Question

Water is flowing in a pipe of diameter 4 cm with a velocity 3 m//s . The water then enters into a tube of diameter 2 cm . The velocity of water in the other pipe is

Answer 1

Given:

Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s . The water then enters into a tube of diameter 2 cm.

To find:

Velocity of water in the other pipe ;

Calculation:

Applying Equation of Continuity :

$\sf{(A1)(v1) = (A2)(v2)}$

$= > \sf{\pi {(r1)}^{2} (v1) = \pi {(r2)}^{2} (v2)}$

$= > \sf{ \cancel{\pi} {(r1)}^{2} (v1) = \cancel{\pi} {(r2)}^{2} (v2)}$

$= > \sf{ {(r1)}^{2} (v1) = {(r2)}^{2} (v2)}$

Putting the values:

$= > \sf{ {( \dfrac{0.04}{2} )}^{2} (3) = {( \dfrac{0.02}{2} )}^{2} (v2)}$

$= > \sf{ {( 0.02)}^{2} (3) = {( 0.01)}^{2} (v2)}$

$= > \sf{ 4 \times {10}^{ - 4} (3) = {10}^{ - 4} (v2)}$

$\sf{ = > (v2) = 12 \: m {s}^{ - 1} }$

So , final answer is:

$\boxed{ \sf{ (v2) = 12 \: m {s}^{ - 1} }}$