Mathematics, 26.02.2020 17:26 babygreg2001p97abr
Find the flow rate through a tube of radius 6 cm, assuming that the velocity of fluid particles at a distance r cm from the center is v(r) = 25-r2cm/s.
Answers: 1
![\dot{V} = \int\limits^6_0 {v(r) 2\pi r} \, dr\\\dot{V} = 2\pi\int\limits^6_0 {(25-r^2)r} \, dr\\\dot{V} = 2\pi\int\limits^6_0 {25r-r^3} \, dr\\\\\dot{V} = 2\pi[12.5r^2 - r^4/4]_0^6\\\dot{V} = 2\pi(12.5*6^2 - 6^4/4 - 12.5*0 - 0)\\\dot{V} = 2\pi*126 = 791.68 cm/s](/tpl/images/0524/9866/0362f.png)
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Find the flow rate through a tube of radius 6 cm, assuming that the velocity of fluid particles at a...
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