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U-tube manometer

No idea where to begin with this one.
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Reply 1
Avatar for 2^1/2
2^1/2
11
you need to balance the forces on either side of the U bend,

hint : the only force will be gravity (F=ma) and mass = density*volume (in this case you can just use the length)

edit: also you should be able to rule out 2 answers straight away, by just thinking which liquid is heavier.
(edited 13 years ago)
Reply 2
Avatar for wdywuk
wdywuk
9
1/2.

Pressure at a depth of 2x on LHS is the same as the pressure at a depth of x on RHS (both sides open to atmosphere.

so rho1 . g . 2x = rho 2 . g . x

rho 1 / rho 2 = 0.5
Reply 3
Avatar for wdywuk
wdywuk
9
The key things to remember with static fluid are

1/ change in static ressure varies by rho x g x z
rho - density of fluid
g gravitational constant
z vertical displacemnt

2/ A corollary - if the same fluid joins two points in a static situation, then the static pressure at those two points is the same.
Original post by wdywuk
1/2.

Pressure at a depth of 2x on LHS is the same as the pressure at a depth of x on RHS (both sides open to atmosphere.

so rho1 . g . 2x = rho 2 . g . x

rho 1 / rho 2 = 0.5


How did you determine that ?

Original post by wdywuk
The key things to remember with static fluid are

1/ change in static ressure varies by rho x g x z
rho - density of fluid
g gravitational constant
z vertical displacemnt

2/ A corollary - if the same fluid joins two points in a static situation, then the static pressure at those two points is the same.


I dont fully understand your second point. Could you explain it a bit more with an example from the question which shows a Corollary point ?
Reply 5
Avatar for wdywuk
wdywuk
9
At the same vertical location, the static pressure will be the same IF the same fluid joins both points. So in your diagram, from the bottom of the U-tube, if we go up a distance x, then the pressure in the lhs is the same as the pressure in the rhs as the vertical location is the same and the same fluid joins both points.

If we go up a further distance x, then while the two points will be at the same vertical location, the static pressure will be different on either side as the two points are not connected by the same fluid.

Oh, and to be absolutely correct you need to note that you are neglecting the miniscule effects caused by the small difference in air pressure on either side and buoyancy.
(edited 13 years ago)
Original post by wdywuk
At the same vertical location, the static pressure will be the same IF the same fluid joins both points. So in your diagram, from the bottom of the U-tube, if we go up a distance x, then the pressure in the lhs is the same as the pressure in the rhs as the vertical location is the same and the same fluid joins both points.

If we go up a further distance x, then while the two points will be at the same vertical location, the static pressure will be different on either side as the two points are not connected by the same fluid.

Oh, and to be absolutely correct you need to note that you are neglecting the miniscule effects caused by the small difference in air pressure on either side and buoyancy.


Ah, yes, wonderful explanation.

I've fully understood it now.

+rep

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