Question

MDB2053/MEB2073 A square duct consists of air flowing through a 0.5 m opening as is shown in FIGURE 2 below. Due to the presence of boundary layer displacement thickness that increases in the direction of flow, the cross-sectional size of the duct is increased if a constant U = 0.8 m/s velocity is to maintained outside boundary layer U-08m du FIGURE 2 Determine the equation of the width of the cross section area of the duct, dix) with respect to the boundary layer displacement thickness 17 marks] 5 Find the boundary layer displacement thickness at x = 3m [5 marks) c. A proposal is made to replace the air with Helium gas (kinematic Viscosity 1.15 X 10* N/m?) to reduce the boundary layer thickness. Evaluate this proposal and give comments 15 marks)

Answer 1

a at a-distrance from inlet boundary layer is formed and was width is blocked So keep Velocity const. width will be keep increasing at ur increases. 0.5m S X width (w) 0.5 +(8x) function of a for Laminar region, 50 for laminar flow 8x = Then

50 by Punk al 2544 puno -5 for air f = 2X10 H = 2x10 Pars f = 1,2 teg/m3 1/2 dy 258 2x10 1.2 X 0.8 / Sx 0.0228 x 1/2 0.5 +0.02282 So width of square duct a(w) (b) at x= 3m 12 0.02280 1/2 0.0228 X 3 du Sabbion 0.0395 m Rexe - SX10 sxios 1.2 x 0.8 X RC sxios 7 xe = 10.417m up to ne flow will be laminar 2x105 1/2 25 un (c) x Ex 25H p Yoo Sxx do You = 1.15X104 m² / - 1/2 Vair = 1.67X10 for Helium Sx = : 0.0599a 25 X 115810 u 0.8 ut sx ^ Helium' will increase boundary layer thick NOM
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