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2. (10 points) A stream of air (with unknown density p) from a 2 cm diameter nozzle strikes a curved vane as shown in the figure. A Pitot tube connected to a water-filled U-tube manometer is placed in the air jet. Calculate the force (horizontal and vertical) exerted in the vane by jet. Assume incompressible and inviscid flow. f Air Open -Stagnation Fixed vane Viet| tube D=2cm dia. LFree air jet 1 1 h=10cm 30° 2 Water V=Vjes

Answer 1

Solution is s and Let density of ain جب کوعلمنيا X ? Step I Find velocity of Jet Vjet h sh sh when heavy liquid in manometer and lighter fluid flows. in pipe and h difference in level of fluid in mancemeter V = 2.9% Assume at standard condition S. - 1.225 kg and sw = 1000 kg m 3 so 0.1 1.225 # 81.53 26 m Jet Velocity vjet = 2x9.81 x 81.5326 Vjet 4omis Vcos (30) 80P Vsin (3) Step I Force in direction SAVC vare - Van Fx = 1.225 I 10.02)2 x 40 [(40) - (- 40605 3.11 Horizontal Fr 1.25N Answer

force in y direction Fy= SQ [uay-V₂y] = SAU [vay-lay] fy = 1.225 x T x 10.02)2x 40 To - (-40 sin 3o) 4 Vertical fy = 0.3078 N Answer