Results 1 to 2 of 2

Math Help - forces again

  1. #1
    Senior Member
    Joined
    Jan 2009
    Posts
    381

    forces again

    When an object moves through a fluid , it experiences a retarding force due to turbulence . For a sphere of radius r moving with a speed of v in a fluid of density , p , the retarding force is given by

     <br />
F=kpr^2v^2<br />

    By relating the retarding force to the transfer of momentum between the fluid and the sphere , explain why the force F is directly proportional to pr^2v^2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Hello thereddevils
    Quote Originally Posted by thereddevils View Post
    When an object moves through a fluid , it experiences a retarding force due to turbulence . For a sphere of radius r moving with a speed of v in a fluid of density , p , the retarding force is given by

     <br />
F=kpr^2v^2<br />

    By relating the retarding force to the transfer of momentum between the fluid and the sphere , explain why the force F is directly proportional to pr^2v^2
    In a small time \delta t, the sphere moves a distance \delta x.We now assume that a volume of fluid proportional to the surface area of the sphere multiplied by the distance \delta x has its velocity changed from zero to the velocity, v, of the sphere, due to impact with the sphere's surface. Since the SA of the sphere is proportional to the square of its radius, the mass of fluid affected in time \delta t is therefore equal to

    k \rho r^2 \delta x

    where \rho is the density of the fluid, and k is a constant.

    Its change in momentum is therefore

    k \rho r^2 \delta x v

    Therefore, using Newton's Second and Third Laws, the force that this mass of fluid exerts on the sphere is equal to the rate of change of its momentum; i.e.

    \frac{k \rho r^2 \delta x v}{\delta t}

    As \delta t \rightarrow 0, \frac{\delta x}{\delta t}\rightarrow v. So the force on the sphere is therefore

    k \rho r^2v^2

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. forces again
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 4th 2011, 02:39 AM
  2. forces 2
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 20th 2010, 10:32 AM
  3. Forces
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 11th 2009, 02:40 PM
  4. Forces
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: December 23rd 2008, 07:15 AM
  5. forces
    Posted in the Trigonometry Forum
    Replies: 13
    Last Post: July 10th 2008, 07:46 AM

Search Tags


/mathhelpforum @mathhelpforum