A fluid of viscosity 7 poise and density 1300 kg/m3 is flowing through a circular pipe of diameter 200 mm. The maximum shear stress at the pipe wall is 200 N/m^{2}. What will be the pressure loss mere of pipe length?

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APPSC Lecturer (Polytechnic Colleges) Held on March 2020

Option 2 : 4000 N/m^{2}

ST 1: Building Material and Concrete Technology

20135

20 Questions
20 Marks
12 Mins

__Concept:-__

**Maximum shear stress** in circular pipe flow is given by:

\(τ = - \left( {\frac{{dp}}{{dx}}} \right)\times\frac{R}{2}\)

where

τ = Shear stress, \(\frac{{dp}}{{dx}}\)= pressure gradient, R = Radius of pipe

__Calculation:__

__Given:__

τ = 200 N/m^{2}, D = 200 mm ⇒ R = 100 mm = 100 × 10^{-3} m

μ = 7 poise ⇒ 0.7 Ns/m^{2 }(∵ 1 poise =0.1 Ns/m^{2})

\(τ = - \left( {\frac{{dp}}{{dx}}} \right)\frac{R}{2}\)

\(\;200 = - \left( {\frac{{dp}}{{dx}}} \right)\frac{{100 × {{10}^{ - 3}}}}{2}\)

\(\frac{{dp}}{{dx}} = \; - 4000\frac{N}{{{m^2}}}\)

__\(τ = - \left( {\frac{{dp}}{{dx}}} \right)\frac{R}{2}\)__

**Shear stress Distribution across a section is linear in laminar flow.**

The** maximum velocity in a pipe **is given by:

\({U_{max}} = - \frac{1}{{4\mu }}\left( {\frac{{dp}}{{dx}}} \right){R^2}\)

Velocity distribution across a section is parabolic in laminar flow.