Question

A streetlight is approximated by a 50cm diameter sphere mounted on a (a) 0.10m diameter cylinder 2.5m long. Estimate, using the data below and stating any assumptions you make, the bending moment at the root of the cylinder due to aerodynamic forces with:- 2 winds of 6.3m/s and an air temperature of 15'C; (i) slightly stronger winds of 7m/s and an air temperature of 22'C (ii) Comment on your answers and what advice would you give with regards the (b) surface finish used for the streetlight Physical properties of air at standard sea-level atmospheric pressure Density p kg/m3 Dynamic viscosity u 10N.s/m2 Temperature T C 17.1 1.293 0 17.6 10 1.248 18.1 20 30 1.205 1.165 18.6 Approximate Transitional Reynolds Numbers Smooth circular cylinder Smooth surfaced sphere 3.7 x 105 2.2 x 105 Coefficient of Drag Laminar Turbulent 1.2 0.3 Cylinder Sphere 0.47 0.2

Answer 1

Given 0,25 Steed wind, V 63m ad Tem Te 15 From the Table, The 15( 2010) A1 1.24 .205 A2265 /m 2 2-S 14.6+18.1 17-RS KID Pa-See G sphere Apouming 4P length X-Diai of spheve (be of characterintic projected Aren ylinder (Re Syg ... X= 0.5m FOr (Rep SUax Sphese M2265x6.3xo SO 1.2265 x6.3 x 0.10 (3.85XID 17.85KID (Re' .*.t in les 1an(R), (-2x1) 14 in LaminaY flow 2.16 X10 O.432 X 1D clearly, Relo? (3ax1 )eritied! 2a14s 44a . t oll abo Far sthere, aficied of Dray . Lammar flow ylinder 9O47 .Fex C 1.2

FOrce on Sphere Gyalinder Drog Force 2. Aven 2 1-2 x1 XI-2245x (25x0u1) x6-3 >2.246 N S7.301 N Taking (Mut Moment aboud the oot of the linder (5J Sphere x (2.5t0.5) + (5X Glnder 2 (2.246 1 2-39t7.301X25) Mreotleqliner IS.302 N-m For Um at iclazie Takiy 205, and aie1.1 Pa-Se For Sphere 1+205 X7 X0.SO Re 1.205 XF XO.16 Re 18.1 X10 18.1710-6 233x10 0.466 x1D ReX Re-2.2 v) Re 3.7 roe) Flow in Turbulent Flow in lamimaY 0.2 C 1.2

phere FoY ylfinder FOr 2 0.2 7 9.2 xX12oS x2,510.10)y 17 8.85N N SI Moment cbout oot of eylinder 14.225 N- of Smoth b The are and Sphere uoed as i Susfaces, whicl ase seduces the Dray Ferce, More The SroothmersLenwill be momend af