Physics, 19.07.2020 14:01 aliyyahlove
A fluid moves through a tube of length 1 meter and radius r=0.002±0.0002 meters under a pressure p=4⋅105±1750 pascals, at a rate v=0.5⋅10−9 m3 per unit time. Use differentials to estimate the maximum error in the viscosity η given by
Answers: 3
![\Delta \eta = \frac{\pi}{8} [ |\frac{r^4}{v} | * \Delta P + | \frac{4 * P * r^3}{v} |* \Delta r + |-\frac{P* r^4}{v^2} |* \Delta v]](/tpl/images/0709/7360/de442.png)
![\Delta \eta = \frac{\pi}{8} [ |\frac{(0.002)^4}{0.5*10^{-9}} | * 1750 + | \frac{4 * 4 *10^{5} * (0.002)^3}{0.5*10^{-9}} |* 0.0002 + |-\frac{ 4*10^{5}* (0.002)^4}{(0.5*10^{-9})^2} |* 0 ]](/tpl/images/0709/7360/3888f.png)
![\Delta \eta = \frac{\pi}{8} [56 + 5120 ]](/tpl/images/0709/7360/abb1b.png)
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A fluid moves through a tube of length 1 meter and radius r=0.002±0.0002 meters under a pressure p=4...
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