CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 311

TheYcoordinate is

(12.60)

whereVavgaverage velocity over period of time t. The equation for the path
of the jet:

(12.61)

ORIFICE DISCHARGE INTO DIVERGING
CONICAL TUBES

This type of tube can greatly increase the flow through an orifice by reducing the
pressure at the orifice below atmospheric. The formula that follows for the pressure
at the entrance to the tube is obtained by writing the Bernoulli equation for
points 1and 3 and points 1 and 2 in Fig. 12.10:

(12.62)

wherep 2 gage pressure at tube entrance, lb/ft^2 (Pa)
wunit weight of water, lb/ft^3 (kg/m^3 )
hhead on centerline of orifice, ft (m)
a 2 area of smallest part of jet (vena contracta, if one exists), ft^2 (m)
a 3 area of discharge end of tube, ft^2 (m^2 )

Discharge is also calculated by writing the Bernoulli equation for points 1 and 3
in Fig. 12.10.
For this analysis to be valid, the tube must flow full, and the pressure in the
throat of the tube must not fall to the vapor pressure of water. Experiments by
Venturi show the most efficient angle to be around 5°.

p 2 wh 1 

a 3

a 2 

2



X^2 C^2 v 4 hY

YVavgt

gt^2

2

1

h

2

θ

3

FIGURE 12.10 Diverging conical tube increases flow from a reser-

voir through an orifice by reducing the pressure below atmospheric.