PLAIN AND CIVIL: 6.0. PIPES

Energy losses from various sources reduce flow discharge when a fluid moves through a pipeline. A boundary layer is formed on the pipe walls which causes continuous resistance. Velocity decreases from the center of the pipe to zero (at the boundary)in the boundary layer.

The total head loss along a specified length of pipeline is commonly referred to as the "head loss due to friction", which is denoted by $h_{f}$ . The rate of energy loss or energy gradient $S_{f}=\frac{h_{f}}{L}$ .

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Applying Bernoulli's equation to two sections on a pipe,

$\frac{V_{1}^{2}}{2g }+\frac{P_{1}}{\gamma }+z_{1}-h_{f}=\frac{V_{2}^{2}}{2g }+\frac{P_{2}}{\gamma }+z_{2}$

head loss is categorized into two.

Major head loss (due to friction)
Minor head loss (local losses)

6.1. HEAD LOSS DUE TO FRICTION

Head loss due to friction is considered a major head loss which is continuous. It is assumed to occur at a uniform rate along the pipe when the size and quality are constant.

There are different formulas used to determine the frictional loss.

6.1.1. DARCY WEISBACH FORMULA

A commonly used formula for pipes, Dary Weisbach's formula expresses the head in terms of velocity head.

   $h_{f}=f\frac{L}{D}\frac{V^{2}}{2g}$

where: f= friction factor
L= length of pipe
D= diameter of pipe
V= velocity of fluid flow
   $h_{f}$ = head loss due to friction

If discharge is considered instead of velocity head.

$V=\frac{Q}{A}$

So

   $h_{f}=f\frac{L}{D}\frac{\left ( \frac{Q}{A} \right )^{2}}{2g}$

$h_{f}=0.0826\frac{fLQ^{2}}{D^{5}}$ [SI units]

6.1.2. F VALUES FOR WATER

The friction factor, f, is a dimensionless coefficient which depends on the velocity of flow, diameter of pips, and density and viscosity of fluid. Fanning's equation identified that friction factor is a function of the Reynold's number and the relative roughness of the pipe material. With the variation of friction factor characteristics with laminar and turbulent flows, the Hagen-Poiseuille equation is used to determine the Fanning equation:

$f=\frac{16}{R_{e}}$ [for laminar flow: Re<2100]

$f=\frac{0.079}{R_{e}^{0.25}}$ [for turbulent flow: Re>2100]

The Fannings table below represents friction factor for laminar flow in new cast iron pipes, welded steel pipes, wood pipes made of planed staves, concrete pressure pipes, and cement-lined steel pipes.

Pipe dia		Mean	Velocity	(V)	in Feet	per	Second
(in)	0.50	1.00	2.00	3.00	4.00	5.00	10.00	15.00	20.00

0.5	0.042	0.038	0.034	0.032	0.030	0.029	0.025	0.024	0.023
0.75	0.041	0.037	0.033	0.031	0.029	0.028	0.025	0.024	0.023
1	0.040	0.035	0.032	0.030	0.028	0.027	0.024	0.023	0.023
1.5	0.038	0.034	0.031	0.029	0.028	0.027	0.024	0.023	0.023
2	0.036	0.033	0.030	0.028	0.027	0.026	0.024	0.023	0.022

3	0.035	0.032	0.029	0.027	0.026	0.025	0.023	0.022	0.022
4	0.034	0.031	0.028	0.026	0.026	0.025	0.023	0.022	0.021
5	0.033	0.030	0.027	0.026	0.025	0.024	0.022	0.022	0.021
6	0.032	0.029	0.026	0.025	0.024	0.024	0.022	0.021	0.021
8	0.030	0.028	0.025	0.024	0.023	0.023	0.021	0.021	0.020

10	0.028	0.026	0.024	0.023	0.022	0.022	0.021	0.020	0.020
12	0.027	0.025	0.023	0.022	0.022	0.021	0.020	0.020	0.019
14	0.026	0.024	0.022	0.022	0.021	0.021	0.020	0.019	0.019
16	0.024	0.023	0.022	0.021	0.020	0.020	0.019	0.019	0.018
18	0.024	0.022	0.021	0.020	0.020	0.020	0.019	0.018	0.018

20	0.023	0.022	0.020	0.020	0.019	0.019	0.018	0.018	0.018
24	0.021	0.020	0.019	0.019	0.018	0.018	0.018	0.017	0.017
30	0.019	0.019	0.018	0.018	0.017	0.017	0.017	0.016	0.016
36	0.018	0.017	0.017	0.016	0.016	0.016	0.016	0.015	0.015
42	0.016	0.016	0.016	0.015	0.015	0.015	0.015	0.015	0.014

48	0.015	0.015	0.015	0.015	0.014	0.014	0.014	0.014	0.014
54	0.014	0.014	0.014	0.014	0.014	0.014	0.013	0.013	0.013
60	0.014	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.012
72	0.013	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012
84	0.012	0.012	0.011	0.011	0.011	0.011	0.011	0.011	0.011