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 Thermodynamics and Fluid Mechanics Thermodynamics and Fluid Mechanics Physics Help Forum May 18th 2011, 04:54 AM   #1
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Join Date: May 2011
Posts: 2
Barn Basement Flood Bernoullis principle

Hi Guys,
I'm really struggling with the following question:

A simplified schematic of the rain drainage system for a barn is shown in the figure (attached). Rain falling on the slanted roof runs off into gutters around the roof edge; it then drains through several downspouts (only one is shown) into a main drainage pipe M below the basement, which carries the water to an even larger pipe. A floor drain in the basement is also connected to drainage pipe M. The question arises, if such design can cope with heavy storm events such as recently experienced in Australia.
Suppose the following apply:

1. the downspouts have height h1 = 11 m
2. the floor drain has height h2 = 1.2 m
3. pipe M has radius 3.0 cm,
4. the barn has a width w = 30 m and a length L = 60 m,
5. all the water striking the roof goes through pipe M ,
6. the initial water speed in a downspout is negligible,
7. the wind speed is negligible (the rain falls vertically).

(a) By applying Bernoullis principle, determine the speed of water in pipe M, when the basement floor is on the verge of being flooded.

(b) Calculate using the continuity equation at what rainfall rate, in centimeters per hour, such flooding will occur?

I tried finding the horizontal and vertical velocities but got stuck when attempting to apply Bernoullis principle (which I don't understand very well). Some hints would be fantastic.
Thanks very much.
Attached Images Screen Snaper Image.bmp (487.0 KB, 18 views)   May 18th 2011, 09:29 AM #2 Senior Member   Join Date: Jun 2010 Location: NC Posts: 418 Hi SupernovaGirl... The meaning of "...can the system COPE with a storm event..." is unclear. What do you suggest that it does to "cope" during a storm. About Bernoulli's Equation check this URL: Torricelli's Theorem (E340) Good Luck Jim   May 18th 2011, 03:01 PM #3 Junior Member   Join Date: May 2011 Posts: 2 Hi, Thanks for the reply. I don't think the definition really matters that much. I just need to answer parts (a) and (b).   Jan 21st 2015, 05:34 AM #4 Junior Member   Join Date: Jan 2015 Posts: 5 Hi I know that I am answering this question 5 years after your posting this question.I am a new member.I think I was able to solve this question and got the correct answer of 7.84 m/s,but with a lot of assumptions! So I am posting this answer to get yours and others' opinion about my solution. My assumptions:- 1) Imagine a rectangle and imagine pulling it from its center,raising a pyramid.I assume the roof to be of this pyramidal shape so that,the exposed surface area of this pyramid is same as that of the base.(This is not the case with all pyramids) 2) Pressure inside the house is the same as the atmospheric pressure. 3) Water collected in the pipe joining the floor drainage and the pipe M is stagnant(at rest) Solution: Let the point in M directly below the floor drainage be called point 1),the point where a downspout begins as point 3) and the point at the floor drainage as point 2). Consider a y axis such that y1=0,y2=h2,y3=h1 Between 1) and 2) P1=P2 + Rg(y2-y1) (water is at rest) P1= Pa + Rgh2 Since 3) is exposed to the atmosphere,P3=Pa Therefore,P1-P3=Rgh2 Applying Bernoulli's equation between 1) and 3):- P1+0.5R(v1^2)+Rgy1=P3+0.5R(v3^2)+Rgy3 Therefore, P1-P3=Rgh1-0.5R(v1^2) P1-P3=Rgh2 Therefore, Rgh2=Rgh1-0.5R(v1^2) This gives v1=13.85929291m/s Volume flow rate=A1v1=0.039186227 Continuity:- Volume flow rate=Rainfall volume rate rate Now,a point on the roof receives a volume (vdt).da in a time dt where v=speed of rain and da=area of point.Therefore,volume rate=vda Integrating,flow rate=lbv where l and b anre length and breadth. lbv=A1v1 Solving the above would give v=2.177 x (10^-5) m/s=7.84 cm/h Please tell me if I am correct or not   Tags basement, bernoullis, flood, principle, barn Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post ching5633 Thermodynamics and Fluid Mechanics 1 Oct 21st 2016 12:23 PM guaiamum Thermodynamics and Fluid Mechanics 7 Aug 1st 2016 04:26 AM abcde Thermodynamics and Fluid Mechanics 1 Sep 21st 2014 10:28 AM Justusphung Thermodynamics and Fluid Mechanics 1 Jul 30th 2013 06:18 AM Aryth Special and General Relativity 4 Oct 21st 2009 07:40 AM 