Question

A fluid moves through a tube of length 1 meter and radius r = 0.002 ± 0.00025 meters under a pressure p = 3 ? 10^5 ± 1000 pascals, at a rate v = 0.875 ? 10?? m³ per unit time. Use differentials to estimate the maximum error in the viscosity ? given by ? = ?/8 * pr?/v. maximum error ?

          A fluid moves through a tube of length 1 meter and radius r = 0.002 ± 0.00025 meters under a pressure p = 3 ? 10^5 ± 1000 pascals, at a rate v = 0.875 ? 10?? m³ per unit time. Use differentials to estimate the maximum error in the viscosity ? given by
? = ?/8 * pr?/v.
maximum error ?

A fluid moves through a tube of length 1 meter and radius r = 0.002 ± 0.00025 meters under a pressure p = 3 ? 10^5 ± 1000 pascals, at a rate v = 0.875 ? 10?? m³ per unit time. Use differentials to estimate the maximum error in the viscosity ? given by
? = ?/8 * pr?/v.
maximum error ?

Added by Alba M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Jacob Fry

03/23/2023

Step 1

Let's differentiate both sides of the equation with respect to $n$, $p$, $r$, and $V$: $$ dn = \frac{\partial n}{\partial p}dp + \frac{\partial n}{\partial r}dr + \frac{\partial n}{\partial V}dV $$ Now, we need to find the partial derivatives: $$ \frac{\partial Show more…

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A fluid moves through a tube of length 1 meter and radius r = 0.002 + 0.00025 meters under pressure p = 3 105 + 1000 pascals, at a rate V = 0.875 10-9 m3 per unit time. Use differentials to estimate the maximum error in the viscosity n given by n pr4 8 maximum error ~