Parallel Piping System - University of Memphis

[Pages:26]Civil Engineering Hydraulics

Pipes in Parallel

Calvin: You know, Hobbes, some days even your lucky rocket ship underpants don't help.

Parallel Pipes

? There are often cases where we find pipes laid in parallel that begin at the same junction and terminate at the same junction

? One of the most common cases is to replace a segment of pipe with two smaller pipes

? This may be a stopgap measure that just seems to remain in place

2

Pipes in Parallel

Monday, October 22, 2012

1

Parallel Pipes

? If you have had circuits in physics or an electrical engineering class, you may recognize some of the same methods for solution that are used for solving parallel resistances

3

Pipes in Parallel

Monday, October 22, 2012

Parallel Pipes

? The fundamentals are also used in solving for water distribution systems through closed loop piping networks

4

Pipes in Parallel

Monday, October 22, 2012

2

Parallel Pipes

? We will start with the simplest form of a parallel network containing two pipes

5

Pipes in Parallel

Monday, October 22, 2012

Parallel Pipes

? The volumetric flow rate approaching point A is known and due to conservation of mass that is the same as the flow exiting at point B

6

Pipes in Parallel

Monday, October 22, 2012

3

Parallel Pipes

? We usually know the length and cross section area of both of the pipes from A to B and we want to know how much flow is going through each pipe.

7

Pipes in Parallel

Monday, October 22, 2012

Parallel Pipes

? Now the view we have of this system is shown from above so all the pipes shown are on the same elevation

8

Pipes in Parallel

Monday, October 22, 2012

4

Parallel Pipes

? If we neglect minor losses, all the pressure drops along the two pipes from A to B are due to friction losses

9

Pipes in Parallel

Monday, October 22, 2012

Parallel Pipes

? The pressure at A is the same for both pipes and the pressure at B is also the same for both pipes

10

Pipes in Parallel

Monday, October 22, 2012

5

Parallel Pipes

? This means that the pressure drop along both pipes must be the same

p3 = p2

11

Pipes in Parallel

Monday, October 22, 2012

Parallel Pipes

? Since both of these pressure drops are due to friction we can replace both of them by the pressure loss due to friction loss terms

p3 = p2 f3L3 v32 = f2L2 v22 D3 2g D2 2g

12

Pipes in Parallel

Monday, October 22, 2012

6

Parallel Pipes

? The diameter and length of each of the pipes is known but we have unknown friction factors and velocities on each side of the expression

p3 = p2 f3L3 v32 = f2L2 v22 D3 2g D2 2g

13

Pipes in Parallel

Monday, October 22, 2012

Parallel Pipes

? Since the friction factor is dependent on the Reynolds number and the Re is a function of the velocity, we have an expression that cannot be solved directly

p3 = p2 f3L3 v32 = f2L2 v22 D3 2g D2 2g

14

Pipes in Parallel

Monday, October 22, 2012

7

Parallel Pipes

? Most of the solution methods assume a flow in one of the pipes (which sets the flow in the other) and then iterates the solution until the difference in pressure drops is within tolerance.

p3 = p2

f3L3 v32 = f2L2 v22 D3 2g D2 2g

15

Pipes in Parallel

Monday, October 22, 2012

Parallel Pipes

f3L3

v32

= f2L2

v

2 2

d3 2g d2 2g

Q32

Q22

f3L3 A32 = f2L2 A22 d3 2g d2 2g

Q32

Q22

f3L3

d32 4

2

=

f2L2

d 4

2 2

2

d3 2g

d2 2g

16

Pipes in Parallel

? One method that is used it to manipulate the expression so that we get an equivalent to an electrical circuit

Monday, October 22, 2012

8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download