Question #182898

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.

Expert's answer

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})".

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