Force on a sphere in flowing water and velocity of water

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SUMMARY

The discussion focuses on the forces acting on a sphere submerged in flowing water, specifically addressing gravity, buoyancy, and potential drag forces. The participant correctly identifies the equation for buoyancy as ((pi*d^3)/6)×ρ(water)×g=mg, which allows for the determination of the sphere's mass based on fluid density. The participant expresses uncertainty regarding the application of drag force, given the sphere's minimal movement through the water. Clarification on the role of viscosity and drag in this context is sought.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly buoyancy and drag forces.
  • Familiarity with basic physics equations involving mass, density, and gravity.
  • Knowledge of viscosity and its effects on submerged objects.
  • Ability to apply Newton's second law (F=ma) in fluid contexts.
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  • Research the concept of drag force in fluid dynamics, particularly for spherical objects.
  • Study the effects of viscosity on the motion of objects in fluids.
  • Learn about the Reynolds number and its significance in determining flow regimes.
  • Explore computational fluid dynamics (CFD) tools for simulating fluid interactions with solid bodies.
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Students studying physics or engineering, particularly those focusing on fluid dynamics, as well as educators seeking to clarify concepts related to forces on submerged objects.

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Homework Statement



The problem has been attached with this post.

Homework Equations



Equation given below.

The Attempt at a Solution



The forces on the sphere could be due to gravity and the buoyancy force.
((pi*d^3)/6)×ρ(water)×g=mg
From this I can find the mass of the sphere in terms of the density of fluid.
Then Fv = m (dv/dt). But, I am stuck here. How should I proceed? Is my approach correct?
 

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Also, though viscosity of water is given in the problem, i doubt if there would be any drag force on the sphere since the sphere doesn't seem to be moving significantly through the water. Please throw some light on this concept too.
 

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