IIT JEE , AIEEE Forum - Physics , Mechanics

elastiboysai

Figure shows the top view of a tube
Are the pressures and velocites of the fluid at points 1 and 2 same?
(1 and 2 r along same radial line)
explain ur ans.
i hav an explanation for both the parts:
1.Pressure cant be same bcoz the wen the fluid moves along the curved part, it
has centripetal acceleration. The force for this can come only by pressure variation
2. a=v^2/r
were a is radial acc. and r is radius of curvature .
as streamlined flow acceleration has to be same for all points in fluid??
so v^2 proportional to r.
so v2>v1
This is the ans for the second part but
an entirely different explanation was given .
Am I missing something?
.

coolvignesh

here is my explanation...
pressure is of course different....
acceleration is v^2/r
now... pressure is density*acceleration*difference in displacement along the acceleration vector....
let ther be a seperation of x metres...
then difference in pressure will be density*x*v^2/r...

computer001

my explanation 4 second part wud be..
in stream lined flow u consider inside the pipe the curved cylinder par lik uve drawn(something lik an L shaped joint) ,water flowin thru/unit time shud be same(i think)
now the outer layers of water have to cover a larger dist.. so outer vel will be greater
but i fail to understand how u can account wid radial acc...tht is basically perp to the flow n is countered by normal force due to wall of pipe..so how exactly does tht affect flow vel??

computer001

elasti im not able to understand exactly how u can explain the circular flowing/vel wateva wid radial acc??
the radiall acc will be greater @ outer pts i accept but tht is bcoz of higher vel..i think..but u seem to be sayin the reverse

elastiboysai

See for any particle moving along a curve i can associate wid it a radial acceleration?
Thats wat i have done for the fluids at points 1 and 2.
But the necessary force for radial acceleration cant come from thin air.
So this implies there must be a pressure gradient along the line joining 1 and 2.

elastiboysai

computer001

yeah tht was my pt...wats the given ans?

elastiboysai

ans gvn was same
but explanation was on an entirely different line

computer001

oh well..this was a fiitjee ques if im not wrong...n i dun trust their answer..if thts the source

saurabh_me

hiii

actually my explanation is as follows...

since the points 1 and 2 are along same radial line then point 1 will be higher than 2....so Pressure at 2 is greater than 1 bcoz pressure = height*density*acceleration due to gravity......now since area of cross section for both of them hence force at 2 > force at 1.so this follows acceleration at 2?at1 and hence vel. at 2 > vel. at 1

thanks

computer001

P2>P1 and V2>V1 not possible together remember tht nice fella called Bernoulli????

elastiboysai

@Saurabh it has been clearly said that its a top view. 1 and 2 are on the same horizontal level

ananth_patri

we cant apply bernoulli principle here as they are not along the streamline flow.....

ananth_patri

ifff they are not in same horizontal line....

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