Question

 A fluid moves through a tube of length 1 meter and radius \(r=0.004 \pm 0.0002\) meters under a pressure \(p=3+10^{5} \pm 2000\) pascals, at a rate \(v=0.125 \cdot 10^{-9} \mathrm{~m}^{3}\) per unit time. Estimate the maximum error in the viscosity \(\eta\) if

$$ \eta=\frac{\pi}{8} \frac{p r^{4}}{v} $$

Hint: The error in \(\eta\) is approximated by \(d \eta\), where (by the chain rule) \(d \eta=\frac{\text { iv }}{\text { dr }} d r+\frac{\partial_{p}}{\partial p} d p\).

maximum error \(\approx 15616 \mathrm{pi}\)

Answer 1

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