We were discussing the basics
of shear stress in turbulent flow,Â minor
head losses in pipe flow,Â hydraulic
gradient and total energy line, basic concept andÂ working
of syphon, flow
through pipes in series and alsoÂ theÂ concept ofÂ flow through pipes in parallel, in the subject of fluid mechanics, in our recent
posts.Â

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Now we will go ahead to see the, flow through
branched pipes, in the subject of fluid mechanics, with the help of this post.Â

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**Flow through branched pipes**Â

Flow through branched pipes could be defined as the
fluid flow through a piping system where three or more than three reservoirs
will be connected with each other with the help of pipes and will have one or
more than one junctions.Â

Now we will see here one figure as displayed here. Three
reservoirs are connected here with the help of piping system and this piping
system and reservoirs are connected with one single junction i.e. junction D.Â

In various branched pipe flow problems, we will have
some specifications of branched piping system and usually we will have to
determine the flow of fluid through each pipe.Â

Let us assume that we have information about the
data for length of pipes, diameter of pipes and coefficient if friction for
each pipe and we need to find the data for flow of water through each pipe.Â

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**AssumptionÂ **

Let us assumed that reservoirs are very large and levels
of water surface in the reservoirs are constant in order to secure the steady
conditions in the pipes. We have also assumed that minor losses are very small
and could be neglected.Â

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**Principle
and equations used for solving such problemsÂ **

We will have to recall the following principles and
we will have to use following equations for securing the desired data for such
problems.Â

- Continuity equationÂ
- Bernoulliâ€™s equationÂ
- Darcy-Weisbach equation

Let us consider that three reservoirs are A, B and C
and piping system will have pipe 1, pipe 2 and pipe 3 and a single junction D as
displayed above in figure.Â

Flow of water from reservoir A will take place to
junction D and flow of water from junction D will be towards reservoir C.Â

Flow of water from junction D to reservoir B will
only possible if piezometric head at D will be more than the piezometric head
at B.Â

Let us consider the following terms from above
figure.Â

Z

_{A, }Z_{B}and_{ }Z_{C}= Datum head at reservoir A, B and C respectivelyÂ
V

_{1}, V_{2 }and V_{3}= Velocity of flow of water through pipe 1, 2 and 3 respectivelyÂ
L

_{1}, L_{2 }and L_{3}= length of pipe 1, 2 and 3 respectivelyÂ
h

_{f1}, h_{f2 }and h_{f3}= loss of head for pipe 1, 2 and 3 respectivelyÂ
Let us now use the concept of Bernoulliâ€™s equation for
flow from A to D and we will have following equation as mentioned here.Â

Let us now use the concept of Bernoulliâ€™s equation for
flow from D to B and we will have following equation as mentioned here.

Let us now use the concept of Bernoulliâ€™s equation for
flow from D to C and we will have following equation as mentioned here.

Now we will use the concept of continuity equation
and we will have following equation as mentioned here.Â

Discharge through AD = Discharge through DB +
Discharge through DCÂ

Now as we can see that we are having with above four
equations and we have to secure the value of V

_{1}, V_{2 }and V_{3}.Â
We will use above four equations to secure the value
of flow of water through each pipe.Â

Further we will go ahead to find out the basic
concept of power transmission through pipes

**,Â**in the subject of fluid mechanics, with the help of our next post.Â
Do you have any suggestions? Please write in comment
box.Â

### Reference:Â Â

Fluid mechanics, By R. K. BansalÂ Â

Image courtesy: GoogleÂ Â

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