My teacher taught us that object immersed will experience buoyant force $B= V_{in yellow}\rho_{y}g+V_{inblue}\rho_{w}g$.
Why does object experiences upward buoyant force by yellow liquid if there is no material of it below the object? Shouldn't object just experience weight of liquid yellow above it pushing it downwards?
Doesn't Buoyant force arises due to pressure difference at different depth? Also the force due to pressure at small Area acts perpendicularly to the surface. So liquid above body (in general case where body is completely submerged inside single fluid)exerts force $\rho g h dA$ vertically downward and at depth $h + dh$ force exerted is $\rho g (h+dh) dA$ vertically upward. So resultant force is $\rho g dh dA$ vertically upward. So how does yellow liquid apply force upwards if after dh distance there is no such liquid
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I don't understand why you say the object is partially immersed when it is completely immersed in the combination of the yellow and blue liquids. – Bob D Feb 22 '23 at 14:43
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object is immerse partially in individual liquids@BobD – Ha'Penny Feb 22 '23 at 14:55
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1Yes but you should state it that way to avoid confusion. – Bob D Feb 22 '23 at 14:56
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3The short answer is: the yellow liquid exerts pressure on the blue liquid, which makes the pressure in the blue liquid higher than it would be in the absence of the yellow liquid. This increased pressure in the blue liquid contributes to the larger buoyant force. Imagine that the yellow liquid is actually the same as the blue liquid, so the boundary between them is purely imaginary. Then the object would be completely submerged and the buoyant force would be equal to the weight of the liquid in the whole volume of the object, not just in its imaginary bottom half. – Alex Sveshnikov Feb 22 '23 at 15:13
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@AlexSveshnikov Force of Buoyancy depends on the volume of body submerged in liquid. Any excess pressure due to yellow liquid would distributed evenly throughout the blue liquid which would reflect ultimately in blue liquids buoyant force got it thanks! – Ha'Penny Feb 22 '23 at 19:11
2 Answers
Just to be clear, all buoyant forces act upwards. That's because the buoyant force increases with fluid pressure which, in turn, increases with depth.
The upward buoyant force on this object, which is totally immersed in the combination of the yellow and blue fluids, equals the total weight of the volume of fluids displaced by volume of the object.
This means $V_{inblue}$ in your equation should be the volume of blue fluid displaced by the fraction of the total volume of the object below the A-B line and $V_{inyellow}$ should be the volume of the yellow fluid displaced by the fraction of the total volume of the object above the A-B line.
Insofar as why the object experiences an upward buoyant force by the yellow liquid when there is no yellow liquid below it, keep in mind that the weight of the yellow fluid on top of the blue increases the pressure within the blue fluid which, in turn, creates a greater upward buoyant force than if the yellow fluid were not there.
Hope this helps.
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Doesn't Buoyant force arise due to pressure difference at different depth? Also the force due to pressure at small Area acts perpendicularly to the surface. So liquid above body (in general case where body is completely submerged inside single fluid)exerts force $\rho g h dA$ vertically downward and at depth $h + dh$ force exerted is $\rho g (h+dh) dA$ vertically upward. So resultant force is $\rho g dh dA$ vertically upward. So how does yellow liquid apply force upwards if after dh distance there is no such liquid – Ha'Penny Feb 22 '23 at 19:06
My answer is for school students. take away the volume of the grey body and replace it with the same volume of yellow liquid. You are sure that this volume stays at its place and does not go up or down, but it has sone weight $ F=\rho\cdot V\cdot g$ so you know the force wicht keeps it in place is F going upward , if you put the grey volume back it of cause experiences the same force upwards.
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