Derive an expression for velocity distribution for laminar f

Question

Derive an expression for velocity distribution for laminar flow through a circular pipe. Show that the friction coefficient is equal to 16/Re where Re is the Reynolds number.

24 Feb 2025

Answer :

Word Count : 307

In fluid mechanics, the velocity distribution for laminar flow through a circular pipe can be derived using the Navier-Stokes equation under steady, incompressible, and fully developed flow conditions.

Consider a circular pipe of radius \( R \) with a fluid flowing through it in the axial direction. The governing equation in cylindrical coordinates (\( r, \theta, z \)) for a fully developed, steady, incompressible, and laminar flow is:

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\frac{d}{dr} \left( r \frac{d u}{d r} _________ ________ __________ ____ _________ ______.
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