Question

The velocity in a 2 cm diameter pipe is 20 m/s. If the pipe increased to 5 cm diameter velocity, in m/s, will be

Answer 1

use formula,
$\boxed{\bf{\pi r_1^2V_1=\pi r_2^2V_2}}$

where $r_1$ is the initial radius of pipe.
$V_1$ is the initial velocity , $r_2$ is final radius of pipe and $V_2$ is final velocity of pipe.
here, $r_1=2cm/2=1cm$
$r_2=5cm/2=2.5cm$
$V_1=20m/s$

so, 1² × 20 = (2.5)² × $V_2$

$V_2=3.2m/s$

hence, velocity will be 3.2 m/s

Answer 2

Case 1: Diameter of pipe 1 = d = 2 cm

Radius of pipe 1 = r1 = 2/2 = 1 cm = 0.01 m

Area of pipe 1 = A1 = πr^2 =  (3.1416)(0.01)^2

                                          = 0.0003

Velocity through pipe 1 = v1 = 20 m/s

Case 2: Diameter of pipe 2 = d = 5 cm

Radius of pipe 2 = r2 = 5/2 = 2.5 cm = 0.025 m

Area of pipe 1 = A2 = πr^2 =  (3.1416)(0.025)^2

                                          = 0.0019

Velocity through pipe 2 = v2 = ?

By Equation of CONTINUITY, we have

                              A2v2 = A1v1

                    (0.0019)v2 = (0.0003)(20)

                    (0.0019)v2 =  0.006

                                   v2 = 0.006/0.0019

                                   v2 = 3.16 m/s

The velocity through a pipe of diameter 5 cm will be v2 = 3.16 m/s