Water flowing through a garden hose of diameter 2.77 cm fills a 20.0-L bucket in
ID: 1488256 • Letter: W
Question
Water flowing through a garden hose of diameter 2.77 cm fills a 20.0-L bucket in 1.10 min. What is the speed of the water leaving the end of the hose? Your response differs from the correct answer by more than 10%. Double check your calculations. m/s A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diameter of the hose, what is the speed of the water leaving the nozzle? Your response differs from the correct answer by more than 10%. Double check your calculations. m/sExplanation / Answer
volume rate = speed * area
volume rate = 20 L / 1.1 min
volume rate = 20 L / (1.1 * 60) sec
volume rate = (20 * 0.001) m^3 / (1.1 * 60) sec
volume rate = 0.0003030303 m^3 / sec
0.0003030303 = pi * (0.0277/2)^2 * speed
speed = 0.502847 m/s
by continuity equation
area1 * velocity1 = area2 * velocity2
new diameter = 0.0277 / 3 m
pi * (0.0277/2)^2 * 0.502847 = pi * (0.0277/6)^2 * velocity2
velocity2 = 4.5256 m/s
velocity after leaving nozzle = 4.5256 m/s
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