Question

6. A garden hose attached to a nozzle is used to fill a 15-gal bucket. The inner diameter of the hose is 1.5 cm, and it reduces to 0.8 cm at the nozzle exit. If it takes 50 s to fill the bucket with water (density = 1 kg/L), determine (a) the volume and mass flow rates of water through the hose, and (b) the average velocity of water at the nozzle exit.

Answer 1

Answer: 1.135 L/s; 1.35 kg/s, 22.57 m/s

Explanation:

Given

Volume of bucket $V=15\ gal\approx 56.78\ L$

time to fill it $t=50\ s$

Volume flow rate

$\dot{V}=\dfrac{56.78}{50}=1.135\ L/s\approx 1.135\times 10^{-3}\ m^3/s$

The inner diameter of the hose $D=1.5\ cm$

diameter of the nozzle exit $d=0.8\ cm$

we can volume flow rate as

$\Rightarrow \dot{V}=Av\quad \quad \text{v=average velocity through nozzle exit}\\\\\Rightarrow 1.135\times 10^{-3}=\frac{\pi }{4}d^2\times v\\\\\Rightarrow 1.135\times 10^{-3}=\frac{\pi }{4}(0.8\times 10^{-2})^2\times v\\\\\Rightarrow v=\dfrac{4\times 1.135\times 10^{-3}}{\pi \times 64\times 10^{-6}}=22.57\ m/s$

Mass flow rate

$\Rightarrow \dot{m}=\rho \times \dot{V}\\\Rightarrow \dot{m}=1\ kg/L\times 1.135\ L/s=1.35\ kg/s$