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

  • Thread starter Thread starter scarlson1193
  • Start date Start date
  • Tags Tags
    Fluids
Click For Summary

Homework Help Overview

The discussion revolves around a physics problem involving fluid dynamics, specifically the application of Bernoulli's Principle and pressure variation in a scenario where a man is trying to water a rooftop lawn using a sprinkler system. The setup includes a sprinkler with multiple holes and a faucet positioned above the roof level, with specific constraints on the water flow distance.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial calculations involving Bernoulli's Principle and pressure variation with depth, questioning the validity of the derived pressure value. There is an emphasis on determining the necessary speed of the water as it exits the sprinkler to ensure it reaches the edge of the lawn.

Discussion Status

The conversation is ongoing, with participants seeking clarification on the calculations and the physical setup. Some guidance has been offered regarding the need to calculate the exit velocity of the water from the sprinkler, but there is no consensus on the approach or the correctness of the initial calculations.

Contextual Notes

Participants note the complexity of visualizing the problem without a diagram, and there is an acknowledgment of the need for further calculations to determine the required parameters for the sprinkler system to function as intended.

scarlson1193
Messages
5
Reaction score
0

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:
tumblr_lo9evoBZLP1qew352o1_400.png


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.
 
Physics news on Phys.org
scarlson1193 said:

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:
tumblr_lo9evoBZLP1qew352o1_400.png


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?
 
I'm sorry, I meant to say that we used Variation of Pressure with Depth to find 6860 Pa.
 
scarlson1193 said:
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?
 

Similar threads

What is the relationship between water stream diameter and distance from faucet?
  • · Replies 1 ·
Replies
1
Views
2K
How Fast Does Water Exit the Sprinkler Holes According to Bernoulli's Equation?
  • · Replies 1 ·
Replies
1
Views
2K
Maximum height for water from a fire hose
  • · Replies 4 ·
Replies
4
Views
4K
How Fast Can Water Flow from a Kitchen Faucet on the Third Floor?
  • · Replies 2 ·
Replies
2
Views
5K
Water Flow from 17.0mm Faucet: When Does it Narrow to 10mm?
  • · Replies 1 ·
Replies
1
Views
3K
How Does Bernoulli's Principle Apply to Varying Pipe Diameters and Water Flow?
  • · Replies 3 ·
Replies
3
Views
2K
Solve Fluid Flow Problem: Find Water Rise in Cylindrical Bucket
  • · Replies 3 ·
Replies
3
Views
3K
Water flowing in and out of a bucket
  • · Replies 1 ·
Replies
1
Views
4K
Fluid Flow: Water Pipe with Vertical Pipes
  • · Replies 4 ·
Replies
4
Views
14K
Calculating Distance of Water Landing from Pool Hole | Torricelli's Theorem
  • · Replies 10 ·
Replies
10
Views
3K