A tank, shaped like a cone has height 12 meter and base radius 1 meter. It is placed so that the circular part is upward. It is full of water, and we have to pump it all out by a pipe that is always leveled at the surface of the water. Assume that a cubic meter of water weighs 10 000 N , i. e. the density of water is 10000 N m 3 . How much work does it require to pump all water out of the tank

376966.991 Joules

Explanation:

Given that :

the height = 12  m

Let assume the tank have a thickness  = dh

The radius of the tank by using the concept of similar triangle is :

The area of the tank =

The area of the tank =

The area of the tank =

The volume of the tank is  = area × thickness

=

Weight of the element =

where;

= density of water ; which is given as 10000 N/m³

So;

Weight of the element =

Weight of the element =

However; the work required to pump this water = weight × height  rise

where the height rise = 12 - h

the work required to pump this water  = (12 - h)

the work required to pump this water  =

We can determine the total workdone by integrating the work required to pump this water

SO;

Workdone =

=

=  

=

=

=

= 376966.991 Joules