Page 186 - Water Engineering Hydraulics, Distribution and Treatment

164
Chapter 5
Water Hydraulics, Transmission, and Appurtenances
Thus
2. Pressure relief valves or overflow towers on one or
more summits to keep the pressure in the line below a
given value by letting water discharge to waste when
C = actual mean velocity/ideal mean velocity
v
the pressure builds up beyond the design value
0.5
(5.47a)
C = v∕v = v∕ (2gh)
3. Self-acting shutoff valves triggered to close when
i
v
the pipe velocity exceeds a predetermined value as
0.5
v = C (2gh)
a result of an accident
v
4. Altitude-control valves that shut off the inlet to ser-
where
vice reservoirs, elevated tanks, and standpipes before
C = coefficient of velocity, dimensionless
v
overflow levels are reached
v = actual mean velocity, ft/s (m/s)
5. Venturi or other meters and recorders to measure the
v = ideal or theoretical velocity, ft/s (m/s) (5.47b)
i
flows
The coefficient of contraction C is the ratio of the area
c
5.10 ADDITIONAL HYDRAULICS TOPICS of the contracted section of a fluid stream (jet) to the area of
the opening through which the fluid flows.
The following additional hydraulic topics are important to
those who plan to take professional engineering (PE) exam-
C = area of stream (jet)/area of opening
inations in North America. Several of the included solved c
examples and homework problems were given previously in C = A ∕A = C ∕C v (5.48a)
d
jet
c
o
PE examinations.
C = C C (5.48b)
d v c
5.10.1 Measurement of Fluid Flow and
Hydraulic Coefficients where
C = coefficient of contraction, dimensionless
c
2
2
Various coefficients of hydraulics have been developed and A jet = area of jet stream, ft (m )
used in civil and environmental engineering practice mainly A = area of opening, ft (m )
2
2
o
for measuring fluids flow. The common fluid measurement
devices include pitot tubes, nozzles, orifices, venturi meters, The area of jet, A , is measured at the “vena contracta”
jet
and flumes. Application of Bernoulli equation and hydraulic 1
(v.c.), which is located at ∕ orifice diameter downstream
2
coefficients is important for calibration of fluid measurement
from the orifice. Hence, C and C can be redefined according
v
c
devices.
to v.c.:
The coefficient of discharge, C , is the ratio of actual
d
discharge through a hydraulic device to the ideal discharge.
C = area at v.c./area of orifice (5.48c)
c
This coefficient is expressed as
C = actual velocity at v.c./theoretical velocity at v.c.
v
C = actual flow/ideal flow
d
(5.47c)
C = Q∕A (2gh) 0.5 (5.44) 0.5
d
v = (2gh) (5.47d)
i
Q = C A (2gh) 0.5 = Av (5.45)
d
The head loss, h , in hydraulic measuring devices can be
f
v = C (2gh) 0.5 (5.46) expressed as
d
where 2 2
C = coefficient of discharge, dimensionless h = {[(1∕(C ) ]− 1}(v ) ∕2g (5.49)
jet
v
f
d
3
3
Q = actual flow, ft /s (m /s)
A = cross-sectional area of flow through the hydraulic Where
2
2
device, ft (m ) v jet = jet stream velocity, ft/s or m/s
2
2
g = 32.2 ft/s (9.81 m/s )
h = total head, ft (m) The coordinates (x, y) of a hydraulic jet can be deter-
v = ideal velocity, ft/s (m/s) mined according to the following two kinematic equations:
The coefficient of velocity C is the ratio of the actual x = vt (5.50)
v
mean velocity in the cross-section of the flow stream (jet) to 1 2
the ideal mean velocity, which would occur without friction. y = ∕ gt (5.51)
2