Mathematics: 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.

Find the flow rate through a tube of radius 6 cm,

Ответ:

jake9919

19.01.2022

Mathematics

791.68 cm/s

Step-by-step explanation:

The volume flow rate can be interpreted as the integral of fluid velocity over area

$\dot{V} = \int\limits^6_0 {v(r) 2\pi r} \, dr\\\dot{V} = 2\pi\int\limits^6_0 {(25-r^2)r} \, dr\\\dot{V} = 2\pi\int\limits^6_0 {25r-r^3} \, dr\\\\\dot{V} = 2\pi[12.5r^2 - r^4/4]_0^6\\\dot{V} = 2\pi(12.5*6^2 - 6^4/4 - 12.5*0 - 0)\\\dot{V} = 2\pi*126 = 791.68 cm/s$

0,0(0 оценок)

Ответ:

smarcalli6457

06.05.2023

Mathematics

B and C

Step-by-step explanation:

0,0(0 оценок)

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.

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question