Calculating the Speed of Water Exiting from a Sprinkler

In summary, the question is asking at what speed the water will leave the sprinkler, given that the garden hose has an internal diameter of 1.5cm and the sprinkler has 14 holes with a diameter of .20cm each. The water in the hose is moving at a speed of 3.0m/s and the volume of water passing through the hose must equal the volume passing through the sprinkler in the same amount of time. The volume of water passing through a point in the hose for a length of time \Delta T is also being considered.
  • #1
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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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  • #2
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 [itex]\Delta T[/itex]?
 
  • #3


Great question! To calculate the speed of the water exiting the sprinkler, we can use the equation for continuity, which states that the flow rate of a fluid (in this case water) remains constant throughout a pipe or hose. The equation is A1V1 = A2V2, where A1 and V1 are the area and velocity of the water in the hose, and A2 and V2 are the area and velocity of the water exiting the sprinkler.

Using the equation for area, we can calculate the area of the water in the hose as A1 = 1/2 * pi * (0.75cm)^2 = 0.44 cm^2. Since there are 14 holes in the sprinkler, the total area of the holes is A2 = 14 * 1/2 * pi * (0.10cm)^2 = 0.11 cm^2. Now we can plug these values into the continuity equation and solve for V2:

A1V1 = A2V2
(0.44 cm^2)(3.0 m/s) = (0.11 cm^2) V2
V2 = (0.44 cm^2)(3.0 m/s) / (0.11 cm^2)
V2 = 12.0 m/s

So the water will exit the sprinkler at a speed of 12.0 m/s. This is significantly faster than the speed of the water in the hose, which makes sense because the water is being forced through smaller holes, increasing its velocity.
 

1. How do you measure the speed of water exiting from a sprinkler?

The speed of water exiting from a sprinkler can be measured using a flow meter or by timing how long it takes for a certain amount of water to fill a container placed under the sprinkler. The formula for calculating speed is distance divided by time.

2. What factors affect the speed of water exiting from a sprinkler?

The speed of water exiting from a sprinkler can be affected by the pressure of the water source, the size and shape of the sprinkler nozzle, and any obstructions or blockages in the sprinkler system.

3. How does the speed of water exiting from a sprinkler impact the coverage area?

The speed of water exiting from a sprinkler can impact the coverage area by determining how far the water will reach and how evenly it will be distributed. Higher speeds may result in a larger coverage area but can also lead to uneven distribution and water waste.

4. Can the speed of water exiting from a sprinkler be adjusted?

Yes, the speed of water exiting from a sprinkler can be adjusted by changing the water pressure, nozzle size, or angle of the sprinkler. This can help optimize the coverage area and conserve water.

5. How can the speed of water exiting from a sprinkler be used in irrigation systems?

The speed of water exiting from a sprinkler is an important factor in designing efficient irrigation systems. By calculating the speed and adjusting the sprinklers accordingly, water can be evenly distributed across a designated area, minimizing water waste and ensuring proper plant growth.

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