6.5. OTHER PIPE FORMULAS

Other formulas apart from Darcy Weisbach's have been used in computation of head loss in flowing fluids. These formulas, based from experiments, are intended for water only at a specific temperature range - less than about . 

With ordinary engineering hydraulic problems involving water as fluid, the choice of formula is a matter of personal preference which would be based on simplicity and convenience.

6.5.1. MANNING'S FORMULA

This formula is more used on open channels but still quite common in pipes.

                               

where:   V  = velocity of fluid flow
             n  = roughness coefficient
             R  = hydraulic radius
                    
                   S  = slope of the energy gradient
                   


Note: The roughness coefficient increases with the conduit's degree of roughness.

6.5.2. ROUGHNESS COEFFICIENT OF MANNING'S FORMULA

KIND OF PIPE	VARIATION		USE IN DESIGNING
	FROM	TO	FROM	TO
Brass and glass pipe	0.009	0.013	0.009	0.011
Asbestos-cement pipe	--	--	0.010	0.012
Wrought-iron and welded-steel pipe	0.010	0.014	0.011	0.013
Wood-stave pipe	0.010	0.014	0.011	0.013
Clean cast-iron pipe	0.010	0.015	0.011	0.013
Concrete pipe	0.010	0.017	--	--
very smooth	--	--	0.011	0.012
"wet mix," steel forms	--	--	0.012	0.014
"dry mix'" rough forms	--	--	0.015	0.016
with rough joints	--	--	0.016	0.017
Common-clay drainage tile	0.011	0.017	0.012	0.014
Vitrified sewer pipe	0.010	0.017	0.013	0.015
Riveted-steel pipe	0.013	0.017	0.015	0.017
Dirty or tuberculated cast-iron pipe	0.015	0.035	--	--
Corrugated-iron pipe	--	--	0.020	0.022

6.5.3. THE HAZEN-WILLIAMS FORMULA

This formula is the one adopted in United States for the design of water supply systems. Although it can also be used for pipes and open channels, this formula is more commonly adopted for pipes.

                           

where:   V  = velocity of fluid flow
             C1  = roughness coefficient
             R  = hydraulic radius
                    
                   S  = slope of the energy gradient
                   

6.5.4. VALUES FOR 

DESCRIPTION OF PIPE	C1
Extremely smooth and straight	140
Very smooth	130
Smooth wooden or wood stave	120
New riveted steel	110
Vitrified	110

After a series of years in use of the pipe, the controlling factor somehow varies:

PIPES AFTER YEARS OF USE	C1
Cast-iron pipe	100
Riveted Steel	95
Old iron pipes in bad condition	80 to 60
Small pipes badly tuberculated	40
Asbestos-cement pipe	140

6.5.5. PIPE DIAGRAMS

Pipe diagrams are also used to solve problems on flow. For both the diagrams below, the procedure is to plot the given values and check on the intersection to find another parameter. Additionally, both graphs below are just representations of a specific value of the roughness coefficient. For example, the manning diagram is only for n=0.013. There are also different diagrams for different roughness coefficients. Similarly, Hazen-William's nomograph is for C1=130 only. Another set of nomograph is used for another C1.

A. THE MANNING DIAGRAM

B. HAZEN-WILLIAM'S NOMOGRAPH