Question

a fire hose of diameter 2.5 cm and is required to direct a jet of water to a height of at least 40m the minimum power needed​

Answer 1

Given:

• Diameter of fire hose $= 2.5 cm$

• Height$= 40m$

To Find:

• The minimum power of the pump needed for fire hose.

Solution:

When water from pipe goes upto $40 m$ then,

 Kinetic energy is changed into potential energy

                $\frac{1}{2} mv^2 = mgh$

                      $v = \sqrt {2gh}$                   $...................eq(i)$

Power          $(P) = \frac{kinetic \ benergy }{t}$

                    $P = \frac{\frac{1}{2} mv^2}{t}$

                     $m = volume \times density$          

                    $m = Area \times velocity \times density$

                   $m = \frac{\pi \times D^2 }{ 4} \times \sqrt{2gh} \times \rho$                    $from \ eq(i)$

So,

                    $P = \frac{1}{2} \times \frac{\pi \times D^2 }{ 4} \times \sqrt{2gh} \times \rho \times 2gh$

                    $P = \frac{\pi \times D^2 }{ 8} \times \sqrt[3]{2gh} \times \rho$

                   $P = \frac{1}{8} \times 3.14 \times 2.5 \times 10^{-2} \times\sqrt[3]{ (2 \times 9.8 \times 40)} \times 1000$

                  $P = 21.5KJ$

Thus, The minimum power of the pump needed for fire hose is $21.5 KJ$