Basics of
Reservoir
Operations
Computer Aided Negotiations
Fall 2008
Megan Wiley Rivera
0:10
1:45
Watershed water balance
2:40
Water Budgets—Conservation of
Mass
• Mass is not created or destroyed
• What goes in – what comes out = change
in what’s inside
3:30
Apply conservation of mass to an
atm interaction
•
•
•
•
Starting balance: $2000
Deposit a check for $50
Take out $30
Ending balance: $2020
$50
$30
ATM
$2000 in
account
What goes in – what comes out =
change in what’s inside (final balance –
initial balance)
$50 – $30 = $2020 - $2000
4:05
A dollar is easier to track than a
unit of water
• Water is “incompressible”
• a unit volume of water is not created or
destroyed
• Must define boundaries to apply equation
(control volume)
5:15
Time must be considered as well
• Often times, inflows and outflows are
measured as flow rates
• The change in storage must therefore also
be specified over some length of time
6:20
Try it for a Britta Filter
• How long can you leave your Britta pitcher
filling in the sink before it starts
overflowing?
6:50
Draw a Control Volume
7:00
Some Numbers
• Inflow, Qin = 2.5 gpm
• Outflow, Qout = 1 gpm
(note, this is a cheat. The
outflow flow rate increases
as the chamber fills)
• Chamber dimensions:
8” tall, 24 in2 cross
sectional area
• 1 cubic in = 0.00433
gals
8:40
The Equation
• What goes in – what
comes out = change
in what’s inside
• Qin – Qout = dV/dt
• Work with a partner to
figure it out
Feel free to ask someone else if you
get stuck (there are different approaches)
• Inflow, Qin = 2.5 gpm
• Outflow, Qout = 1 gpm
(note, this is a cheat. The
outflow flow rate increases
as the chamber fills)
• Chamber dimensions:
8” tall, 24 in2 cross
sectional area
• 1 cubic in = 0.00433
gals
Qin – Qout = dV/dt
12:30
The Answer
• Initial volume = 0
• Final volume = 24 in2 * 8” = 192 in3
• Convert to gallons:
192 in3 * (0.00433 gal/1 in3) = 0.83
gal
• Apply equation:
2.5 gpm – 1 gpm = 0.83 gal/x min
• Solve equation:
x min = 0.83 gal/(1.5 gpm) = 0.55
min or about 30 second
13:00
Now Let’s Apply It to a Reservoir
town
dam
lake
Draw Control Volume and Specify
Inflows and Outflows
14:50
Draw Control Volume and Specify
Inflows and Outflows
evaporation
precipitation
Effluent
(returns) Water supply diversions
(demands)
Dam release
Groundwater exchange
runoff
16:15
An Aside: Identifying Consumptive
Uses (water removed from the basin)
evaporation
evaporation
irrigation
Groundwater exchange
runoff
infiltration
An Aside: Identifying Consumptive
Uses (water removed from the basin)
evaporation
Effluent
(returns) Water supply diversions
(demands)
Other
consumptive
runoff uses (e.g.
manufacturing)
24:45
Back to Conservation of Mass
Net demands, D
Net Evapotransporation, ET
evaporation
precipitation
Effluent
(returns) Water supply diversions
(demands)
Dam release
Groundwater exchange
Qout
Unimpaired inflow, I
runoff
25:35
What Is Unimpaired Inflow?
26:25
Why Might We Want to Calculate It
• If you want to model different operational
scenarios, you need to know how much
water is reaching the river via runoff (as
opposed to upstream operations)
• Also gives information about flow in the
river without the presence of reservoirs
(possible point of comparison)
32:20
Use the equation to calculate
unimpaired inflows (daily average)
Net demands, D
Net Evapotransporation, ET
evaporation
precipitation
Effluent
(returns) Water supply diversions
(demands)
Dam release
Groundwater exchange
Qout
Unimpaired inflow, I
runoff
Use the equation to calculate
unimpaired inflows (daily average)
Measured/modeled/estimated from meteorological info
measured
Net Evapotransporation, ET
Net demands, D
Qout
measured
Unimpaired inflow, I
measured
Beginning
and end of
day stages
32:30
Storage-Area-Elevation Table
Surface area
elevation
Storage = volume of water
Mean sea level
Storage
(af)
Area
(acres)
Elevation
(ft)
0
5.8
32
1181
378
43
9930
1780
53
11957
2272
54
34055
4978
60
32:40
Use the equation to calculate
unimpaired inflows (daily average)
Net Evapotransporation, ET
Net demands, D
Qout
Unimpaired inflow, I
•
•
•
•
•
Beginning
and end of
day stages
What goes in – what comes out = change in what’s inside
Qin – Qout = dV/dt, or over the day:
Qin,daily ave – Qout, daily ave = Storageend of day – Storagebeginning of day
I – ET – Qout – D =Work
Storage
end ofpartner
day – Storage
beginning of day
with your
again
I = ET + Qout + D + Storageend of day – Storagebeginning of day
35:20
Use the equation to calculate
unimpaired inflows (daily average)
Net Evapotransporation, ET
Net demands, D
Qout
Unimpaired inflow, I
•
•
•
•
•
Beginning
and end of
day stages
What goes in – what comes out = change in what’s inside
Qin – Qout = dV/dt, or over the day:
Qin,daily ave – Qout, daily ave = Storageend of day – Storagebeginning of day
I – ET – Qout – D = Storageend of day – Storagebeginning of day
I = ET + Qout + D + Storageend of day – Storagebeginning of day
Fun with units
Net Evapotransporation, ET
Net demands, D
Qout
Unimpaired inflow, I
Beginning
and end of
day stages
• I = ET + Qout + D + Storageend of day – Storagebeginning of day
0.3”
50 mgd
100 cfs
Stage = 54’
Do calculations first in af/day and then mgd
Stage = 53’
39:30
Storage (af)
Area (acres)
Elevation (ft)
0
5.8
32
1181
378
43
9930
1780
53
11957
2272
54
34055
4978
60
Net Evapotransporation, ET
Net demands, D
Qout
Unimpaired inflow, I
Beginning
and end of
day stages
• I = ET + Qout + D + Storageend of day – Storagebeginning of day
0.3”
50 mgd
100 cfs
Stage = 54’
Do calculations first in af/day and then mgd
Stage = 53’
• I = ET + Qout + D + Storageend of day – Storagebeginning of day
0.3”
50 mgd
100 cfs
Stage = 54’
Stage = 53’
ET: Multiply by average surface area for the day (see SAE) = 2026 acres
0.3” * 2026 acres = 0.025’ * 2026 acres = 50.7 af in one day
Outflow: 100 cfs * 1.98 af/day / 1cfs = 198 af/day
Demands: 50 mgd * 1 af/day / 3.069 mgd = 16 af/day
I = 50.7 af/day + 198 af/day + 16 af/day + (11957 af – 9930 af)/day = 2292 af/day
This is 747 mgd