Page 381 - Civil Engineering Formulas

310 CHAPTER TWELVE

Values of C for submerged orifices do not differ greatly from those for nonsub-
merged orifices.

Discharge under Falling Head
The flow from a reservoir or vessel when the inflow is less than the outflow
represents a condition of falling head. The time required for a certain quantity
of water to flow from a reservoir can be calculated by equating the volume of
water that flows through the orifice or pipe in time dt to the volume decrease in
the reservoir. If the area of the reservoir is constant,

2A h 1 h 2
t (12.55)
Ca 2g
where h head at the start, ft (m)
1
h head at the end, ft (m)
2
t time interval for head to fall from h to h , s
2
1
FLUID JETS

Where the effect of air resistance is small, a fluid discharged through an orifice
into the air follows the path of a projectile. The initial velocity of the jet is

V 0 C v 2gh (12.56)

where h head on center line of orifice, ft (m); and C coefficient of velocity.
v
The direction of the initial velocity depends on the orientation of the surface
in which the orifice is located. For simplicity, the following equations were
determined assuming the orifice is located in a vertical surface (see Fig. 12.8).
The velocity of the jet in the X direction (horizontal) remains constant:

V x V 0 C v 2gh (12.57)

The velocity in the Y direction is initially zero and thereafter a function of time
and the acceleration of gravity:
V y gt (12.58)

The X coordinate at time t is

X V x t tC v 2gh (12.59)