Bernoulli's Equation and a water pipe

In summary, The conversation discusses a problem involving the water supply of a building. The problem includes a main pipe with a 6.00cm diameter and a tap with a 2.00cm diameter located 2.00m above the main pipe. The question asks for the speed of the water leaving the tap and the gauge pressure in the 6cm main pipe. The solution involves using the equation of continuity to find the speed of the water leaving the tap and Bernoulli's equation to find the gauge pressure. After some clarification and correcting for units, the final answers are determined to be 2.65m/s and 2.3 x 10^4 Pa, respectively.
  • #1
Zaros
22
0

Homework Statement



The water supply of a building is fed through a main pipe 6.00cm in diameter. A 2.00cm diameter tap is located 2.00m above the main pipe. When the tap is turned on it fills a 25.0L container in 30.0s if no other taps are turned on at the same time.
a) What is the speed at which the water leaves the tap?
b) What is the gauge pressure in the 6cm main pipe?

Homework Equations



P1+0.5pv1^2 + pgy1 = P2 +0.5pv2^2 + pgy2
Pg = Ps - Pa

The Attempt at a Solution



I solved part (a) easily enough by dividing 25 by 30 to get 0.833 L/s
and I'm sure i have to use Bernoulli's equation to solve this but have been having problems understanding the equation and the concept behind it and how i would use this in the particular problem I'm faced with.

Thanks for helping
Zaros
 
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  • #2
Is anyone able to help with this problem. I may be getting at it from the wrong direction so you might want to disregard some of the equations I'v used.
 
  • #3
apply the equation of continuity for the first part.
Q(rate of flow) = 0.833 x 10-3 m3/s
Q=A2V2
calculate V from here which is the answer.

Use Bernouillis equation for the second part

P1+0.5pV1^2 = Pa +0.5pV2^2 + pgh here h=height of the tap from the main pipe.

P1 will be your answer ( I got it as 2.3 x 104 Pa)
 
  • #4
Great thanks for this you really helped. I was wondering how to use Bernoulli's equation but never thought that the second pressure would be that of the atmosphere.

Thanks.
Zaros
 
  • #5
i think i must be doing something wrong. Is V1 = V2 if not what should it be. Also if i try this i get 3011370600 Pa which is outrageously big. For part a i got a speed of 2.65 * 103 m/s any ideas what i did wrong
 
  • #6
You messed up with some units. V2 is 2.65m/s
V1 is not equal to V2

Calculate V1 from A1V1=A2V2
 

FAQ: Bernoulli's Equation and a water pipe

1. What is Bernoulli's Equation?

Bernoulli's Equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a flowing fluid. It states that as the velocity of a fluid increases, the pressure decreases, and vice versa.

2. How is Bernoulli's Equation applied to a water pipe?

In a water pipe, Bernoulli's Equation can be used to calculate the pressure difference between two points along the pipe, given the velocity and elevation at each point. This is useful for determining the flow rate and efficiency of a water system.

3. Can Bernoulli's Equation be applied to any fluid?

Yes, Bernoulli's Equation can be applied to any fluid, whether it is a liquid or a gas. However, it assumes certain conditions such as incompressibility and steady flow.

4. What are some real-life applications of Bernoulli's Equation and water pipes?

Bernoulli's Equation is used in many engineering applications, including the design of pipelines, pumps, and turbines. It is also used in the aviation industry to explain the lift force on an airplane wing, which is created by differences in air pressure.

5. How does the shape of a water pipe affect Bernoulli's Equation?

The shape of a water pipe can affect Bernoulli's Equation by changing the cross-sectional area, which in turn affects the velocity and pressure of the fluid inside. A narrower pipe will result in higher velocity and lower pressure, while a wider pipe will have lower velocity and higher pressure.

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