Faucet connected to water tower

  • Thread starter toothpaste666
  • Start date
  • Tags
    Tower Water
In summary, the conversation discusses the calculation of gauge pressure at a faucet connected to a water tower through a 1 cm radius pipe. The first part addresses the gauge pressure when the faucet is closed, while the second part deals with the gauge pressure when there is a flow of 0.2 Liter/s assuming laminar flow. Bernoulli's equation is used to solve for the gauge pressure in the second part, taking into account the density of water and the height of the tower. A factor of g was missing in the first equation, but the overall method is correct.
  • #1
toothpaste666
516
20

Homework Statement


A 1 cm radius pipe connects a 3 m tall water tower to a faucet.
(a) What is the gauge pressure at the faucet when the faucet is closed
(b)12 What is the gauge pressure at the faucet if the faucet is opene
d so that there is a flow of 0.2 Liter/s? Assume that the water flow is laminar.

Homework Equations


P_1 + .5d(v_1)^2 + d(y_1) = P_2 + .5d(v_2)^2 + d(y_2)
d = density , P = pressure ,y = height, v = velocity
(A_1)(v_1) = (A_2)(v_2)
A = area v = velocity

The Attempt at a Solution


for part a)
if the faucet is closed, gauge pressure at the faucet would simply be
P = dgy = (1000 kg/m^2)(9.8 m/s^2)(3 m)

for part b)

bernoullis-png.75869.png

i must use bernoulli's equation. looking at the picture i drew I can say P_2 is 0, v_2 is 0 (because it is negligible), y_2 = 3 m , and y_1 = 0

to find v_1 :
use Av where v = l/t
Av = A(l/t) = Vol/t (which they give us as .2 liter/s = 2E-4 m^3/s)
A = pi r^2 = pi (.01 m) ^2 = 3.14 E-4
Av = Vol/t
(3.14E-4)v = 2E-4
v = 2/3.14 = .637 = v_1

using bernoullis:
P_1 + .5d(v_1)^2 + d(y_1) = P_2 + .5d(v_2)^2 + d(y_2)
P_1 + .5d(.637)^2 + d(0) = 0 + .5d(0)^2 + d(3)
P_1 + .5(1000)(.637)^2 = 3(1000)
P_1 = 3000 - .5(1000)(.637)^2

im not as worried about the actual numbers but is my method correct?
 

Attachments

  • bernoullis.png
    bernoullis.png
    1.4 KB · Views: 594
Physics news on Phys.org
  • #2
You left out a factor of g in Bernoulli's Equation, but besides that your method looks good
 
  • Like
Likes toothpaste666
  • #3
toothpaste666 said:
##P = dgy = (1000 kg/m^2)(9.8 m/s^2)(3 m)##
##(1000 kg/m^3)##
toothpaste666 said:
##P_1 + .5d(v_1)^2 + d(y_1) = P_2 + .5d(v_2)^2 + d(y_2)##
What dimension does ##d(y_1)## have? Something missing?
 
  • Like
Likes toothpaste666
  • #4
oops! it should be d(y_1)g

and good catch i meant 1000 kg/m^3
sorry for the sloppiness =[
 
  • #5


Your method for part a) is correct. For part b), your reasoning and approach are correct, but there are a few errors in your calculations.
Firstly, the density of water should be 1000 kg/m^3, not 1000 kg/m^2.
Secondly, when calculating the velocity, you should use the volumetric flow rate (0.2 L/s) divided by the cross-sectional area of the pipe (3.14E-4 m^2), not the volume divided by time.
Lastly, when substituting in values for P_1 and P_2, you should use the gauge pressure (P - P_atm) instead of absolute pressure.
With these corrections, your final answer should be:
P_1 = 3000 - .5(1000)(0.637)^2 = 2978 kPa (gauge pressure)
 

What is a faucet connected to a water tower?

A faucet connected to a water tower is a plumbing fixture that allows for the controlled release of water from a water tower into a building or outdoor area. The faucet is usually connected to a pipe that runs from the water tower and has a valve that can be turned on or off to regulate the flow of water.

How does a faucet connected to a water tower work?

A faucet connected to a water tower works by utilizing gravity to create pressure in the water tower, which then allows water to flow through the connected pipe and out of the faucet. When the valve is opened, the water is released from the tower and flows through the faucet until the valve is closed again.

What is the purpose of a faucet connected to a water tower?

The purpose of a faucet connected to a water tower is to provide a convenient and controlled source of water for a building or outdoor area. It also helps to regulate and maintain water pressure in the building, as the water tower acts as a reservoir to store and supply water.

What are the benefits of having a faucet connected to a water tower?

Having a faucet connected to a water tower can provide a reliable source of water for a building or outdoor area, especially in areas where water supply may be limited. It also helps to maintain water pressure and can save on energy costs, as the gravity-fed system does not require a pump to distribute water.

How is a faucet connected to a water tower maintained?

A faucet connected to a water tower should be regularly inspected and maintained to ensure proper function. This may include checking for any leaks, cleaning the faucet and valve, and making any necessary repairs or replacements. The water tower itself may also require maintenance, such as regular cleaning and inspection for any structural issues.

Similar threads

  • Introductory Physics Homework Help
2
Replies
47
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
953
  • Introductory Physics Homework Help
Replies
5
Views
993
  • Introductory Physics Homework Help
Replies
4
Views
532
  • Introductory Physics Homework Help
Replies
5
Views
1K
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
10K
  • Introductory Physics Homework Help
Replies
16
Views
1K
Back
Top