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172 Chapter 5 Water Hydraulics, Transmission, and Appurtenances
Table 5.2 Values of k for Form Losses

Fitting k-value Fitting k-value
Pipe Entrance 90 Smooth Bend
Bellmouth 0.03–0.05 Bend radius D 4 0.16–0.18
Rounded 0.12–0.25 Bend radius D 2 0.19–0.25
Sharp Edged 0.50 Bend radius D 1 0.35–0.40
Projecting 0.80
Mitered Bend
Contraction–Suden 15 0.05
D 2 D 1 0.80 0.18 30 0.10
D 2 D 1 0.50 0.37 45 0.20
D 2 D 1 0.20 0.49 60 0.35
90 0.80
Contraction–Conical
D 2 D 1 0.80 0.05 Tee
D 2 D 1 0.50 0.07 Line Flow 0.30–0.40
D 2 D 1 0.20 0.08 Branch Flow 0.75–1.80

Expansion–Suden Cross
D 2 D 1 0.80 0.16 Line Flow 0.50
D 2 D 1 0.50 0.57 Branch Flow 0.75
D 2 D 1 0.20 0.92
45 Wye
Expansion–Conical Line Flow 0.30
D 2 D 1 0.80 0.03 Branch Flow 0.50
D 2 D 1 0.50 0.08
D 2 D 1 0.20 0.13

Source: Courtesy of Haestad Methods Water Solutions, Bentley Institute Press.

2
L h >s Kv >2gs KD>f (see Appendix 17). The outstanding exception is the loss on
f
e
2
sudden expansion or enlargement (v v ) >2g, where v is the velocity in the original
1
1
2
conduit and v the velocity in the expanded conduit; even it, however, is sometimes con-
2
2
2
verted, for convenience, into kv >2g. Because continuity as a v a v equates k v >2g
1 1
1 1
2 2
2
2
with (v >2g) (1 a >a ) , the loss at the point of discharge of a pipeline into a reservoir
1
2
1
2
(making a very large in comparison with a ) equals approximately v >2g; consequently,
1
1
2
there is no recovery of energy. In all but special cases like this, k must be determined exper-
imentally. When there is no experimental information, the values of k in Table 5.2 give use-
ful first approximations on likely losses.
5.2.4 Hydraulic Transients
Transmission lines are subjected to transient pressures when valves are opened or closed or
when pumps are started or stopped. Water hammer and surge are among such transient
phenomena.
Water hammer is the pressure rise accompanying a sudden change in velocity. When
velocity is decreased in this way, energy of motion must be stored by elastic deformation
of the system. The sequence of phenomena that follows sudden closure of a gate, for exam-
ple, is quite like what would ensue if a long, rigid spring, traveling at uniform speed, were
suddenly stopped and held stationary at its forward end. A pressure wave would travel
back along the spring as it compressed against the point of stoppage. Kinetic energy would