Question

please list assumptions, show work, and

explain your reasoning carefully! please don't forget all this thanks

4. The aerodynamic behavior of a flying insect is to investigate in a water tunnel using a 10X scale model. The lift force F is believed to be a function of wing size L, flight speed u, flapping frequency w, fluid density P, and fluid viscosity u. Assume that air has a density 1/1000th and a dynamic viscosity 1/100th that of water. (a). List all parameters, n. (2 points) (b). List all primary dimensions, r. (2 points) (c). Find all dimensionless parameters. (Hint: Buckingham Theorem) (6 points)

Answer 1

Solu given Date Scale Sw model, Sair . Lm Lp 210 ; Maira ll watu joo 1000 All parameters. 6) Primary dimensions O lift force (F) kg m/s² [mielt?] m/s 4 wing size (L) flight speed (u) ② density is) GM's cosity (4) @ frequency (f) ③ dimensionless parameters kg/m (L') [lity] (m'i to Em Elf (7) Iglms na š' ) * Here Total no. of parameters (m) = 6 Total fundamental dimensions used (m) < 3 (M,LT) no. of the term z mona 6-3 z 3 density is) and frequency (f) #let's take; ewing size (L) as repeating variables for II-term

Ti = a gbff The Lash fu La gb tu Tly = for ast T-term, T, = [LJ[mica CriJºc mient?] : [molto J = mbtl 2.-3b +1 L T both sides, equate power of similar terms on Ś b+=0 b= j a-3b+) SO | cara a +3 +1 = 0 as-4 TL, -4-1-2 LS'f F Il ד SfPL4 for and The term, Te 2 b Lagh girl = (molot"]= [La CM' L-3gb [figo Cit] mo Lº Tº = mb a-sbtl ra L T i. equating powers, b=0 a-36+1=0 L- -C-Izo a-) (201 Tla 1'sºfly Tq z Lf -Am Fon 3rd T-term, Ty= 2² gb fu mocºrº, [L'ICM'csy" (Tigº Cm'e'f']

moLot z btl m a-3b-1 L" T equating powers of of similar terms, brzo a-3b-lo . (-120 b=-1 a +3=0 Car] a = -2 : 13 = -l-1 L ? sf لل ll Tg Am List d) for insect f=50 Š Jin in air W: I mis find water tunnel speed 4 wing flapping frequenry from and a team, ч u z u lat forom gre TL-term za u Lesf ist) inset (best) list) flight & ll watch * ㅗ X * L fair Swatu Gun) N لاله لر finsect f flight (103ext 2. L (100) x 1 1000 z 50 f fright f if fight 5 Ave flapping frequeny 25 times per sewnd.

Jinsect = from second. It term, z Linsel x Mair finsect fflight feight 50 5 * 1 * 10 I mis - Ane water tunnel speed Imis. ① Ratio of drag fora (+34 x A) wate ( so'ra) Ftanne Fair Is water) lewater Sair uair Linset flight, 1. Ftunnel z 1000 X () exftade Fair 1000 x I too Flannel = 10 Fair Ary 2 Ratio of zlo force drag

If you find my work helpful please give thumbs up

If you have any query regarding solution please let me know in comment box