We read a lot of news about 'x' MAF of storage, or 'y' lakhs (hundred thousands) of cusecs of water, but do we know that how these two are related to each other?
Relation between these two can be explained in a single following line
This relation can be defined by a simple equation as following.
flow = volume change / time
(Note: in engineering, symbol used for flowrate is Q, intutively it is a bit mis-guiding for non engineers, but F is reserved for force)
defining this relationship in SI units is much easier.
Example
we want to empty a lake of size 1 BCM ( billion cubic meter or a cubic kilometer).
lake has five drain tunnels, 1 cumec, 10 cumecs, 100 cumecs, 1000 cumecs and 10000 cumecs.
calculate the time for emptying the lake using each tunnel individually.
solution
we know that
flow = volume/time
or time = flow/volume
using this relationship, times taken for each tunnel to drain this lake are
1 cumec tunnel will take 1 billion seconds (more than 31 years) to drain this 1 BCM capacity lake
10 cumec tunnel will take 100 million seconds (about 3 years and 2 months) to drain this 1 BCM capacity lake
100 cumec tunnel will take 10 million seconds (about 17 weeks) to drain this 1 BCM capacity lake
1000 cumec tunnel will take 1 million seconds (about 12 days) to drain this 1 BCM capacity lake
10000 cumec tunnel will take 100000 seconds (about 28 hours) to drain this 1 BCM capacity lake
so, its not difficult to calculate these, but ...........we don't use metric units in Pakistan.
We use cusecs and MAF instead, which adds an additional step in the relation.
concept is same, flow = volume/time, but we have to plug the value of acre foot (1 acre foot = 43560 cubic feet)
let us do some realistic math in next example.
Example
Tarbela's reservoir has a live storage capacity of 6.8 MAF.
with net impounded inflow of 200000 cusecs, how many days will it take to fill the lake?
Solution
don't worry about the complex terms involved, concept is as simple as tub and tap.
we simply have to plug in the value of 1 acre foot = 43560 cubic feet
let's do it.
we know that flow = volume/time
hence time = volume/flow
or time = (6800000 acre foot)/(200000 cusec)
time = (6800000 x 43560)/(200000 cusec)
time = 1481040 seconds
or 17.14 days
a useful conversion thumb rule
volume = flow x time
volume (acre feet in one second) = (cusecs /43560)
Volume (MAF in a day) = (cusecs x 86400) / (43560 x 1000000)
another example
Calculate volume of water involved in a flow of 500000 cusecs for one day
Volume (MAF in a day) = (cusecs x 86400) / (43560 x 1000000)
= 500000 x 86400) / (43560 x 1000000)
= 0.99173 MAF
in short, 5 lakh cusecs flow for a day involves about one MAF water
Relation between these two can be explained in a single following line
"One MAF water is equal to 5 lakh cusecs flow for 24 hours"
We saw in flow example, flow rate depends upon volume change over a given time period.This relation can be defined by a simple equation as following.
flow = volume change / time
(Note: in engineering, symbol used for flowrate is Q, intutively it is a bit mis-guiding for non engineers, but F is reserved for force)
defining this relationship in SI units is much easier.
Example
we want to empty a lake of size 1 BCM ( billion cubic meter or a cubic kilometer).
lake has five drain tunnels, 1 cumec, 10 cumecs, 100 cumecs, 1000 cumecs and 10000 cumecs.
calculate the time for emptying the lake using each tunnel individually.
solution
we know that
flow = volume/time
or time = flow/volume
using this relationship, times taken for each tunnel to drain this lake are
1 cumec tunnel will take 1 billion seconds (more than 31 years) to drain this 1 BCM capacity lake
10 cumec tunnel will take 100 million seconds (about 3 years and 2 months) to drain this 1 BCM capacity lake
100 cumec tunnel will take 10 million seconds (about 17 weeks) to drain this 1 BCM capacity lake
1000 cumec tunnel will take 1 million seconds (about 12 days) to drain this 1 BCM capacity lake
10000 cumec tunnel will take 100000 seconds (about 28 hours) to drain this 1 BCM capacity lake
so, its not difficult to calculate these, but ...........we don't use metric units in Pakistan.
We use cusecs and MAF instead, which adds an additional step in the relation.
concept is same, flow = volume/time, but we have to plug the value of acre foot (1 acre foot = 43560 cubic feet)
let us do some realistic math in next example.
Example
Tarbela's reservoir has a live storage capacity of 6.8 MAF.
with net impounded inflow of 200000 cusecs, how many days will it take to fill the lake?
Solution
don't worry about the complex terms involved, concept is as simple as tub and tap.
we simply have to plug in the value of 1 acre foot = 43560 cubic feet
let's do it.
we know that flow = volume/time
hence time = volume/flow
or time = (6800000 acre foot)/(200000 cusec)
time = (6800000 x 43560)/(200000 cusec)
time = 1481040 seconds
or 17.14 days
a useful conversion thumb rule
volume = flow x time
volume (acre feet in one second) = (cusecs /43560)
Volume (MAF in a day) = (cusecs x 86400) / (43560 x 1000000)
another example
Calculate volume of water involved in a flow of 500000 cusecs for one day
Volume (MAF in a day) = (cusecs x 86400) / (43560 x 1000000)
= 500000 x 86400) / (43560 x 1000000)
= 0.99173 MAF
in short, 5 lakh cusecs flow for a day involves about one MAF water
Good work Inam bahi.very well done.i hope your voice is heared on sawan water soloution
ReplyDelete