CIVIL ENGINEERING FORMULAS

306 CHAPTER TWELVE

All three expressions are approximately of the form

(12.40)

whereKconstant dependent on pipe roughness.
If these expressions are equated and simplified, the following relationship
betweenf,n, and Cis obtained:

(SI units) (12.41)

(U.S. customary units) (12.42)

When one of the coefficients is known, the other two can be calculated. The
resulting values will lead to identical slopes of the energy grade line, as calcu-
lated with these formulas.

PRESSURE (HEAD) CHANGES CAUSED
BY PIPE SIZE CHANGE

Energy losses occur in pipe contractions, bends, enlargements, and valves and
other pipe fittings. These losses can usually be neglected if the length of the
pipeline is greater than 1500 times the pipe diameter. However, in short pipe-
lines, because these losses may exceed the friction losses, minor losses must be
considered.

Sudden Enlargements

The following equation for the head loss, ft (m), across a sudden enlargement
of pipe diameter has been determined analytically and agrees well with experi-
mental results:

(12.43)

whereV 1 velocity before enlargement, ft/s (m/s)
V 2 velocity after enlargement, ft/s (m/s)
g32.2 ft/s^2 (9.81 m/s^2 )

It was derived by applying the Bernoulli equation and the momentum equation
across an enlargement.
Another equation for the head loss caused by sudden enlargements was
determined experimentally by Archer. This equation gives slightly better agree-
ment with experimental results than the preceding formula:

hL (12.44)

1.1(V 1 V 2 )1.92

2 g

hL

(V 1 V 2 )^2

2 g

0.0252f

4.66n^2

D^1 ^3



4.73D0.13

C1.85Q0.15

0.0827f

10.3n^2

D^1 ^3



10.7D0.13

C1.85D0.15

S

KQ^2

D^5