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Mechanics

Blazing goIITian

 Joined: 7 Mar 2007 Post: 784
7 Mar 2007 16:48:14 IST
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(FLUID MECHANICS)!
Engineering Entrance , Medical Entrance , AIPMT , JEE Main , AIIMS , JEE Advanced , Physics , Mechanics

A rectangular tank of height 10 m filled with water is placed near the bottom of a plane inclined at an angle 30 degree with the horizontal .A t height h from the bottom a small hole is made such that the stream coming out from the hole, strikes theinclined plane normally.Calculate h.

Blazing goIITian

Joined: 9 Feb 2007
Posts: 471
7 Mar 2007 18:12:39 IST
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Blazing goIITian

Joined: 9 Feb 2007
Posts: 471
7 Mar 2007 18:17:56 IST
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use kinematic equation the distance X covered by the fluid and the distance y covered by it are related as
X=(3)^0.5y
.....u knw the initial and final velocity along X andY
and then u can solve it

Blazing goIITian

Joined: 31 Jan 2007
Posts: 780
7 Mar 2007 18:30:01 IST
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how did u do it ?? avdesh

Blazing goIITian

Joined: 31 Jan 2007
Posts: 780
7 Mar 2007 18:31:49 IST
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i also used the same method but not getting the answer.plzz. post ur solution !!

Blazing goIITian

Joined: 9 Feb 2007
Posts: 471
7 Mar 2007 19:06:52 IST
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velocity along the plane is vcos30..
vcos30=gsin30t.......v=(2g(10-h))^0.5
X=(3)^0.5y....
therefore.vt=(3)^0.5(h-0.5gt^2)

Blazing goIITian

Joined: 31 Jan 2007
Posts: 780
7 Mar 2007 19:28:33 IST
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my answer is 5.22 cm .but tell me one thing .these equations that we are applying of kinematics, these are applied to what ?? bcoz earlier this were used for discrete particles but here it is continuos stream of water !!!

Forum Expert
Joined: 27 Dec 2006
Posts: 565
7 Mar 2007 19:44:40 IST
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well to solve such problems
we assume the base of the rectangle to be origin
the unit vector along the plane is
L=sqroot(3)/2i+1/2j
now velocity of the water beam is given by
v=sqroot(2g(H-h)) i-gt j
now if it strikes plane normally
then L.v=0 dot product will be zero
we will get value of t
now again take the again take a parabola eqn in terms of y and x
and find its pt of intersection with
y=tan30 x
we will get pts y and x
and then solve!!

Blazing goIITian

Joined: 31 Jan 2007
Posts: 780
7 Mar 2007 19:49:31 IST
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tell us the answer man !!! (shakir u too ,if u have got it )

Blazing goIITian

Joined: 9 Feb 2007
Posts: 471
7 Mar 2007 21:43:16 IST
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solve the equation u urself and find the answer rajat as ive given u answer

Blazing goIITian

Joined: 31 Jan 2007
Posts: 780
7 Mar 2007 22:01:26 IST
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who said that is the ryt answer ???

Blazing goIITian

Joined: 9 Feb 2007
Posts: 471
7 Mar 2007 22:02:24 IST
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THEN U PROVE ME WHAT WRONG IVE DONE!
PLZZZ ILL BE GLAD PLZZ TELL ME WHAT WRONG IVE DONE!

Blazing goIITian

Joined: 7 Mar 2007
Posts: 784
8 Mar 2007 12:53:25 IST
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well the answer is 8.33m.but i couldn't get it

Blazing goIITian

Joined: 7 Mar 2007
Posts: 784
8 Mar 2007 13:14:08 IST
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avdesh i could not get your soln.explain properly

Blazing goIITian

Joined: 31 Jan 2007
Posts: 780
8 Mar 2007 15:07:59 IST
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EXPERTS PLEASE SEE THIS and also avdesh

hey,avdesh if u are so confident about ur solution ,which is indeed right ,i think u should answer  my following queries successfully .
1. why will the stream coming out of the orifice make an angle of 30 with the x-  axis (taken parallel to the  incline)

2. why will the stream fall normal to the incline ,because gravity is always acting to increase its speed(along x-axis) and falling normally means that finally,the component of velocity along x-axis is zero .but there is no reason for it to become zero. (i.e tell me the reason why it becomes zero).

and lastly i think that there's some prblem in the question and it should be "normal to the floor " and not "normal to the incline "

Forum Expert
Joined: 6 Jan 2007
Posts: 706
12 Mar 2007 10:02:02 IST
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The solution is as follows....
Let the small hole be the origin.
Then the eqn of inclined plane is y+h=x/(root3)
or x=(root3)(y+h)........(1)
For the water coming out x=vt  where v=root(2g(10-h))
and -y=gt2/2
So y=x2/4(h-10)
So dy/dx=x/2(h-10).....(2) which is the slope of the tangent at the point where water meets the inclined plane.
From (1) slope of the normal is 1/(root3)
So x/2(h-10)= -(root3)
or x=2(root3)(10-h)
So y=3(h-10)
Substtute this in (1) you will get h=50/6=8.33m

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