
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 24th, 2017, 02:44 PM  #1 
Newbie Joined: Feb 2017 From: Kennesaw, Ga Posts: 1 Thanks: 0  Calculus 2 : Work Required to Pump Tank of Water A water tank in the shape of a hemispherical bowl of radius 4 m is filled with water to a depth of 2 m. How much work is required to pump all the water over the top of the tank? (The density of the water is 1000 kg/m3. Assume g = 9.8 m/s2.) The answer is 352800π but I do not understand how the book came to this answer. Please I would like an explanation 
February 24th, 2017, 07:30 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,037 Thanks: 1063 
consider a disk of water at height $h$ of infinitesimal thickness $dh$ The radius of the disk is $r=\sqrt{16(4h)^2}$ as shown in the picture. Thus the volume of the disk is $dV = \pi (16(4h)^2~dh = \pi (8h  h^2)~dh$ That disk of water has to be lifted from height $h$ to $4~m$ The work done in doing this is $dW = g (4h)~dm = \rho_{water} g (4h)~ dV = \rho_{water} \pi g (4h)(8hh^2)~dh$ the total work is $\displaystyle{\int_0^2}~ = \rho_{water} \pi g (4h)(8hh^2)~dh = 36 \pi g \rho_{water} = 352800 \pi$ 
February 24th, 2017, 08:24 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,285 Thanks: 1681 
Note that the person who replied on another website tried to use the same method, but set up the integral incorrectly.


Tags 
calc, calc2, calculus, calculus 2, pump, required, slicing, tank, water, work, work done 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Integral: finding Work needed to pump a tank  LoseUrself2Dance  Calculus  4  May 10th, 2016 06:55 AM 
Work required to pump water out of a triangular tank  leo255  Calculus  3  October 29th, 2014 02:54 AM 
Work done pumping water out of a spherical tank  mymyz4  Calculus  1  May 4th, 2013 11:22 AM 
Work to pump water out of a tank  Decave  Calculus  3  February 15th, 2012 05:50 PM 
Work to pump out a tank  aaronmath  Calculus  2  October 27th, 2011 06:15 AM 