Question

Water flowing through a garden hose of diameter 2.75 cm fills a 24.0-L bucket in 1.30 min.

(a) What is the speed of the water leaving the end of the hose?
m/s

(b) A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diameter of the hose, what is the speed of the water leaving the nozzle?
m/s

Answer 1

1 Liter = 10^-3 m³

Volume of the bucket = V = 24 L = 24 x 10^-3 m³ = 0.024 m³

Time taken to fill the bucket = T = 1.3 min = 1.3 x 60 sec = 78 sec

Volumetric flow rate of water = Q

V = QT

0.024 = Q(78)

Q = 3.077 x 10^-4 m³/s

Diameter of the garden hose = D₁ = 2.75 cm = 0.0275 m

Cross-sectional area of the garden hose = A₁

A₁ = D₁²/4

A₁ = (0.0275)²/4

A₁ = 5.94 x 10^-4 m²

Speed of water in the garden hose = v₁

Q = A₁v₁

3.077x10^-4 = (5.94x10^-4)v₁

v₁ = 0.518 m/s

Diameter of the nozzle attached to the garden hose = D₂ = D₁/3 = 0.0275/3 = 9.167 x 10^-3 m

Cross-sectional area of the nozzle = A₂

A₂ = D₂²/4

A₂ = (9.167x10^-3)²/4

A₂ = 6.6 x 10^-5 m²

Speed of water in the nozzle = v₂

Q = A₂v₂

3.077x10^-4 = (6.6x10^-5)v₂

v₂ = 4.66 m/s

a) Speed of water leaving the end of the hose = 0.518 m/s

b) Speed of water leaving the nozzle = 4.66 m/s