Question

Selena uses a garden hose to fill a bucket of water. The water enters the house through a faucet with a 6.0-cm diameter. The speed of the water at the faucet is 5 m/s. If the faucet and the nozzle are at the same height, and the water leaves the nozzle with a speed of 20 m/s, what is the diameter of the nozzle?

Answer 1

the diameter of the nozzle = 3 cm

Step-by-step explanation:

let the diameter of nozzle be x cm.

then, area of cross-section at nozzle =
`\pi(x^2)/(4)`

nozzle with a speed of 20 m/s, and speed of the water at the faucet is 5 m/s.

area of cross section at faucet =
`\pi(6^2)/(4)`= 9π

now , area×velocity has to be constant (since area×velocity gives volume flow rate which should be same at both ends).

therefore

5×9π = 20×π×x^2/4

=>45 = 5×x^2

=>9 = x^2

=> x = 3 cm (as 3^2 =9)

therefore, the diameter of the nozzle = 3 cm

Answer 2

3 cm

Step-by-step explanation:

diameter of faucet, D = 6 cm

Velocity at faucet, V = 5 m/s

velocity at nozzle, v = 20 m/s

Let the diameter of the nozzle is d.

use the equation of continuity

A x V = a x v

where, A be the area of faucet, a be the area of nozzle.

π D^2 / 4 x V = πd^2 /4 x v

D^2 x V = d^2 x v

6 x 6 x 5 = d^2 x 20

d^2 = 9

d = 3 cm

Thus, the diameter of the nozzle is 3 cm .