To determine

To find:

The work required to pump the water out of the spout.

Answer

45000 ft-lb

Explanation

1) Concept:

The work is calculated by using the formula W=∫abf(x)dx

And weight=gravity·volume

2) Given:

3) Calculation:

From the given figure, let the distance above the bottom of tank be  x

Let the horizontal slice of water having thickness ∆x lying at a distance  x

Let the width of the slice lying at distance x be w,

By similar triangles,

612=xw⇒w=2x

This slice has a volume 10(2x)∆x ft³

The weight of the slice is about (62.5)20x∆x

and the water must be lifted (6-x) m by the pump.

Therefore, work needed is about  62.56-x20x∆x ft-lb.

andtherefore, the total work required is

W=∫abf(x)dx

W≈∫0662.56-x20x dx

=1250∫066x-x2dx

=12506x22-x3306

=1250362-1363

=1250108-72

=45000 ft-lb

Conclusion:

The work required to pump the water out of the spout is ≈45000 ft-lb