# pumping the tank

• Mar 21st 2010, 06:24 PM
slapmaxwell1
pumping the tank
ok im working on a problem and want to know if my setup is correct, can someone check it out and let me know..thanks alot. here is a copy of my work. Attachment 16013
• Mar 21st 2010, 07:21 PM
ione
Quote:

Originally Posted by slapmaxwell1
ok im working on a problem and want to know if my setup is correct, can someone check it out and let me know..thanks alot. here is a copy of my work. Attachment 16013

The end of the tank is a circle. Place the circle on a coordinate system with the center at the origin. Then the equation of the circle is
$\displaystyle x^2+y^2=(1.5)^2$
A slice of gasoline perpendicular to the y-axis could be approximated by a right rectangular prism with dimensions 2x, 4 and dy.
$\displaystyle V=8\sqrt{2.25-y^2}\,dy$
F=(density of gasoline)(volume)
In the coordinate system a point that is 5 above the top of the tank would have y-coordinate 6.5
The distance the slice would have to travel is 6.5-y
$\displaystyle W=\int_{-1.5}^{1.5}8\rho\sqrt{2.25-y^2}(6.5-y)\,dy$