Question

1. Consider a design of a low-speed open-circuit subsonic wind tunnel. The goal is to achieve a free stream velocity of 150 m/s at the test section of this tunnel. This wind tunnel is equipped with a U-tube mercury manometer that measures the pressure difference between the inlet (the settling chamber) and the test section. If the fan of the wind tunnel is able to generate the maximum pressure difference corresponding to a height difference of 10 cm on the U-tube mercury manometer (The density of liquid mercury is 1.36 x 104 kg/m3), what is the inlet-to- throat area ratio of the nuzzle? In addition, what is the exit velocity of the tunnel if the area ratio of the diffuser is 3? Air density is 1.23 kg/m² Airplane model Fan V2 Motor P2, A2 Į P1 | A P3 A3 Test section Diffuser Settling | Nozzle chamber (reservoir)

Answer 1

Low speed subsonic Inlind tunnel (incompressible) free stream V2 = 150 m/s 2 10 cm velocity Pressure difference (Pi-P2) Liquid mercury densing of of Hy 2 1-36 x 104 kg/m3 inler area ratio Ai A 2 ? Exit velocity V3 = ? AB Diffiner area ratio 3. A 2 ais S = 1.23 kg/m² Density of olm Pressure (P1-P2) = difference 10 cm of reg oftg. (P.-P2) sgh 21.36x604x9.8 x 0) (Po-P2)2 1•3328 X10 N)m? / 13328mpa Applying bernoullis equation for seltion oľ© 2 2 Ž Su,2 P2 + £ 8 V2 SaS,=82 Low speed. Pit (P,-P2) ? Źs (ve'-v" > 0

2 mass Conserration SAMI = 8 AzV2 V.= A 2 lag A AVI Va A2 D =) , -P2) - ² 3 ( High - (A2) v2² ) (P1–82) = $ ve? ( - (03-)) 2 2 2 (P, -P2) £ 3X₂² (P1-P2) i sve? 1. 3328x104 Ź x1.23X1502 2 "A2 AZAL 20.1918. 5.21 2 AI AL area to throat Inlet b). mass conservation & A 2 V2 28 A3 V3 Vzx (A2) 1508 ( x ($) V3 V3 a Exit velocity 50 mis