Calculating the Speed of Water Exiting from a Sprinkler

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SUMMARY

The discussion focuses on calculating the speed of water exiting from a sprinkler connected to a garden hose. The hose has an internal diameter of 1.5 cm and the sprinkler features 14 holes, each with a diameter of 0.20 cm. Given that water flows through the hose at a speed of 3.0 m/s, the principle of conservation of mass dictates that the water must exit the sprinkler at a higher speed due to the smaller cross-sectional area of the holes. The relevant equations involve calculating the cross-sectional areas and applying the continuity equation to determine the exit velocity.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically the continuity equation.
  • Knowledge of cross-sectional area calculations using the formula A = πr².
  • Familiarity with basic physics concepts related to velocity and flow rates.
  • Ability to perform unit conversions and calculations involving diameters and radii.
NEXT STEPS
  • Calculate the cross-sectional area of the garden hose and the sprinkler holes using A = πr².
  • Apply the continuity equation to derive the speed of water exiting the sprinkler.
  • Explore the effects of hole diameter on water velocity and flow rate in fluid systems.
  • Investigate real-world applications of fluid dynamics in irrigation systems and sprinkler design.
USEFUL FOR

This discussion is beneficial for physics students, engineers, and anyone interested in fluid dynamics, particularly in applications related to irrigation and sprinkler systems.

bww
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1. A garden hose has an internal diameter of 1.5cm. It's connected to a sprinkler that consists merely of an enclosure with 14 holes, each .20 cm in diameter. The water in the hose moves with a speed of 3.0m/s. At what speed does the water leave the sprinkler?


OK, so some relevant equations I think would be area- 1/2*pi*r^2. Where i go from there I'm not sure. I also know that the water should leave at a faster speed since it is being forced through many smaller holes.

Your thoughts?
 
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The volume of water passing a point in the thick section in a certain time must equal the volume passing through the sprinkler in the same time. That makes sense since if this was not true some water would have gone missing somewhere. What will be the volume of water passing a point in the hose for a length of time \Delta T?
 

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