Register to reply

Work required to pump water out of conical tank

by akbar786
Tags: conical, pump, required, tank, water, work
Share this thread:
akbar786
#1
Jun14-10, 09:37 PM
P: 18
1. The problem statement, all variables and given/known data
Find the work done in pumping all the water out of a conical reservoir of radius 10ft at the top and altitude 8ft if at the beginning the reservoir is filled to a depth of 5ft and the water is pumped just to the top of the reservoir.
2. Relevant equations
None

3. The attempt at a solution
This is my work so far. I am taking the integral from -8 to -3. The top center of the cone is on (0,0). I have the integral going from -8 to -3 of (100 pi) *(62.4) (0-y) dy. The 100 is from the radius squared. The (0-y) is the distance the water has to travel up any given y. Any help?
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
Dick
#2
Jun14-10, 10:03 PM
Sci Advisor
HW Helper
Thanks
P: 25,251
You want to integrate pi*r^2*(-y)*dy from -8 to -3, right? So you want to express r as a function of y, don't you? Why are you using 100, the radius squared at the top and where did 62.4 come from?
akbar786
#3
Jun14-10, 10:22 PM
P: 18
Quote Quote by Dick View Post
You want to integrate pi*r^2*(-y)*dy from -8 to -3, right? So you want to express r as a function of y, don't you? Why are you using 100, the radius squared at the top and where did 62.4 come from?
62.4 is the density of water the teacher wanted us to use.I decided to keep all my numbers positive which will also make it much easier to integrate.Here is my new integral with expressing r as a function of y. 62.4*pi * integral from 0 to 5 of ((5/4y)^2) * (8-y)
8-y is the distance the water has to travel given the generic y and on each of those y's the radius will be 5/4 of the y term. Is this right? I am solving for work and 62.4 is my density for water

Dick
#4
Jun14-10, 10:26 PM
Sci Advisor
HW Helper
Thanks
P: 25,251
Work required to pump water out of conical tank

Quote Quote by akbar786 View Post
62.4 is the density of water the teacher wanted us to use.I decided to keep all my numbers positive which will also make it much easier to integrate.Here is my new integral with expressing r as a function of y. 62.4*pi * integral from 0 to 5 of ((5/4y)^2) * (8-y)
8-y is the distance the water has to travel given the generic y and on each of those y's the radius will be 5/4 of the y term. Is this right? I am solving for work and 62.4 is my density for water
Now that looks right to me. Putting the origin at the bottom does make it much less confusing.
akbar786
#5
Jun14-10, 10:55 PM
P: 18
Awesome, thanks a lot for your help.


Register to reply

Related Discussions
Calculate the work to pump water out of tank Introductory Physics Homework 1
Work needed to pump water out of spherical tank Calculus & Beyond Homework 3
Work required to pump - Very tricky Calculus & Beyond Homework 5
Optimization question - water in a conical tank Calculus & Beyond Homework 1
Water Pressure in Conical Tank Question Engineering Systems & Design 3