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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.
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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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