Question

solved answers for a water pipe entering a hose has a diameter of 2 cm and the speed of water is 0.1ms-1.Eventually, the pipe tapers to a diameter of 1cm. what is the speed of the water in tapered portion.​

Answer 1

Given:

A hose has a diameter of 2 cm and the speed of water is 0.1m/s. Eventually, the pipe tapers to a diameter of 1cm.

To find:

Speed of water in the tapered portion ?

Calculation:

In these kind of questions, it is best to use EQUATION OF CONTINUITY:

• Initial radius = d/2 = 2/2 = 1 cm.
• Final radius = d/2 = 1/2 = 0.5 cm.

So, applying Equation of Continuity:

$\therefore \: a_{1}v_{1} = a_{2}v_{2}$

$\implies \: \bigg \{\pi {(r_{1})}^{2} \bigg \}v_{1} = \bigg \{\pi {(r_{2})}^{2} \bigg \}v_{2}$

$\implies \: \bigg \{ {(r_{1})}^{2} \bigg \}v_{1} = \bigg \{{(r_{2})}^{2} \bigg \}v_{2}$

$\implies \: {(1)}^{2} \times 0.1 = {(0.5)}^{2} \times v_{2}$

$\implies \: 1 \times 0.1 =0.25\times v_{2}$

$\implies \: v_{2} = 0.4 \: m {s}^{ - 1}$

So velocity of tapered part is 0.4 m/s.