Viscous Drag and Terminal Velocity

In summary, the conversation discussed the estimation of the terminal velocity of droplets in air with given data of mass and radius using Stoke's Law and the concept of upthrust. The conclusion was that the terminal velocity is approximately 0.3mms^-1, but there may be an error in the data provided.
  • #1
paradiselost
2
0

Homework Statement



Droplets in a deodorant spray have mass of about (4x10^-12) kg and a radius of about 0.1mm. Estimate the terminal velocity of the droplets in Air of Viscosity (2x10^-5)Nsm^-2.

Homework Equations


Stoke's Law, F = 6pi rvu
where r = radius, v = velocity and u = viscosity.

Upthrust of an object = vpg (v = volume, p = density, g = gravitational acceleration)

The Attempt at a Solution


Since at terminal velocity, it is obvious that W = F + U. (where W = weight, F = viscous drag, U = upthrust.)

So we have,
F = W-U
6pi (0.1x10^-3)(2x10^-5)(v) = (4x10^-12)(9.8) - (4/3)(pi)(0.1x10^-3)^3(1.24)(9.8)
**Based on the assumption that the droplet is a sphere and the density of air is 1.24kg/m^3

We have,
v = (approx) 0.3mms^-1.

Is this true?

(@ ehild : Oops. Forgot the negative sign)
 
Last edited:
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  • #2
"Droplets in a deodorant spray have mass of (4x10^12) kg "

Is this serious?:smile:

ehild
 
  • #3
Something is still wrong with the data. What is the density of the droplets if the mass is 4^*10^-12 and the radius is 0.1 mm? ehild
 

FAQ: Viscous Drag and Terminal Velocity

1. What is viscous drag?

Viscous drag is a type of drag force that is caused by the friction between a fluid and a solid object moving through it. It is also known as fluid resistance or skin friction.

2. How does viscosity affect drag?

The higher the viscosity of a fluid, the more resistance it will provide to an object moving through it, resulting in a higher drag force. This is because a more viscous fluid will have a greater tendency to stick to the surface of the object, creating more friction.

3. What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid, when the drag force equals the force of gravity. At this point, the object will continue to fall at a constant velocity without accelerating.

4. How is terminal velocity affected by the shape and size of an object?

The shape and size of an object can greatly affect its terminal velocity. Objects with a larger surface area or a more streamlined shape will experience greater drag and reach their terminal velocity more quickly. Smaller, more compact objects will have a lower terminal velocity as they experience less drag.

5. Can you reduce drag and increase terminal velocity?

Yes, there are several ways to reduce drag and increase an object's terminal velocity. These include streamlining the object's shape, reducing its surface roughness, and using materials with lower coefficients of friction. However, it is important to note that there will always be some amount of drag present, and reaching terminal velocity is not always desirable in certain situations.

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