CIVIL ENGINEERING FORMULAS

304 CHAPTER TWELVE

For pipes flowing full:

(12.29)

(12.30)

(12.31)

(12.32)

where Vvelocity, ft /s (m /s)
C 1 coefficient, dependent on surface roughness (given in engineering
handbooks)
Rhydraulic radius, ft (m)
Shead loss due to friction, ft/ft (m/m) of pipe
Ddiameter of pipe, ft (m)
Llength of pipe, ft (m)
Qdischarge, ft^3 /s (m^3 /s)
hffriction loss, ft (m)

Figure 12.7 shows a typical three-reservoir problem. The elevations of the
hydraulic grade lines for the three pipes are equal at point D. The Hazen–Williams
equation for friction loss can be written for each pipe meeting at D. With the conti-
nuity equation for quantity of flow, there are as many equations as there are
unknowns:

ZbZd

PD

w



4.727LB

D4.87B 

QB

CB

1.85

ZaZd

PD

w



4.727LA

D4.87A 

QA

CA

1.85

D

1.376

S0.205 

Q

C 1 

0.38

hf

4.727

D4.87

L

Q

C 1 

1.85

Q0.432C 1 D2.63S0.54

V0.55C 1 D0.63S0.54

Za

Zc

Datum

Zd

Zb

A

C

PD

W

B

D

FIGURE 12.7 Flow between reservoirs.