Lakes (1)

Lake is a natural or man made water body of significat size with relatively still water.
There are various natural types of lakes. We will discuss important types by example.
We start with mountain lakes.
Mountains and river valleys of Northern Pakistan have formed through a constant process of landslides.
Rain, glaciers and stream water erodes and dissolves the base of all vallies that seeds further landslides. This process is very slow but never stops.
After every landslide ,stream or river in that valley tries to burst that natural dam. outcome depends upon size of river and landslide.
If stream is too small as compared to landslide, valley becomes a longer term lake, with a thin and long spillway and some waterfalls. Lake Saiful Muluk is one such example.

Attabad lake is a recent example of such phenomenon.
Attabad's landslide blocked Hunza river in 2010. Although river has better flowrate at that location, but amount of landslide was too big. This natural Lake will stay for a long time.

Pakistan is land of geographical extremes, and holds the record of biggest flood of recorded history. in Jan 1841, A Spur of Nanaga Parbat collapsed and blocked Indus river for about six months. This made a thousand meters high natural dam, that ultimately bursted in June 1841. estimated flow rate  of the flood wave was 190 lakh cusecs, about 20 times more than 2010 floods.


Another example is the lake Pangogng Tso, inside Indian occupied Kashmir and Tibet. About a hundred thousand years ago, this lake was cut-off from Indus river due to a massive landslide. This lake was the shooting site of last scenes of Bollywood movie 3 Idiots.

 

Pakistan's total annual water

Pakistan gets about 142 MAF of river water every year. I'v seen people arguing this figure for political reasons, and they say that actual annual water is as low as 106 MAF. we will discuss the cause and effects of this debate later, but let us see, how much water is it.

In first picture below, 142 MAF cube is parked near Karachi's international airport.
Second picture is zoomed out to compare it with map of Pakistan.

same water is hardly visible on map of Pakisatn

 

MAF cusecs relation

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

"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

Units and Measurements 2(Flow)

You don't need to know calculus to understand water flow measurements. The math involved is easier for a high school student, as without noticing, we practice similar rate measurements in everyday life like speed or wages.

Water flow is commonly measured as amount of water flowing every second.
For example, if a tap connected with a 100 liters tank empties it in 100 seconds, tap's flow rate is 1 litre per second.
Similarly if a tap fills a 100 liters tub in 100 seconds, tap's flowrate is 1 litre per second.
for bigger flows like canal or river flow, cusecs and cumecs are used.

1 Cusec flow is 1 cubic meter per second.
1 Cumec flow is 1 cubic meter per second.
Cumec is comparatively  bigger unit. It is iequal to 35.3147 cusecs
Cusec is most commonly used flow rate unit in Pakistan.

many large irrigation canals and link canals in Pakistan have flow rates between 10 to 25 thousand cusecs.

Our rivers have obviously larger average flowrates during summer, ranging from 50 to 250 thousand cusecs

 2010 Indus flood was measured around 1250 thousand cusecs in Sindh.

 

Units and Measurements 1(Volume)

Here are some useful units used in Pakistan
Land measurements
Murabba Gaz (square yard) = 3 feet x 3 feet
1 Karm = 3.361 Murabba Gaz (square yards)
1 Marla = 9 Karm
1 Kanal = 20 Marlas
1 Killa = 1 Acre =8 Kanals (4,840 square yards or 43,560 square feet)

one acre was historically considered as the amount of land a yoke of oxen could plough in one day
another bigger unit is Murabba, a status symbol in Agriculture of Pakistan. its size varies, but usually it is considered equal to 25 Acres

Volume measurements
Most countries use cubic meter as the basic unit for water volume.

Acre foot
water measurements in Pakistan are mostly done in acre foot.
it is simply the amount of on foot deep water on an area of one acre.
1 acre foot = 1233.48184 cubic meters

million acre foot (MAF) is commonly used to measure large volumes of water.

similarly billion cubic meter (BCM) is used in countries following SI system.

1 million acre feet (MAF) = 1.23348184 Billion cubic meters (BCM)

Contours

Contours
Contours are used to show elevations in a flat map.

A contour line on map connects the path of fixed elevation points across a map. Contour interval is the difference of height between two adjacent contour lines. Different maps may have different contour intervals depending upon the scale or area type.

In a map, more distance between adjacent contours reflects flatter area, while crowded contours tell about steepness of a feature.
every fifth contour line is kept thicker for ease of counting.
try to find contour lines in this map of Muzaffarabad.

In computer age, we have many new ways to visualize and compute a 3D area, but this hasn't harmed the usefulness of contours.
contours are used to design drainage channels, canals, roads, railway lines or calaculate the capacity of a new lake. Military maps need contours for planning operations.
Before computers, contour maps were costly to make, and modify. It included aerial survey, photogrammetry and stereoscopy to manually draw contour maps.
Nowadays, satellites generate data elevation models of globe with
computerized 3D terrain data-sets have made life much easier. custom contours can be drawn in seconds with flexibility of detail and resolution.
It took few seconds to draw contours of Karakorams near K-2 in the picture below. Before computers, it would have taken years if not decades to draw such a map.

 

Slope

Slope
We use word slop in everyday conversation, and it means the same in engineering.
slop is the rate of rise or fall of a line or surface, as it moves forward.
see the picture below, and it will confirm your experience that mild slopes are easy to climb, and steep slopes are harder.

for calculations, we can use any of intutive ways to define a slope.
it can be angle of the inclination, percentage rise or ratio of height difference vs distance travelled.

Water always travels down a slope and it travels faster on a steeper slope. it can not travel up a slope.

riverbeds (path of a river) have very mild slope in planes, but are steeper in hilly or mountaineous areas. still riverbed has the easiest slope inside montain areas. Permanent roads in mountains are always constructed along a river bank to avoid bad slopes. Karakoram highway is a common example.

In an area with seasonal rivers, like Balochistan, mostly dry stream beds can be used as natural roads for traveling, but be aware of flash floods.

riverbeds are steepest inside nerrow valleys and gorges. we will discuss this topic in detail on a separate page.