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Rain Water Run Out Flow Estimation

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#1 Narayanan.u

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Posted 07 October 2008 - 03:27 AM

Hi To Everyone,

Could anyone please give guideline or a formula for estimating the total load of rain water in a catchment area, say 20 sq m, for a rain fall of 30mm for first 10 minutes or 20 mm/MIN. continueous.

When it is said 30mm , does it mean per minute or per any area unit ?

Also give some reference for finding details.

Regards,

Narayan

#2 mbeychok

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Posted 07 October 2008 - 10:39 PM

Naryan:

In the United States, rainfall is reported in inches of rainfall per square inch during a certain period of time (a day, a week, or a month).

For example, the average rainfall per month in the Houston Deer Park area of Harris County, Texas is reported as ranging from 3 to 5 inches per square inch per month (depending on the specific month). That amounts to 75 to 125 mm per square inch per month. Since a square inch is 645 square mm, that is equivalent to a range of 0.12 to 0.19 mm per square mm per month.

In general terms, we can say that rainfall is expressed as units of height per a given area per a given amount of time.

It can also be said that 1 inch of rain per square inch per month is the same as saying 1 cubic inch of rain per month (or 1 mm of rain per square mm per month is the same as saying 1 cubic mm of rain per month).

Also, remember that "rainfall" is larger than "runoff" because some of the rainfall will evaporate and some will be absorbed in the soil.

I realize this doesn't directly answer your question but I hope it helps.

#3 katmar

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Posted 08 October 2008 - 01:24 AM

I do not think that mbeychok is correct here. I have always understood "inches of rain" to be a purely linear measurement, and not a "per square inch" measurement.

If you collected rain in a flat horizontal pan with vertical sides, and you had 1 inch of rain, the level in that pan would rise by 1 inch irrespective of whether the pan had an area of 1 square inch or 1 square yard. The only difference in the pan size is that the larger the pan the better your averaging effect.

Converting the rainfall from one set of units to another would therefore simply be a linear length conversion. 1 inch of rain would be the same as 25.4 mm of rain, and no "per area" term needs to be converted.

A rainfall of 20 mm/minute continuous is rather extreme. I suspect someone has given you bad data here. Your name isn't Noah is it? I'm getting worried about where this message came from.

#4 Narayanan.u

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Posted 08 October 2008 - 04:16 AM

Hi,

Thanks for the replies.

We are using a formula known as Rational Method as below.

Q = CIA

Q = Peak flow rate at the particular point in the drain system cu m /min.
C = Run off coefficient for the catchment area (Ratio of run-off flowing to the total amount of rain fall)
I = Design rainfall intensity for the calculated time of concentration. (m/min)
A = The size of the catchment area contributing run off to the drains.

20 mm continueous is misleading to me too. 20 mm for a month can take us to m/min. So as i understood 20 mm per square mm per month. Height can be any units to match the units of area.

Hope above gives a better understanding.
Regards,

Naraynan

#5 Rama

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Posted 08 October 2008 - 10:10 AM

Dear Mr. Narayan,

You are using the right formula which is used generally for storm water drain designs. But the concept seems to have been misunderstood.

1. Rainfall is always measured in length units (height of rainfall) – generally over a period of time. The normal period is a day, as reported in weather reports. In the case of weather data of a place such reports give inches or mm of average rain, month wise, for the entire year. If you see a rain gauge you will understand how and why it is reported this way

2. Peak hour intensity of rain is often used to calculate the run off as in the case of drainage design or for Rain water harvesting system designs. Here the unit will be length per unit time. Say 20mm /hr. Such high intensity of rain is rarely continuous over a long period of time; but possible in short bursts of a few minutes or so. It is important for designing storm water drains.

3. Therefore having known the rainfall per day, the collection of water in volume units is = catchment area X rainfall height (use compatible units!); the run off (rate - volume per unit time) can be calculated using your formula, but here you should use the peak intensity of rain, generally in mm or inches per hour. The figure 20 mm / min is rather high, but about 300mm / hr. is possible in areas which are monsoon fed or in equatorial countries, in short spells! Peak intensity of rain mm per hour is what is generally used for Storm water Drain calculations. Such data may be available from specific agencies. Please see: http://www.cityofpal...asp?BlobID=2292 and http://www.ies.org.s...4i1/v44i1_5.pdf (coefficient C is available from: http://www.lmnoeng.c...gy/rational.htm

Ram.

#6 mbeychok

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Posted 09 October 2008 - 11:30 PM

Katmar:

I have always greatly valued your knowledge. However, in this case I am compelled to say that my response above is correct.

Rainfall is usually "reported" as inches of rain. However, what is really being measured in a rain gauge is cubic inches of rain.

Read page 263 of John William Moore (2007), Meteorology Practical and Applied, Nord Press, ISBN 1-4086-2788-4 which states:

"When we speak of an inch of rain, we mean that sufficient has fallen to fill to overflowing a vessel which is 1 inch in length, 1 inch in breadth and 1 inch in width - that is, a volume of 1 cubic inch."

Also read the Procedures section on page 1 of the pdf at http://www.earthsciw...es/July2009.pdf which states:

"Rain gauges measure the amount of rain in cubic inches"

If I had the time to spare, I could refer you to many similar references.

Keep in mind that rain gauges with cross-sections smaller or larger than 1 square inch are marked 1 at height equal to 1 cubic inch, 2 at a height equal to 2 cubic inchs, 3 at a hieght equal to 3 inches, etc.

Also note what the original poster, Narayan, says in his second posting:

"I understood 20 mm per square mm per month. Height can be any units to match the units of area"

which is exactly what I said, namely: "Units of height per a given area per a given time".

Best regards, Milt Beychok

#7 Qalander (Chem)

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Posted 10 October 2008 - 06:07 AM

Dear mbeychok/katmar Hello and Good Eveening,

Except for the envisging and express narration, I derive that you both are having almost similar conceptuality.

Pleae do review again each other's posts with cool mind without any presumption.
Best Regards
Qalander

#8 katmar

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Posted 10 October 2008 - 06:19 AM

Milt:

I equally value your knowledge, and I have learned a lot from your postings and from your web site, so it is with the greatest respect that I tell you that you are wrong.

Referring to the quote from Moore
"When we speak of an inch of rain, we mean that sufficient has fallen to fill to overflowing a vessel which is 1 inch in length, 1 inch in breadth and 1 inch in width - that is, a volume of 1 cubic inch."

This is correct, but only shows that the reference to area is redundant. If sufficient rain has fallen to fill a vessel 1" by 1" to a depth of 1" then that same amount of rain will fill a vessel 1 ft by 1 ft also to a depth of 1". The area is irrelevant and so we can rightly talk of rainfall in linear inches (or mm).

Your second quote, from EarthSciWeek saying "Rain gauges measure the amount of rain in cubic inches" is a kids science project and is an unfortunate example of supposed experts giving kids wrong advice. These instructions say that any bottle can be used, irrespective of the diameter of the opening, and then they go on to calibrate the bottle in cubic inches. This is patent nonsense. If my bottle has a bigger neck than yours then I will measure more cubic inches than you in a given rain event and it makes any comparison of measurements meaningless.

I'm sorry but I get very angry when I see stuff like this published in the name of "education" and this is the sort of stuff that makes people say "don't believe everything you read on the internet".

To quote from a more reputable source
http://www.metoffice...bservation.html

"It should be pointed out that 1 mm of rainfall recorded on a site means that if all the rain which fell in the surrounding area had not drained or evaporated away, it would have covered the entire surface to a depth of 1 mm."

They make no mention of a specific area.

The way a rain gauge is calibrated is that the volume is divided by the area of the top opening to give a linear measurement. This way my little domestic 3 inch gauge has a chance of measuring the same value as the weather office's fancy big 6" gauge. Their gauge will collect a larger volume than mine by virtue of its larger opening, but by dividing that volume by the area of the opening it brings all the measurements to a comparable basis.

To bring all this back to the original posters question, and his own answer, a dimensional analysis of his formula ( Q = CIA ) reveals that to get a cubic value for Q from an area (A) it has to be mutiplied by a linear value (I). The fact that Q and I are time related does not change this.

Regards, Harvey

#9 Rama

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Posted 11 October 2008 - 05:53 AM

This simple topic is becoming more interesting now! With due respect to both Milton & Harvey, I would like to add the following references.

The following is extracted from a website which could be considered as more reliable here:
http://www.metoffice...g_rainfall.html

Quote

The basic measurement of rainfall is that of how much rain falls in a specified period of time. By how much, we mean the depth of rain accumulating on a level surface without soaking in, running away or evaporating. The depth is usually measured in millimetres. The standard periods are the hour, the day, the month and the year. Measurements of rainfall depth over a period of an hour or less are usually only required for specialised purposes, and have to be made using automatic instruments.

The most common measurement of rainfall is the amount falling in a day. Meteorologists in the UK use a standardised day which runs from 9 o'clock GMT each morning to 9 o'clock GMT the next morning. Daily rainfall amounts measured routinely can be added together to provide monthly and annual totals.

Since the required observation is that of the amount of rainfall, then the simplest way of obtaining this is to accumulate the rainfall in a container and measure the amount at the end of each day.

The combination of a storage container and a device for measuring the amount of rain collected is usually called a storage gauge. Most storage gauges for professional use are intended for measuring daily rainfall amounts, although larger versions are made for measuring monthly totals at inaccessible locations.

All observing stations run by the Met Office, use the Met Office copper 5" standard gauge. It consists of a 5" diameter funnel with a sharp rim, the spout of the funnel being inserted into a glass collecting jar. The jar is in an inner copper can and the two are contained in the main body of the gauge, the lower part of which is sunk into the ground.

Unquote

The diagram given in the web site shows the whole gauge arrangement. The measuring tube (looks like a test tube with a conical bottom to magnify very low rainfalls) is graduated to measure the height of rain fall directly and not the volume in cubic inches or cubic mm. Generally the measuring tube is sized to magnify the reading by a factor of 10.
See: http://ccc.atmos.col...o/help/rain.htm for a different type of rain gauge.

Regarding the formula, as mentioned earlier, and also by Harvey, the Flow Q (Volume per unit time) = I [Rainfall intensity (length per unit time)] x Area. Here the intensity of rain is still length (per hour generally) but measured in more sophisticated instruments like tipping – bucket rain gauges (TBRs) and other types of gauges (optical, weighting, floating/siphoning, etc.). While it is easy to obtain the quantity of rainfall from published sources or the web, it is more difficult to get the intensity of rainfall without approaching specialist agencies.

Regards,
Ram.

#10 sgkim

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Posted 11 October 2008 - 09:04 AM

<Quote/>
Could anyone please give guideline or a formula for estimating the total load of rain water in a catchment area, say 20 sq m, for a rain fall of 30mm for first 10 minutes or 20 mm/MIN. continueous.

When it is said 30mm , does it mean per minute or per any area unit ?

Also give some reference for finding details.
</Unquote>

Dear Narayan and All

I'd like to introduce an interesting story on "Rainfall Meter":

The world's first rainfall meseasuring device named as "Cheuk-woo-gi" which means "Rainfall Measuring Bottle" in Korean was invented by Korean King "Sejong" in 1441, much (more than 189 years) earlier than that made by Italian Torchelli in 1639.

First device had the dimensions of 160 mm inside diameter and 410 mm in depth. One year later he reduced the size to ID 140 mm x 310 mm H after he found every rainfal seldom marked such high depth. He let staffs duplicate the reduced "Rainfall Meters" and distribute to every states and districts in the whole country and ordered to measure every rainfalls and report them to the central government. For dristrict levels, the meters were made of bronze but for the smaller areas ceramics such as porcelain or earthenware.

As Korean Peninsula is mountainous, to Korean people both stormy and dry weather used to be disarstrous-flood or drought. King Sejong made an agency "Gwansanggam" similar to present the Weather Bureau and ordered local offices to report "every" rainfals. The rainfalls had to be measured in "Chi (about 30.3 mm)" and "Pun(abunt 3.03mm)". Local government leaders who were idle in measuring and reporting rainfall records should have suffered bitter clubs on their hips.

Detail story and the picture could be found in :
http://images.google...&am...83‰&gbv=2
http://ocp.go.kr/l_g.../school/33.html

Rainfalls seem to be measured in depth (or height) since 1441. They are not dependent on the area measured but on the counting period. King Sejong measured as "per-rain" basis.

"30mm per 10 min" is equal to the hourly rate of 180 mm/h. Korean weatehr bureau reported that hourly 300mm of stormy rainfalls are not scarce nowadays even in Korea due to the Green House Effects on the Earth. In tropical monsoon areas, heavy rains with higher rates than 300 mm/h might be a common occurence. Cats and dogs, cats and dogs..

.................................

To go to your original questionnaire...

For the rainfall of 30 mm per 10 min in such a small area as 20 m2 it may require only 60 liters of stormy water holding tank, but for the larger areas a wide-and-deep reservoir and trench with a suitable slope will be required. Sometimes a stormy water holding sump and drainage pump may be required if the drain trenches are to be built within limited slope.

The following equation would be helpful for the design of open trenches for the discharge of such rain water. I once used these for the estimation of flow rates on the river.

Chezy's Equation (1769):
Q = C (Rh*Sf)^0.5.............(1)

Manning's Equation(1889)
C = (1/n)*(Rh)^(1/6)..........(2)

then,
Q= (1/n)*A*{(Rh)^(2/3)}*(Sf)^1/2...........(3)

Where
Q= Volume Rate flowing open trench or river, m3/s
Rh= Hydraulic Radius = Cross-sectional Area/Wetted Perimeter, m
Sf=Slope of trench or river, dimensionless, or m/m
A=Cross-sectional Area of the Trench or River
n=Mannin's Coefficient, dimension less,
n= 0.035 for major rivers, 0.03 for clean and straight rivers
n=0.014 for Unfinishe Concrete, 0.012 for Finished Concrete

Refernce: http://www.lmnoeng.com/manningn.htm

Hope these help

Stefano/081011

#11 Rama

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Posted 13 October 2008 - 03:38 AM

Hi!

Here is one more interesting write up on the history of rainfall measurement dating back to 340 BC! (It's a pdf file)
http://www.new.dli.e...0005af4_148.pdf

#12 Narayanan.u

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Posted 14 October 2008 - 03:53 AM

QUOTE (katmar @ Oct 10 2008, 04:19 PM) <{POST_SNAPBACK}>
Milt:

I equally value your knowledge, and I have learned a lot from your postings and from your web site, so it is with the greatest respect that I tell you that you are wrong.

Referring to the quote from Moore
"When we speak of an inch of rain, we mean that sufficient has fallen to fill to overflowing a vessel which is 1 inch in length, 1 inch in breadth and 1 inch in width - that is, a volume of 1 cubic inch."

This is correct, but only shows that the reference to area is redundant. If sufficient rain has fallen to fill a vessel 1" by 1" to a depth of 1" then that same amount of rain will fill a vessel 1 ft by 1 ft also to a depth of 1". The area is irrelevant and so we can rightly talk of rainfall in linear inches (or mm).

Your second quote, from EarthSciWeek saying "Rain gauges measure the amount of rain in cubic inches" is a kids science project and is an unfortunate example of supposed experts giving kids wrong advice. These instructions say that any bottle can be used, irrespective of the diameter of the opening, and then they go on to calibrate the bottle in cubic inches. This is patent nonsense. If my bottle has a bigger neck than yours then I will measure more cubic inches than you in a given rain event and it makes any comparison of measurements meaningless.

I'm sorry but I get very angry when I see stuff like this published in the name of "education" and this is the sort of stuff that makes people say "don't believe everything you read on the internet".

To quote from a more reputable source
http://www.metoffice...bservation.html

"It should be pointed out that 1 mm of rainfall recorded on a site means that if all the rain which fell in the surrounding area had not drained or evaporated away, it would have covered the entire surface to a depth of 1 mm."

They make no mention of a specific area.

The way a rain gauge is calibrated is that the volume is divided by the area of the top opening to give a linear measurement. This way my little domestic 3 inch gauge has a chance of measuring the same value as the weather office's fancy big 6" gauge. Their gauge will collect a larger volume than mine by virtue of its larger opening, but by dividing that volume by the area of the opening it brings all the measurements to a comparable basis.

To bring all this back to the original posters question, and his own answer, a dimensional analysis of his formula ( Q = CIA ) reveals that to get a cubic value for Q from an area (A) it has to be mutiplied by a linear value (I). The fact that Q and I are time related does not change this.

Regards, Harvey

Ram and all others,

I am glad and greatfull to all for the replies. What Ram explained is right. It is quite clear now.

We are correcting ourselves accordingly.

Regards to all,

Narayanan