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![[Post New]](/templates/default/images/icon_minipost_new.gif) 20 Feb 2008 02:26:13 IST
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A tapered section of pipe has a cross sectional area of 0.196 m^2 reducing to 0.126 m^2 , the centre of the larger section positioned 3.6 m vertically above the centre of the smaller section.
The pressure at the larger section is equivalent to a head of water of 4m and that at the smaller section to a head of water of 5m.
If 0.51 m^3 / sec of water flows from the higher to the lower section, determine the energy loss per kg of water flowing.
Show working.
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- Gaurav Ragtah (spideyunlimited)
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20 Feb 2008 09:09:36 IST
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well i am not sure what the question wants but nevertheless--
since 0.51m^3 of water flows per second
it is the volume distributed over a length v and A=0.196m^2
therefore Av=0.51
v=2.6m/s at the upper part
using bernoulli's theorem--
P/dg+h+v^2/2g= const
4 +3.6 +2.6^2/20 =5 +0 +v^2/20
v^2/20=2.938
v^2=58.76
this v is for vel at bottom
now just a guess--
if the question is asking how much energy is lost per kg of water flowing out , it seems to be kinetic energy of water
=1/2mv^2
=29.38J
but this is certainly wrong so i would like someone to correct me
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20 Feb 2008 14:33:37 IST
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i am getting something like 20 J/kg (edited)
whts the answer anyway
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20 Feb 2008 14:39:19 IST
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well whatever the answer be
chetan pls post your soln
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at the top , P/ = gh = 9.8 (4m) = 39.2
Av = .51 m^3/s
0.196 m^2 v = .51
v = 2.602m/s
total energy per unit mass at top = P/ + 1/2 v2 + gh
= 39.2 + 1/2 (2.602)2 + 9.8(3.6)
= 77.865 J ........................(1)
at the bottom, P/ = gh = 9.8 (5m) = 49
Av = .51m^3/s
0.126 m^2v = .51m^3/s
v = 4.048 m/s
total energy per unit mass at bottom = P/ + 1/2 v2 + gh
= 49 + 1/2(4.048)2 + 0
= 57.193J ..................(2)
from (1) and (2) loss in energy per unit mass,
= 77.865 - 57.193
= 20.672 J/kg
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20 Feb 2008 15:32:34 IST
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chetan's answer is convincing
i think you are right chetan
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20 Feb 2008 17:13:54 IST
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Ekdum badiya Chetan Bhai !
I'm not sure of the answer but I'm satisfied with your solution's working.
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- Gaurav Ragtah (spideyunlimited)
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20 Feb 2008 18:01:34 IST
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yes Chetan is perfectly right. We are doing such kinds of problems in College (We have a subject called Solid and Fluid Mechanics)
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Will nip in at times to solve problems :)
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