Water Flow through a Garden Hose Nozzle A garden hose attached with a nozzle is used to fill a 10-gal bucket. The inner diameter of the hose is 2 cm, and it reduces to 0.8 cm at the nozzle exit (Fig. 5-9). If it takes 50 s to fill the bucket with water, determine (a) the volume and mass flow rates

Question

Water Flow through a Garden Hose Nozzle

A garden hose attached with a nozzle is used to fill a 10-gal bucket. The inner diameter of the hose is 2 cm, and it reduces to 0.8 cm at the nozzle exit (Fig. 5-9). If it takes 50 s to fill the bucket with water, determine (a) the volume and mass flow rates of water through the hose, and (b) the average velocity of water at the nozzle exit.

Accepted Answer

A garden hose is used to fill a water bucket. The volume and mass flow rates of water and the exit velocity are to be determined.

Assumptions 1 Water is an incompressible substance. 2 Flow through the hose is steady. 3 There is no waste of water by splashing.
Properties We take the density of water to be 1000 kg /m[latex]^{3}[/latex]=1 kg/L.

Analysis (a) Noting that 10 gal of water are discharged in 50 s, the volume and mass flow rates of water are

[latex]\begin{aligned}&\dot{V}=\frac{V}{\Delta t}=\frac{10 \mathrm{gal}}{50 \mathrm{~s}}\left(\frac{3.7854 \mathrm{~L}}{\mathrm{1 gal}} ight)=0.757 \mathrm{~L} / \mathrm{s} \&\dot{m}= ho \dot{V}=(1 \mathrm{~kg} / \mathrm{L})(0.757 \mathrm{~L} / \mathrm{s})=0.757 \mathrm{~kg} / \mathrm{s}\end{aligned}[/latex]

(b) The cross-sectional area of the nozzle exit is

[latex]A_{e}=\pi r_{e}^{2}=\pi(0.4 \mathrm{~cm})^{2}=0.5027 \mathrm{~cm}^{2}=0.5027 imes 10^{-4} \mathrm{~m}^{2}[/latex]

The volume flow rate through the hose and the nozzle is constant. Then the average velocity of water at the nozzle exit becomes

[latex]V_{e}=\frac{\dot{V}}{A_{e}}=\frac{0.757 \mathrm{~L} / \mathrm{s}}{0.5027 imes 10^{-4} \mathrm{~m}^{2}}\left(\frac{1 \mathrm{~m}^{3}}{1000 \mathrm{~L}} ight)=15.1 \mathrm{~m} / \mathrm{s}[/latex]

Discussion It can be shown that the average velocity in the hose is 2.4 m/s. Therefore, the nozzle increases the water velocity by over six times.

Question 5.1: Water Flow through a Garden Hose Nozzle A garden hose attach...

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