Michaela S.

asked • 07/15/14

Archimedes Principle: Expression for Uncertainty

Pfl=((T-T'')/(T-T')) Pw     Assume that all of the tensions (T, T', and T'') were measured and Pw  is a known constant.  Give a valid expression for the uncertainty of Pfl. So far I have
u=T-T'' and z=T-T'
 
Pfl=(u/z)Pw--->(ΔPfl/Pfl)=(Δu/u)+(Δz/z)Pw---->Δu=zΔx+Δy--->
(ΔPfl/Pfl)=((Δx+Δy)/(T-T''))+(Δz/z)
 
Can someone please help me with this problem?

Jeff C.

tutor
Archimedes Principle: The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. This problem statement appears to be flawed in several ways. Where and why do x and y enter the story here? The use of the word 'tension' seems improper in the problem statement. It is also important to give those answering questions like this an idea of what mathematical tools you have available. For example, do you know what partial derivatives are? Additionally, is the density of the liquid constant, is temperature constant and what is it? I assume the liquid is non-compressible but a good problem statement would tell you this. It is quite difficult to offer assistance with so many unknowns.
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06/30/24

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