A horizontal main water line (Pipe M) of radius carries water at a speed of to a…

PHYSICS · Single correct · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids

Problem

A horizontal main water line (Pipe M) of radius

3.0\,\text{cm}

carries water at a speed of

2.2\,\text{m}\!/\!\text{s}

to a junction where it splits into Branch 1 and Branch 2. • Branch 1: radius

1.5\,\text{cm}

, speed

3.0\,\text{m}\!/\!\text{s}

away from the junction • Branch 2: radius

2.0\,\text{cm}

, speed

v_2

away from the junction Farther downstream, Branch 2 splits again into Branch 2a and Branch 2b. • Branch 2a: radius

1.0\,\text{cm}

, speed

2.8\,\text{m}\!/\!\text{s}

away from the second junction • Branch 2b: radius

1.2\,\text{cm}

, speed

v_{2b}

away from the second junction Assuming steady, incompressible flow and no storage of water at either junction, what is the average speed

v_{2b}

in Branch 2b? (a)

5.3\,\text{m}\!/\!\text{s}

(b)

7.1\,\text{m}\!/\!\text{s}

(c)

3.3\,\text{m}\!/\!\text{s}

(d)

9.1\,\text{m}\!/\!\text{s}