62
For the flow illustrated in Fig. 2.6 the conservation of energy equation take following form:
P
v
gz P
v
gz
1
1
2
1
2
2
2
2
1
2
1
2
+
+
= +
+
ρ
ρ
ρ
ρ
Where
a 1  = cross-section of area of tube at point 1
v 1  = velocity in the tube at point 1
z 1  = the elevation of the fluid above a fixed reference point at point 1
a 2  = cross-section of area of tube at point 2
v 2  = velocity in the tube at point 2
z 2  = the elevation of the fluid above a fixed reference point at point 2
2.4.3.3 Flow in Channels
A flowing stream of liquid with free surface exposed to the open air is called a liquid
channel.
Artificial channels and rivers convey water with a free surface exposed to air.
Fig. 2.7 Flow in partially
filled conduit
a 1
z 1
1
p 1
a 2
z 1
2
p 2
Point 1
Point 2
Fig. 2.6 Line diagram of
flow with varying
cross-section
2 Fundamentals of Physics for Environmental and Medical Professionals