Water flows at speed v in a pipe of radius r. Neglecting viscosity, at what speed does the water flow through a constriction in which the radius of the pipe is r/3

9v

Explanation:

Given that the water flows at speed v in a pipe of radius r.

Let is the speed of water flow where the radius of the pipe is r/3.

By using the continuity equation, the mass flow rate of water is the same at all the cross-sections of the pipe, wh have

Where and are the density, area of the cross-section and speed at cross-section 1 and   and are the density, area of the cross-section and speed at cross-section 2.

As the density of the water remains constant. so .

Hence, the speed of the water flow where the radius is r/3 is .

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s