Question

ure where we will consider Problem 3: (20 pts) (Show work for partial credit] The Washington Monument in D.C. is an obelisk-type structure where we will the geometry to be a composite consisting of a square pillar with side length of 501 and height 550 ft, and a pyramidal cap with a square base also of size 50 ft and ape height 50ft. A uniform flow (standard air at sea level) of 20 ft/s is directed towards the corner of the square base, not the flat side, where we are neglecting ground erecte, Assume the drag coefficient of the pyramidal section is Cpp = 0.8 and the me action of the drag force on the pyramidal section passes through a point one-third on the height of the section measured up from its base. (a) (17 pts Calculate the reaction moment in the base of this structure. (b) [3 pts Compute an approximate Reynolds number (I will accept a few possibilities) and comment on the choice of length scale used. Does this justify your choice of CDs1 the drag coefficient on the square pillar section? U = 20 ft/s 50 ft 550 ft

Answer 1

Solutím :- Given that: - (a) Drag force fo- C xt SAUR p=0.8 $= 0.0765 Vm20 A = 1/2 bh fp = 0.8** *0.0765x4 x50x50x620 Fo= 0.8x0.50.0765 40.5 X50X50 x 400 fp = 15300 lebt (b) Yoment at the base M = Fx (550*59) = 15300 ( 50+5%) = 1020000 lbfift 55067

Re = luule u Sair = 0.0765 445/43 0.0765 X20X50 4th Re= 3.5X167 l'air = 3.5/10?list Re = 2101.42x105 75x105 the flow is turbulent - for turbulant flow Cp = 2 0.074 (Re)'s 0.074 (211.62x105) 's 1,591 X263 = So cp is not appropriate ccp is calculated only for pyramid section - for rectangular pillar Re = suole luoxsso le me -0.0765 x 20x550 3.58107 so, the = 24042. Es x105 > sxios flow is turhlant

-0.074 Co= 5 1 . (Rel's ¿ 0.024 C24042 x 105 )Y5 Co= 9.84x10" Drag force on rectangular pillar Fp = Coxxp 4x4 = 9.84*x löyx0.0765X550X50X20V Fo= 414.056 lbb