Question

A rectangular tank that is 3 feet long, 6 feet wide, and 3 feet tall is filled with a liquid that has a density of p pounds per cubic foot. If a spout is connected to the top of the tank, how much work will it take to pump all of the liquid out of the tank through the spout

Answer 1

Answer:

Therefore work required to pump out of all liquid is 81p ft-lb.

Step-by-step explanation:

Given that,

A rectangle tank dimension is 3 feet long, 6 feet wide and 3 feet tall.

The density of the liquid in the rectangular tank is p.

The volume of water  $\triangle y$ of strip is

=long ×wide ×$\triangle y$

=(3 ×6 ×$\triangle y$) ft³

Force is = (3 ×6 ×$\triangle y$)×p pound

Total work done

$W=\int_0^3 3\times 6 \times p\times \triangle y(3- y)$

    $=\int_0^318p (3- y)dy$

     $=18p\int_0^3(3-y)dy$

     $=18p[3y-\frac{y^2}{2}]_0^3$

    $=18p[(3.3-\frac{3^2}{2})-(3.0-\frac{0^2}{2})]$

    $=18p[9-\frac{9}{2}]$

   $=18p\times \frac92$

    =81p ft-lb

Therefore work required to pump out of all liquid is 81p ft-lb.