Question

Q3. The jet of water having a cross-sectional area of 2 x 10-m² and a velocity of 45 m/s strikes the vane of a turbine, causing it to move at 20 m/s. Determine (a) the dynamic force (Fx & Fy) of the water on the vane [15 points]; (b) the anchoring force (Fx & Fy) required to hold the vane stationary [15 points). Neglect the weight of water and vane for simplicity. Hint: pwater = 1000 kg/m, Assume VA = VB = 45 m/s. 45 m/s A 20 m/s 30° W

Answer 1

Cross section area of yer 9; = 2x10 m² cu solute velocity of set V, 2 48 ms Velocity of vane e = zomps Relarive recociny of water entering to blade vya Viru = 45 - 20 - 25 m/s o let the friction is absent s/w yet water and vane 1. so at exit relative velocity is (Vr2 = Vory a 25ml At inlet vx = Ur R 111 TIT 0 = 30° ܠܪ ܢ Vorzcoso AT exit veza - Wrz cose vasino v2 =-va since { There are since it go holes along we axis. Gros relan've discharge - Avg mira relative mass flow rate entering to & vane = CAN Mgra 1020 x 2710 x 25 - 5

a The agnanic force (hx and R) use impulle momentum ean Fx - sale of charge of nuumentum in x wire enim fx = {ms. Vix - Enir von Fx = nirwx) - vir Vry fx a mir (Vr) - mine (-Vry. Loso) fx = mir [vergt Vrlose ] Unga Vaz 20 ml Fx = 50169 (25+256520] I Fx = 2322053 a dynamic force 917 X-direction, 11 Fy - Rare of change of momentum in y-direcion. a) by a mir winir Vay Fy samin (-1/2 sino) Bay - S0(12) * 2514) x sinzo Try = 625N) (1)

Posllten re Mai11 if we neglect 6 let the anchoring force is (fx and Ry) required - to hold the vane in this are u (veicity of vane) zen (stationary) - speed of jet = 45 m So velocity of ejer entering towane VA = 45n4 e neglect any losses VB a 45 nys mass of water entering to Blade - l AVA = 1010 x 2x10x45 imi - golos Holding force (6x) wing impulse momenrum can fx = mv, x-nivex Ex : ( V ) - ( (-va Cu o ) , ( 4 (ox @ ) fe : 90 x 45*(1 + Cos30) - 12550 N fe is the force appued by water to wane so we need to apply the force in opposite direction to f ire. ). s vry = no component in directions mivo - wi Vzy Z ara clero P a-mi (-usino) Py = 90 745 x sin 30 - 2025 N. Thij - 2025 N (M) / Force apreied by Kobe wavertovane So we need to appey the force opposity to fy leo Holding force -12 S5ow fy - 2025 N