2.3 Water in Motion: Hydrodynamics
31
VI
-'2g
energy grade line
datum
Fig. 2.8: Energy balance for water flow from tank
cross-section is Al and A2 is the nozzle area. Then, by the mass conservation
principle we have:
(2.26)
The application of the Bernoulli equation is facilitated by the fact that it does
not require a control-volume analysis, only a selection of two points, 1 and 2,
along a given streamline. The Bernoulli equation written for these two points
yields:
VI 2
PI
vl P2
- + - + ZI = - + - + Z2 = H = Const.
2g
Pwg
2g
Pwg
(2.27)
As the points 1 and 2 are exposed to atmospheric pressure, PI = P2 = Pa and
the pressure terms cancel on both sides of Eq. (2.27), which now becomes:
(2.28)
and using Eq. (2.26) gives:
2
2gh
V2 = -~( A-)"'"2 .
1- ~
(2.29)
Usually, the nozzle area A2 is much smaller than tank area, AI, so (A2/ AI)2 --+ 0
and finally, the outlet velocity is:
(2.30)