CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 315

A 1 area before size change in pipe, ft^2 (m^2 )

A 2 area after size change in pipe, ft^2 (m^2 )

F 2 mforce due to momentum of water in section 2V 2 Qw/g

F 1 mforce due to momentum of water in section 1V 1 Qw/g

P 2 pressure of water in section 2 times area of section 2 p 2 A 2

P 1 pressure of water in section 1 times area of section 1 p 1 A 1

wunit weight of liquid, lb/ft^3 (kg/m^3 )

Qdischarge, ft^3 /s (m^3 /s)

If the pressure loss in the bend is neglected and there is no change in magnitude
of velocity around the bend, a quick solution is

(12.68)

whereRresultant force on bend, lb (N)
angleRmakes with F 1 m
ppressure, lb/ft^2 (kPa)
wunit weight of water, 62.4 lb/ft^3 (998.4 kg/m^3 )
Vvelocity of flow, ft/s (m/s)
gacceleration due to gravity, 32.2 ft/s^2 (9.81 m/s^2 )
Aarea of pipe, ft^2 (m^2 )
angle between pipes (0° 180°)

CULVERTS

A culvert is a closed conduit for the passage of surface drainage under a high-
way, a railroad, a canal, or other embankment. The slope of a culvert and its
inlet and outlet conditions are usually determined by the topography of the site.
Because of the many combinations obtained by varying the entrance condi-
tions, exit conditions, and slope, no single formula can be given that applies to
all culvert problems.
The basic method for determining discharge through a culvert requires
application of the Bernoulli equation between a point just outside the entrance
and a point somewhere downstream.

Entrance and Exit Submerged

When both the exit and entrance are submerged (Fig. 12.13), the culvert flows full,
and the discharge is independent of the slope. This is normal pipe flow and is easily
solved by using the Manning or Darcy–Weisbach formula for friction loss.



2

R 2 Aw

V^2

g

p cos

2