Question

laser region is shown in the figure in the fluid is helium at 20 C and I am and it 108 ms and som T-20°C loto 4-10 8mo What is the maximum velocity? Show it on the figure? (5 points) - Is the trud 2-Dor 3-D? Explain your rational. (5 points) c) What is the velocity of the fluid at the wall? (5 points) d) Estimate the wall shear stress, Twin Pa (10 points) e Find the position in the boundary layer where ris one-half of tw . (10 points) 2) monoom velocity - - = S Boundary Layer reigion Plate

Answer 1

Griver: - U(4) = Usin (AY) OLYSS = 10.8 m/s . 8 = 3cm = 0.03 m 8= 3cm - 1 a> in the boundary layer region at a distance of 8 from plate where viscous flow velocity is 99%. of free stream vel So, maximum velocity = 0.99x10.8 : 10.692 m)s b) It is a 2-0 flow Because thero is no flow across the stream e stream line. ko.qqu - -4-8 plate a> u = Usin (Ay) u at wall (i.e y=0) u= Usin (Ixo) = 0 .. Ju=0 m/s d> we know that Tw= l dylun u= Usin (ky) dy - o cosmo CO2O) = 11 dy lg-o = U ces (0) 10.88 Ã ayly 0 - Tuzo = = 565.4867 2x0.03 sec Also, at 20°c u of water = 103 N / m2 i. Tw= 10 x 565 4867 = 0.56548 N/m2 7W = 0.56548 Pa]

2 = u du = 0.56548 2 28 ? 28 2 65 48 from equation © → UX U CO3(BAY) x = 0.56548 > 10*x108 60 (19)x - 0.56548 cos (KY ) = 0.5 caso is 0.5 when o= 60 or A 2x0.03 2x0.03 2X0.03 3 > y = 2X0:03 at 0.02 from = 0.02 m plate I is one-half of Two Hence