Answer to Question #182898 in Civil and Environmental Engineering for Md.Nayan Hossain

Question

A garden hose attached with a nozzle us used to fill a 15-gal bucket. The 

inner diameter of the hose is 4 cm, and it reduces to 1 cm at the nozzle 

exit. If it takes 1 minute 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.

Answer 1

The time to full the bucket is determined from the volume rate flow and the volume of the bucket:

$\Delta t = \frac{V}{\dot{V}} \Rightarrow \dot{V} = \frac{V}{\Delta t }$

$\dot{V} = \frac{3.789 \cdot 15^{-2}}{50} = 0.7578 \cdot 15^{-3} (\frac{m^3}{s})$

The average velocity can be determined from the volume flow rate and cross-sectional area at the nozzle exit:

$\dot{V} = Av = \frac{\pi D^2}{4}v \Rightarrow v = \frac{4 \dot{V}}{\pi D^2}$

$v = \frac{4 \cdot 0.7578 \cdot15^{-3}}{3.1415 \cdot (0.8 \cdot 15^{-2})^2} = 16.4 (\frac{m}{s})$.