0.002 0.0002 meters under a pressure-9A fluid moves through a tube of length 1 meter and radius r =p = 1.105 + 2000 pascals, at a rate v = 0.375 10-⁹ m³ per unit time. Use differentials to estimate themaximum error in the viscosity n given bymaximum errorηπ pr48 v

Given: meters (uncertainty in radius) pascals (uncertainty in pressure) pascals (pressure) meters…

Answered: A fluid moves through a tube of length…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 6E: Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a...

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Related questions

Question

0.002 0.0002 meters under a pressure
-9
A fluid moves through a tube of length 1 meter and radius r =
p = 1.105 + 2000 pascals, at a rate v = 0.375 10-⁹ m³ per unit time. Use differentials to estimate the
maximum error in the viscosity n given by
maximum error
η
π pr4
8 v

Expert Solution

Step 1: Introduction:

Given:
$capital delta r equals 0.0002$ meters (uncertainty in radius)
$capital delta p equals 2000$ pascals (uncertainty in pressure)
$p equals 1 cross times 10 to the power of 5$ pascals (pressure)
$r equals 0.002$ meters (radius)
$v equals 0.375 cross times 10 to the power of negative 9 end exponent$ m³ per unit time (flow rate)

To find:

Estimate the maximum error in the viscosity, $eta$ , using differentials.

Formula used:

The formula used for error propagation is:

$capital delta eta almost equal to open vertical bar fraction numerator partial differential eta over denominator partial differential p end fraction close vertical bar capital delta p plus open vertical bar fraction numerator partial differential eta over denominator partial differential r end fraction close vertical bar capital delta r plus open vertical bar fraction numerator partial differential eta over denominator partial differential v end fraction close vertical bar capital delta v$

Here, $capital delta eta$ represents the maximum error in $eta$ , $capital delta p$ represents the maximum error in pressure (p), $capital delta r$ represents the uncertainty in radius $left parenthesis r right parenthesis$ , and $capital delta v$ represents the maximum error in the rate of fluid flow $left parenthesis v right parenthesis$ .