Drag - Terminal Velocity of a solid sphere.

In summary, the problem involves determining the terminal velocity of a solid sphere with a diameter of 20mm and a specific gravity of 1.3 when dropped in water with a viscosity of 1*10^-3 and a density of 1000. The suggested solution involves guessing at the terminal velocity, determining the Reynolds number, finding the drag coefficient, computing the drag force, and comparing it with the initial guess. Additional resources such as the kinematic viscosity of water, Reynolds number for a sphere, and drag coefficient data can be used to aid in solving the problem.
  • #1
MrWinesy
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0

Homework Statement



A solid sphere - 20mm in diameter, σ (specific gravity) = 1.3

dropped in water μ=1*10^-3 and ρ=1000

determine the terminal velocity for the sphere.

(hint- guess the value for the drag coefficient then iterate)


Homework Equations



Fd=(1/2)*Cd*ρ*(U^2)*A

The Attempt at a Solution



tried guessing the drag coefficient but have no confidence in estimate or of the next step.

(also the relationship equation connecting viscosity, specific gravity and density would be much appreciated).

Thank you in advance for your help.
 
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  • #2
What they have in mind I guess is this:
1. guess at the terminal velocity.
2. determine the Reynolds number for a sphere in water at that velocity.
3. Determine the drag coefficient based on the Reynolds number.
4. Compute the drag force based on c and v.
5. Compare with your guess of v.
6. Re-guess v etc.

There are several Websites that together can give you all the info you need:
1. kinematic viscosity of water
2. Reynolds number for a sphere at a given velocity
3. Drag coeff. as a function of the Reynolds number for a sphere.

Along the way you can pick up any theory and data you didn't know.
 

Related to Drag - Terminal Velocity of a solid sphere.

1. What is terminal velocity?

Terminal velocity is the maximum velocity that an object can reach when falling through a fluid, such as air or water. It is the point at which the force of gravity is balanced by the force of drag, resulting in a constant velocity.

2. How is terminal velocity calculated?

The terminal velocity of an object can be calculated by equating the drag force and the weight of the object. This can be represented by the equation Fd = mg, where Fd is the drag force, m is the mass of the object, and g is the acceleration due to gravity. By rearranging this equation, we can solve for the terminal velocity (Vt = √(2mg/ρACd), where ρ is the density of the fluid, A is the cross-sectional area of the object, and Cd is the drag coefficient.

3. What factors affect the terminal velocity of a solid sphere?

The terminal velocity of a solid sphere is affected by several factors, including the size and shape of the sphere, the density and viscosity of the fluid, and the presence of any external forces, such as wind. Additionally, the terminal velocity can be influenced by the surface roughness of the sphere, as well as its initial velocity and orientation.

4. How does the drag coefficient affect terminal velocity?

The drag coefficient is a dimensionless quantity that represents the drag force experienced by an object in a fluid flow. It is affected by the shape and surface properties of the object, as well as the properties of the fluid. As the drag coefficient increases, the terminal velocity of a solid sphere will decrease, as there is a greater force acting against the motion of the object.

5. Can the terminal velocity of a solid sphere be exceeded?

In most cases, the terminal velocity of a solid sphere cannot be exceeded, as the drag force will continue to increase as the object falls faster, eventually balancing out the force of gravity. However, in certain circumstances, such as in a vacuum or at extremely high altitudes, the terminal velocity may not be reached, and the object may continue to accelerate until it reaches a different terminal velocity or encounters another force.

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