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$**Velocity Profile Analysis** A fluid flows through a pipe of radius $ R $ with a Reynolds number of $ 2 \times 10^5 $. **Question (a):** At what location, $ r / R $, does the fluid velocity equal the average velocity? - **Answer (a):** $ r / R = 0.778 $ **Question (b):** Repeat if the Reynolds number is 1000. - **Answer (b):** $ r / R = 0.7071 $ **Explanation:** This analysis determines the specific radial location $(r)$ within a pipe where the fluid velocity equals the average velocity, for two different flow conditions based on Reynolds numbers. The Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations.$

Transcribed Image Text:**Velocity Profile Analysis** A fluid flows through a pipe of radius $ R $ with a Reynolds number of $ 2 \times 10^5 $. **Question (a):** At what location, $ r / R $, does the fluid velocity equal the average velocity? - **Answer (a):** $ r / R = 0.778 $ **Question (b):** Repeat if the Reynolds number is 1000. - **Answer (b):** $ r / R = 0.7071 $ **Explanation:** This analysis determines the specific radial location $(r)$ within a pipe where the fluid velocity equals the average velocity, for two different flow conditions based on Reynolds numbers. The Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations.

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(Velocity profile) A fluid flows through a pipe of radius R with a Reynolds number of 2 x 105. (a) At what location, r/R, does the fluid velocity equal the average velocity? (b) Repeat if the Reynolds number is 1000. (a)r/R = 0.778