Advanced Fluid Mechanics Problems And Solutions Upd -

For a power-law fluid: ( \tau_rz = K \left| \fracdudr \right|^n-1 \fracdudr ) (( n>0 )), laminar steady flow in a circular pipe of radius ( R ) driven by pressure gradient ( -\fracdpdz = G > 0 ). Find the velocity profile and total flow rate.

ϕ=U∞rcosθ+κcosθrphi equals cap U sub infinity end-sub r cosine theta plus the fraction with numerator kappa cosine theta and denominator r end-fraction At , the radial velocity must be zero (impenetrable wall). Solving for Strength ( ): advanced fluid mechanics problems and solutions

[ M_2^2 = \frac1 + 0.2(6.25)1.4(6.25) - 0.2 = \frac2.258.55 \approx 0.263 \Rightarrow M_2 \approx 0.513 ] For a power-law fluid: ( \tau_rz = K