very high Reynolds numbers in turbulent regimes. Stating values between one and one hundred ignores the specific high viscosity conditions of castor oil. Two hundred overestimates the drag resistance for this specific sphere size and terminal velocity.
- Subject
- Engineering
- Category
- Civil Engineering
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- —
- Difficulty
- medium
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