Answer to Question #130134 in Mechanics | Relativity for Ariyo Emmanuel

Question

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. density of water 1000 kg/m3; 1 gal = 3.789 x 10-3 m3.

If it takes 50 s to fill the bucket with water, determine the volume flow rates of water through the hose, and 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:

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

$\dot{V} = \frac{3.789 \cdot 10^{-2}}{50} = 0.7578 \cdot 10^{-3} (\frac{m^3}{s})$

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

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

$v = \frac{4 \cdot 0.7578 \cdot10^{-3}}{3.1415 \cdot (0.8 \cdot 10^{-2})^2} = 15.1 (\frac{m}{s})$.