Environmental Engineering FOURTH EDITION

Water Supply 12 1

Table 6-2. Viscosity of Water as a Function of Temperature

Temperature Viscosity

"F "C lb-s/ft2 Centipoise

40 4.4 3.1 10-~ 1.5

50 10.0 2.7 x 10-~ 1.3

60 15.5 2.3 10-~ 1.1

68.4 20.0 2.1 10-~ 1 .o

70 21.0 2.0 10-~ 0.96

80 26.6 1.8 x 10-~ 0.86

90 32.2 1.6 x 10-~ 0.77

The kinematic viscosity u is the absolute viscosity divided by the fluid density, or

v = PIP.

The dimensions of kinematic viscosity are cm2/s.

viscosity of water are shown in Table 6-2.

Fluid viscosity is a function of temperature. Some representative values of the

Closed-Conduit Flow

One of the most fundamental principles of hydraulics states that in a system, the total
energy of a perfect liquid under ideal conditions does not change as it flows from point
to point. The total energy is the sum of the position energy, the pressure energy, and
the velocity energy. These are usually stated in terms of meters or feet of fluid, so that:

Z = static head = elevation (in m or ft),

P = pressure (in kg/m2 or lb/ft2),

w = specific weight of the fluid (in kg/m3),

v = velocity (in m/s or ft/s),

g = gravitational acceleration (in m/s2 or ft/s2),

Plw = pressure energy or pressure head, and

v2/2g = velocity energy or velocity head.

Consider a system like that shown in Fig. 6-10. Water is flowing through the pipe
from a reservoir with constant surface elevation. Assuming no losses in the system,
the total energy or total head of water remains constant, although energy or head may
be converted from one form to another within the system. At Point 1, at the surface
of the reservoir, all the energy is static head, while at Points 3,4, and 5, the energy is
distributed among static, pressure, and velocity head. At Point 6 the jet of water enters
the atmosphere and the energy of the jet is the sum of the velocity head and the static
head. The total energy, however, is constant at all points in the system.