Question

1. Water flows at Re = 104 up a vertical smooth walled pipe ( L = 10m ; D= 2 cm). At z=L/2 find : (a) the shear stress Tiz at the wall and at r=R/2;(b) the gage pressure change APg; (c) estimate the effective turbulent eddy viscosity , n, at r=R/2 (eq’n 8.27), and the ratio of turbulent-to-molecular viscosities n/u at this point [use the ut(y) core distribution eq’n 8.30 to get du/dy). Show steps clearly. Approx. Ans: (a) Tw~0.8 N/m²; (b) AP~120 kPa; (c) n/u~25

Answer 1

dy ☺ Re> 4000, then the flow is Turbeelart. so, Re= 10,000 , and is Turbulant flour To su duen + nalu je t= ty + Zt – Dynamic Visconto di Ex- shear sheers due to discosity et = shear stress due to Trabalance n & Eddly Virsconto du e velocity. os 4 ts 30, Wall sheas skess to leading the Re = exe des de 10000 = - 1000xdelay 10 986 0.9 mm/see 4xX/12 430.9m M 1000 10,000 - tooo axlo, w ie D = 4 - 9000 30.9 mm|sec 10,000 = 1000 Kau buy ; du = 9 x10 0.9x13 so, shear steces es mas @toor and mininum at ro estrena 163) Tshear stress @ wall le dar | 1. e= 900x (9x103) + (900x9x108x.com) N/m r=0 for Lamilar and n = 1000 (4) at fully so, 1 = 1000 (100) = 900 at fully turbuelant les mer zer &90 (Z = 0.81 N/mm) Ang so, Twell = 0.8111mm and tem== 0.8) CS$canned wiêream Tarat R = 0.405Nm 1 tusbulan

e D- Diameter = 20mg Gauge pressure Ew= APXD Dp = 0.81xxl 4XL - Length = lom spa RwX 4XL Ap = 1600 apa) ie 1.6 kpa Ang pi) Effective turbulant Eddy likwisty is fun (4) je poolm) at RER andas = 1oooxs 1000xĄ looo Cscanned with CamScanner.