Solving Pipe Flow: Understanding Why $\tau =\mu(-dV/dR)$

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Homework Help Overview

The discussion revolves around the shear stress formula in fluid mechanics, specifically addressing the expression for shear stress, τ, in relation to velocity gradients in pipe flow. Participants are exploring the implications of the negative sign in the formula τ = μ(-dV/dR).

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the reasoning behind the negative sign in the shear stress formula and its relation to the choice of reference points (center line of the pipe versus the wall). There are attempts to understand how the sign changes based on the perspective of measuring distance from different points.

Discussion Status

There is an active exploration of the reasoning behind the negative sign in the shear stress equation, with participants raising questions about the implications of different reference points for measuring velocity. No consensus has been reached, but the discussion is focused on clarifying these conceptual points.

Contextual Notes

Participants are navigating assumptions about the reference frame used in the shear stress formula and how it affects the interpretation of velocity gradients in pipe flow.

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Homework Statement


why the shaer stress ( tau) formula is given by μ(dv/ dy ) = μ(-dV / dR) , why there is a negative sign there ?

Homework Equations

The Attempt at a Solution

 

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The negative sign is included because you are considering the velocity as a function of the distance from the center line of the pipe, not from the wall.
 
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mfig said:
The negative sign is included because you are considering the velocity as a function of the distance from the center line of the pipe, not from the wall.
why when we are considering the velocity as a function of the distance from the the wall , it's positive ? or we can also consider the distance from the wall as positive ?
 
mfig said:
The negative sign is included because you are considering the velocity as a function of the distance from the center line of the pipe, not from the wall.
can we consider the distance from the centerline of pipe to wall as positive ?
 

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