This document discusses flow through pipes in series, parallel, and equivalent pipes. It defines compound or series pipes as pipes of different lengths and diameters connected together to form a pipeline. The total head loss in a series pipe system is equal to the sum of the head losses in each pipe section. It also defines parallel or looping pipes as pipes that branch out from the same point and rejoin downstream, where the discharge is split between the pipes and the head loss is the same across each pipe. The document introduces the concept of an equivalent pipe that can replace a compound or parallel pipe system, having the same total discharge and head loss. It presents Dupuit's equation for calculating the diameter of an equivalent pipe for a compound system.

1. Flow Through Pipes
Prof. Sumit Kolapkar
Assistant Professor
Civil Engineering Department
Sanjivani College of Engineering Kopargaon.
Dist.-Ahmednagar

2. Flow Through Pipes in Series or Compound:-
When the pipes of different lengths and diameters are
connected to each other to form a pipeline then such a
pipeline is called as a compound pipe or pipe in series.
The difference in liquid surface levels is equal to the sum of the head losses in all the sections.
Also the discharge through each pipe will be same.
Therefore Q=A1V1=A2V2 =A3V3

3. Therefore, we have
Total Head Loss = Major Losses + Minor Losses
Therefore, Major Loss
Also,
Minor Losses= Entrance Loss +
Contraction Loss + Expansion
Loss + Exit Loss =
22 2
3 3 31 1 1 2 2 2
1 2 3
f L Vf L V f L V
= + +
2gd 2gd 2gd
( )
2 22 2
2 3 31 2
0.5 0.5
2 2 2 2
V V VV V
g g g g
−
+ + +

4. If minor losses are neglected as compared to
the head loss due to friction in pipe, then
Total head loss = Major loss
22 2
3 3 31 1 1 2 2 2
1 2 3
f L Vf L V f L V1
H= + +
2g d d d
 
 
 
In term of discharge it is given by
22 2
3 3 31 1 1 2 2 2
5 5 5
1 2 3
f Lf L f L
H= + +
12.1d 12.1d 12.1d
QQ Q

5. Equivalent Pipe OR Dupit’s Equation:-
In equivalent pipe a compound pipe is replaced
by a pipe of uniform diameter and the same
length as that of compound pipe.
Note:- 1. The uniform diameter of the
equivalent pipe is known as equivalent diameter
of the compound pipe
2. It is a single pipe of uniform diameter whose
discharge and loss of head are same as that of
the compound pipe.

6. Let,
L1= Length of pipe 1 and d1= Diameter of pipe 1
L2= Length of pipe 2 and d2= Diameter of pipe 2
L3= Length of pipe 3 and d3= Diameter of pipe 3
H = Total head loss
L = Length of equivalent pipe
d = Diameter of the equivalent pipe
Therefore, length of equivalent pipe
(L)= L1 + L2 + L3
In equivalent pipe discharge is same
Therefore, for equivalent pipe
Head loss in equivalent pipe= Head loss in pipe 1 + Head loss in pipe
2 + Head loss in pipe3
22 22
3 3 31 1 1 2 2 2
1 2 3
f L Vf L V f L VfLV
= + +
2gd 2gd 2gd 2gd

7. In term of discharge it is given by
22 22
3 3 31 1 1 2 2 2
5 5 5 5
1 2 3
f Lf L f LfL
= + +
12.1d 12.1d 12.1d 12.1d
QQ QQ
As it is equivalent pipe and if f = f1 = f2 = f3 then we
have
2 2
31 2
5 5 5 5
1 2 3
LL Lf f
= + +
12.1 d 12.1 d d d
Q L Q    
        
31 2
5 5 5 5
1 2 3
LL L
= + +
d d d d
L   
     
This equation is known as Dupit’s equation.

8. Pipes in Parallel (Looping Pipes):-
When two or more pipes are connected in such a way that they
branch out from the same point and afterwards join on the
downstream side at the same point to form a single pipe they are
said to be in parallel as shown in fig.
For pipes in parallel
1. The discharge Q is shared by the pipes
Therefore, Q = Q1 + Q2 + Q3 + ………………………
2. The loss of head across each pipe in parallel is same (i.e. from fig. loss of head between points
A and B is same for each pipe)
Therefore, hf1 = hf2 = hf3 = ……………….

9. Equivalent Pipe for Pipes in Parallel:-
From Fig. L1, D1, f1 are the length, diameter and friction
factor for pipe 1, Similarly for pipe 2 and 3.
Definition:-These pipe can be replaced by a single uniform
pipe which will carry the same total discharge as passing
through the system (i.e. Q = Q1 + Q2 + Q3 + ..) for the same
loss of head as for the system (i.e. hf1 = hf2 = hf3 = …)
across it. Such a pipe is called as equivalent pipe for a
system of parallel pipe

10. We have, 2
5
1/25
fL
12.1D
12.1D
f x
f
f
Q
h
h
Q
L
=
 
 =   
 
As, Q = Q1 + Q2 + Q3
31
1/21/21/2 1/2 555 5
31 2 2
1 1 2 2 3 3
12.1D12.1D12.1D 12.1D
f x f x f x f x
fff f hhh h
L L L L
     
 = + +            
      
Since, hf = hf1 = hf2 = hf3….
1/21/2 1/21/2 55 55
31 2
1 1 2 2 3 3f x f x f x f x
DD DD
L L L L
     
 = + +      
       

11. Numericals:- 1.

12. 2.

13. 3.

15. THANK YOU…