How Fast Should Water Flow from a Faucet to Properly Water a Rooftop Lawn?

[scarlson1193]

Homework Statement

A man has a garden on the roof of his building. He has a patio and a small lawn. He wants to water the lawn. He has a sprinkler in the form of a disk with 40 holes of diameter 1 mm. A line drawn tangent to the sprinkler at the location of the outer most holes would make an angle of 15 degrees with the horizontal. He places the sprinkler at the center of the lawn with a distance of 2 m from the sprinkler to the edge of the lawn and connects it via a hose to a faucet placed on a wall 70 cm above the roof level. The man does not want the water to extend farther than the edge of the lawn. What should be the speed of the water out of the 1.9 cm diameter faucet for the water to reach no farther than the edge of the lawn? What will be the pressure at the faucet opening?

Homework Equations

Bernoulli's Principle:

The Attempt at a Solution

In all honesty, I'm not even sure where to begin with this problem. The density of the water is 1000 kg/m^3 and gravity is 9.8 m/s^2. When we plugged in our given data to Bernoulli's Principle, our answer was 6860 Pa. However, I'm not entirely sure that answer is even helpful to our problem. Any advice on where to even start going would be great.

 

[Redbelly98]

Homework Statement

A man has a garden on the roof of his building. He has a patio and a small lawn. He wants to water the lawn. He has a sprinkler in the form of a disk with 40 holes of diameter 1 mm. A line drawn tangent to the sprinkler at the location of the outer most holes would make an angle of 15 degrees with the horizontal. He places the sprinkler at the center of the lawn with a distance of 2 m from the sprinkler to the edge of the lawn and connects it via a hose to a faucet placed on a wall 70 cm above the roof level. The man does not want the water to extend farther than the edge of the lawn. What should be the speed of the water out of the 1.9 cm diameter faucet for the water to reach no farther than the edge of the lawn? What will be the pressure at the faucet opening?

Homework Equations

Bernoulli's Principle:

The Attempt at a Solution

In all honesty, I'm not even sure where to begin with this problem. The density of the water is 1000 kg/m^3 and gravity is 9.8 m/s^2. When we plugged in our given data to Bernoulli's Principle, our answer was 6860 Pa. However, I'm not entirely sure that answer is even helpful to our problem. Any advice on where to even start going would be great.

Welcome to Physics Forums.

It is hard to follow how you got 6860 Pa from Bernouli's equation, since you don't know v.

It is also difficult to picture the situation without a figure. That being said, can you calculate what v must be when the water leaves the sprinkler head, in order that the water just reaches the edge of the lawn?

 

[scarlson1193]

I'm sorry, I meant to say that we used Variation of Pressure with Depth to find 6860 Pa.

 

[Redbelly98]

I'm sorry, I meant to say that we used Variation of Pressure with Depth to find 6860 Pa.

Okay.

Can you calculate what v must be when the water leaves the sprinkler head, in order that the water just reaches the edge of the lawn?

 

[rwisz]

As a scientist, my first step would be to gather more information and clarify any assumptions made in the problem. For example, what is the desired depth of water on the lawn? How does the angle of the sprinkler affect the water coverage? Are there any external factors such as wind that could affect the water distribution?

Once these details are clear, I would approach the problem by using fluid dynamics principles such as Bernoulli's equation, the continuity equation, and the Navier-Stokes equation. These equations can help calculate the speed and pressure of the water at different points in the system. Additionally, I would consider the properties of the water, such as its viscosity and surface tension, which can also affect the water's behavior.

I would also suggest conducting experiments or simulations to better understand the behavior of the water in this specific scenario. This can help validate the calculations and provide a more accurate solution.

Overall, as a scientist, I would approach this problem systematically, gathering all relevant information and using mathematical and experimental methods to determine the appropriate speed and pressure for the water to reach the desired distance on the lawn.