Results 1 to 2 of 2

Math Help - pumping out a liquid - work

  1. #1
    Member mybrohshi5's Avatar
    Joined
    Sep 2009
    Posts
    230

    pumping out a liquid - work

    A tank in the shape of an inverted right circular cone has height meters and radius meters. It is filled with meters of hot chocolate.
    Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is

    <br />
A = \pi r^2<br />

    <br />
V = \pi r^2 \triangle{x}<br />

    <br />
\frac{r}{h} = \frac{13}{8}     <br />
\frac {r}{8-x} = \frac{13}{8}     r=\frac{13}{8}(8-x)<br />

    <br />
V = \pi (\frac{13}{8})^2 (8-x)^2 \triangle x<br />

    <br />
F = ma = V*p*g<br />

    <br />
F = \pi (\frac{13}{8})^2 (8-x)^2 (1550)(9.8) \triangle x<br />

    <br />
W = \int^8_1 [\pi (\frac{169}{64}) (8-x)^2 (1550)(9.8)] dx<br />

    <br />
W = \frac{2567110\pi}{64} \int^8_1 (8-x)^2 dx<br />

    <br />
W = 14407454.03 J<br />

    Can anyone see where i went wrong?

    Thanks for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,867
    Thanks
    640
    Quote Originally Posted by mybrohshi5 View Post
    A tank in the shape of an inverted right circular cone has height meters and radius meters. It is filled with meters of hot chocolate.
    Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is
    let the bottom of the tank be the origin.

    one sloping side of the tank runs along the line y = \frac{8}{13}x

    volume of a representative horizontal cross-section is ...

    \pi x^2 \cdot dy = \frac{169\pi}{64}y^2 \, dy

    weight-density = \left(1550 \, \frac{kg}{m^3}\right) \cdot \left(9.8 \, \frac{N}{kg}\right) = 15190 \, \frac{N}{m^3}<br />

    lift distance for a representative horizontal cross-section is (8-y)

    W = \int_0^7 15190 \cdot (8-y) \cdot \frac{169\pi}{64}y^2 \, dy

    W = \frac{1283555 \pi}{32}\int_0^7 8y^2-y^3 \, dy

    W = 3.96 \times 10^7 \, J
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. work problem to pump liquid out of a tank
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 24th 2011, 04:59 PM
  2. work pumping water into hemispherical tank
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 8th 2010, 07:17 PM
  3. work by pumping
    Posted in the Calculus Forum
    Replies: 8
    Last Post: August 19th 2009, 02:09 PM
  4. work by pumping
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 12th 2009, 08:56 AM
  5. work done in pumping something
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 19th 2007, 09:41 AM

Search Tags


/mathhelpforum @mathhelpforum