Can Water Flow in Multiple Directions in a Network of Pipes?

In summary, the author stated that water can flow in one direction only in a network of pipes, but when P is below the surface of B, then water must be out of B and Q1+Q2 = Q3.
  • #1
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4

Homework Statement


in the previous therad
https://www.physicsforums.com/threads/flow-in-branch-pipe.866194/
(post #14) , i was told that water can flow in one direction only in a netwrok of pipes .
However , in the notes uploaded here , the author stated that when P is below surface of B , then water must be out of B and Q1 + Q2 = Q3 ?
I4r4Jk1.jpg

Homework Equations

The Attempt at a Solution


IMO , it should be Q2 = Q1 + Q3 , since i was told that water can only flow in 1 direction , am i right ? [/B]
 

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  • #3
I would not have set this problem up the way that they have set it up. I would have written the following 3 equations:

$$\frac{p_A}{\rho g}+z_A=\frac{p_D}{\rho g}+z_D+\frac{fL_1v_1^2}{gd_1}$$
$$\frac{p_D}{\rho g}+z_D=\frac{p_B}{\rho g}+z_B+\frac{fL_1v_2^2}{gd_1}$$
$$\frac{p_D}{\rho g}+z_D=\frac{p_C}{\rho g}+z_C+\frac{fL_1v_3^2}{gd_1}$$
So,
$$z_A=\frac{p_D}{\rho g}+z_D+\frac{fL_1v_1^2}{gd_1}\tag{1}$$
$$\frac{p_D}{\rho g}+z_D=z_B+\frac{fL_1v_2^2}{gd_1}\tag{2}$$
$$\frac{p_D}{\rho g}+z_D=z_C+\frac{fL_1v_3^2}{gd_1}\tag{3}$$

What would Eqn. 2 have to look like if the flow were from B to D, rather than from D to B?
 
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  • #4
Chestermiller said:
I would not have set this problem up the way that they have set it up. I would have written the following 3 equations:

$$\frac{p_A}{\rho g}+z_A=\frac{p_D}{\rho g}+z_D+\frac{fL_1v_1^2}{gd_1}$$
$$\frac{p_D}{\rho g}+z_D=\frac{p_B}{\rho g}+z_B+\frac{fL_1v_2^2}{gd_1}$$
$$\frac{p_D}{\rho g}+z_D=\frac{p_C}{\rho g}+z_C+\frac{fL_1v_3^2}{gd_1}$$
So,
$$z_A=\frac{p_D}{\rho g}+z_D+\frac{fL_1v_1^2}{gd_1}\tag{1}$$
$$\frac{p_D}{\rho g}+z_D=z_B+\frac{fL_1v_2^2}{gd_1}\tag{2}$$
$$\frac{p_D}{\rho g}+z_D=z_C+\frac{fL_1v_3^2}{gd_1}\tag{3}$$

What would Eqn. 2 have to look like if the flow were from B to D, rather than from D to B?
if the flow were from B to D ,
PB / ρg + zB = PD / ρg + zD +f(L_2)[(v_2)^2] / 2g(D_2) ,
as PB = 0 ,so ,
zB = PD / ρg + zD +f(L_2)[(v_2)^2] / 2g(D_2) , am i right ?
am i right ?
 
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  • #5
is the author wrong ? how could Q1 + Q2 = Q3 ? how could the water flow in different direction ?
in the previous thread , i was told that in order for water from Res. B to flow to the split at D, it must flow against the pressure in the line created by the flow from Res. A , so the water can only flow out from A , and into B and C..
https://www.physicsforums.com/threads/flow-in-branch-pipe.866194/
 
  • #6
foo9008 said:
if the flow were from B to D ,
PB / ρg + zB = PD / ρg + zD +f(L_2)[(v_2)^2] / 2g(D_2) ,
as PB = 0 ,so ,
zB = PD / ρg + zD +f(L_2)[(v_2)^2] / 2g(D_2) , am i right ?
am i right ?
Yes. Now, see if there is a possible solution for this case.
 
  • #7
Chestermiller said:
Yes. Now, see if there is a possible solution for this case.
what do you mean ?
 
  • #8
foo9008 said:
what do you mean ?
This would be applicable to the case where Q1+Q2 = Q3. Do the equations have a solution for this case?
 
  • #9
Chestermiller said:
This would be applicable to the case where Q1+Q2 = Q3. Do the equations have a solution for this case?
IMO , that is not feasible , since i was told that water can only flow in 1 direction
 
  • #10
foo9008 said:
IMO , that is not feasible , since i was told that water can only flow in 1 direction
If that's the case, then when you solve the equations, you will not get a real solution. Why don't you try solving it and see what you get. Who told you that silly thing anyway?
 
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  • #11
Chestermiller said:
If that's the case, then when you solve the equations, you will not get a real solution. Why don't you try solving it and see what you get. Who told you that silly thing anyway?
i was told in the previous thread , refer to the previous thread https://www.physicsforums.com/threads/flow-in-branch-pipe.866194/
 
  • #12
Chestermiller said:
If that's the case, then when you solve the equations, you will not get a real solution. Why don't you try solving it and see what you get. Who told you that silly thing anyway?
so , the statement of water can only flowing in 1 direction is incorrect ?
 
  • #13
anyone can clarify ?
 
  • #14
Chestermiller said:
This would be applicable to the case where Q1+Q2 = Q3. Do the equations have a solution for this case?
how to know that if the equations have solutions ?
 
  • #15
foo9008 said:
anyone can clarify ?
What direction would it be if D1 were equal to zero?
 
  • #16
foo9008 said:
how to know that if the equations have solutions ?
Solve them and see if the solution is real or complex.
 

1. What is flow in branch pipe 2?

Flow in branch pipe 2 refers to the movement of fluid through a pipe that branches off from the main pipe. It is the rate at which the fluid passes through the branch pipe and is typically measured in volume per unit time.

2. What factors affect flow in branch pipe 2?

Flow in branch pipe 2 is affected by several factors, including the diameter and length of the pipe, the fluid viscosity, the pressure difference between the main pipe and the branch pipe, and any obstructions or bends in the pipe.

3. How is flow in branch pipe 2 calculated?

The flow rate in branch pipe 2 can be calculated using the Bernoulli equation, which takes into account the fluid density, velocity, and pressure at different points along the pipe. Other methods, such as using flow meters or performing experiments, can also be used to determine the flow rate.

4. What are some common issues that can affect flow in branch pipe 2?

Some common issues that can affect flow in branch pipe 2 include blockages or clogs, leaks, changes in fluid properties, and improper pipe design or installation. These issues can lead to reduced flow rates, pressure drops, or even pipe failure.

5. How can flow in branch pipe 2 be optimized?

To optimize flow in branch pipe 2, it is important to ensure proper pipe design and installation, regular maintenance and cleaning to prevent blockages, and selecting the right fluid for the application. Additionally, using flow control devices such as valves and pumps can help regulate and improve the flow rate in the branch pipe.

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