S =surface depression
d
Reliability Theories
Analytical models formulated
with derived probability
distribution theory, for screening
level analysis
Reliability
of
detention
systems
The probability density functions of rainfall characteristics are
exponential:
f =ζe
−ζh
h
f =λe
−λt
t
f =ψe −ψb
b
h=rainfall depth
t=rainfall duration
b=interstorm interval
Are independent random variables
The distribution parameters are:
ζ=inverse of expected value of rainfall depth,
λ=inverse of expected value of rainfall duration,
ψ=inverse of expected value of rainfall inter-storm interval.
Detention: f=0
Assuming as certain that the network
can transfer water from the impervious
sub-catchment to the tank, and that
the overflow divider performs correctly,
only the detention system is subject to
failure.
Initial condition
In applying the analytical probabilistic approach to assess the
efficiency of a stormwater detention system, it is important to
obtain the storage facility’s initial condition, e.g., the
available stormwater storage capacity of the facility.
Depending on the conditions preceding a random rainfall
event, the storage facility may be completely or partly
empty when the rainfall event starts.
Simplifying assumptions previously adopted in
literature
1. The storage facility is completely full at the end of
the rainfall event preceding the random rainfall
event under analysis. [ Howard’s conservative
assumption (Howard 1976)] .
2. The storage facility is completely empty when the
analyzed random rainfall event starts
Simplifying assumptions previously adopted in
literature
1. The storage facility is completely full at the end of
the rainfall event preceding the random rainfall
event under analysis. [ Howard’s conservative
assumption (Howard 1976)] .
2. The storage facility is completely empty when the
analyzed random rainfall event starts
Sd=storage depression =0
VASCHE DI LAMINAZIONE
Risk of overflow R is estimated, as the probability that either the
f
rainfall volume is imp h >V or that two consecutive rainfall events
s
occur in a short period of time. At the beginning of the second rainfall
event, tank storage capacity is impQ b=V’ <V and rainfall volume is
0 s s
imp h> V’s
Under the most conservative assumption that the reservoir is full at
the end of the first of two consecutive rainfall events,
Rf =P[b≥Vs/Q imp]·P[h>Vs/imp]+P[b<Vs/Q imp]·P[h>Q b]
0 0 0
Rf =P[b≥Vs/Q imp]·P[h>Vs/imp]+P[b<Vs/Q imp]·P[h>Q b]
0 0 0
h
p ( h ) e
h
b
p (
b ) e
b V s
Q imp
0
b h b h
R e e dh db e e dh db
f V V 0 bQ
s s 0
Q imp imp
0
V
s
Q
imp Q
0
R e 0
f
Q Q
0 0
SE I VOLUMI ACCUMULATI NELLA VASCA DI
LAMINAZIONE VENGONO RIUTILIZZATI PER GLI USI
CONSENTITI, E’ NECESSARIO VALUTARE IL RISCHIO
CHE I VOLUMI RISULTINO INSUFFICIENTI ALLA
LAMINAZIONE E/O AL RIUTILIZZO
Ursino, 2015 Dimensionless
parameters
Rainfall model
ζ = inverse of expected value of rainfall depth and
λ = inverse of expected inter-storm interval
Dimensionless
parameters
The storage facility is completely full at the end of the rainfall event
preceding the random rainfall event under analysis. [ Howard’s conservative
assumption Risk of overflow Dimensionless
parameters
The storage facility is empty at the end of the dry period preceding the
random rainfall event under analysis. [ Howard’s conservative assumption
Risk of water scarcity Dimensionless
parameters
Il volume della
vasca V , influenza
s
influenza piuttosto il
peso relativo dei
due addendi che
compaiono nelle
espressioni di
rischio
RISK ANALYSIS OF
RAINWATER HARVESTING
SYSTEMS AROUND THE
WORLD
Simplifying assumptions previously adopted in
literature
1. The storage facility is completely full at the end of
the rainfall event preceding the random rainfall
event under analysis. [ Howard’s conservative
assumption (Howard 1976)] .
2. The storage facility is completely empty when the
analyzed random rainfall event starts
ESEMPI DI SISTEMI DI RIUTILIZZO
Efficiency is an increasingly good estimate of the system reliability as the number of
years of observation increases.
Jordan averaged monthly Domestic use Abdulla
precipitation data et al., 2009
Brazilia(Brazil) Dayly rainfall -30 washing vehicles Sanches
years Fernandes et al.,
2015
South Africa data forecasted houshold water Mwenge Kahinda
by 6 global requirements et al., 2010
circulation models
Iran Dayly rainfall -50 Reuse systems for Mehrabadi
years residential et al, 2013
buildings
Italy Dayly rainfall -30 Reuse systems for Palla et al., 2011
to 100 years residential
buildings
Australia Monthly average Reuse systems for Zhang et al., 2009
rainfall -80 years residential
buildings
Design is usually
performed with
reference to tank
efficiency
In high demanding
scenarios there will
be a marked
dependence of the
RWH system
efficiency on the
water demand
(Fernandes et al.,
2015).
non-dimensional
analysis
demand ratio: ratio
between annual
demand and annually
collected rainwater
storage fraction: ratio
between storage
capacity of the
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-
Tecnologie industriali, parte 7 - Laminazione
-
Lavorazioni per Deformazione Plastica e Laminazione
-
Risoluzione Esercizi - Laminazione e Calibratura - Deformazione Plastica
-
Tesina su Sistema di sollevamento con attuatore SMA
- Risolvere un problema di matematica
- Riassumere un testo
- Tradurre una frase
- E molto altro ancora...
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