(Or, du /dr = - du /dy since y = R – r ). Analysis The wall shear stress is determined from its definition to be du τ w = − μ = − μ u max d ⎛ ⎜ 1 − r n ⎞ ⎟ n ⎟ = − μ u max − nr n − 1 n = n μ u max dr r = R dr ⎝ R ⎠ r = R R r = R R u ( r ) = u max (1- r n / R n ) Note that the quantity du /dr is negative in pipe flow, and the negative sign is added to the τ w relation for pipes to make shear stress in the positive (flow) direction a positive quantity. Assumptions The viscosity of the fluid is constant. The friction drag force exerted on the pipe by the fluid in the flow direction per unit length of the pipe is to be determined. Limited distribution permitted only t o ⎜ Solution The velocity profile of a fluid flowing though a circular pipe is given. Chapter 2 Properties of Fluids 2- 44 2- 18 PROPRIE T ARY MATERIAL.
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