CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 307

A special application of these two preceding formulas is the discharge from a
pipe into a reservoir. The water in the reservoir has no velocity, so a full velocity
head is lost.

Gradual Enlargements

The equation for the head loss due to a gradual conical enlargement of a pipe
takes the following form:

(12.45)

whereKloss coefficient, as given in engineering handbooks.

Sudden Contraction

The following equation for the head loss across a sudden contraction of a pipe
was determined by the same type of analytic studies as

(12.46)

whereCccoefficient of contraction; and Vvelocity in smaller diameter
pipe, ft/s (m/s). This equation gives best results when the head loss is greater
than 1 ft (0.3 m).
Another formula for determining the loss of head caused by a sudden con-
traction, determined experimentally by Brightmore, is

(12.47)

This equation gives best results if the head loss is less than 1 ft (0.3 m).
A special case of sudden contraction is the entrance loss for pipes. Some
typical values of the loss coefficient KinhLKV^2 /2g, where Vis the velocity
in the pipe, are presented in engineering handbooks.

Bends and Standard Fitting Losses

The head loss that occurs in pipe fittings, such as valves and elbows, and at
bends is given by

(12.48)

To obtain losses in bends other than 90°, the following formula may be used
to adjust the Kvalues:

(12.49)

wheredeflection angle, degrees. Kvalues are given in engineering handbooks.

KK

B

90

hL

KV^2

2 g

hL

0.7(V 1 V 2 )^2

2 g

hL

1

Cc

 (^1) 
(^2) V 2
2 g
hL

K(V 1 V 2 )^2

2 g