Question

Following parts are not related. (a) The triangular flume shown in the figure is used to carry water over a ravine. It is made of unfinished concrete with a Manning coefficient value of 0.014. It has a slope of 0.001. If the intended flow is to be 4 m3/s, determine the depth of flow. (10 points) 459 45 Flume (b) A cruise missile under test is moving horizontally at Ma =2 in the atmosphere at an elevation of 2000 m (Air temperature is 2 °C). Determine the half-angle "alpha" of the Mach cone. (5 points) (c) A Francis turbine is rotating at 75 rpm under a hydraulic head of 30 ft and develops 150 hp with a discharge of 0.1 m3/s. When the guide vanes remain in their fixed position and the hydraulic head is 15 ft, determine the rotation of this turbine and the corresponding power of the turbine. (10 points)

Answer 1

0.0.14 a] Giyen : Triangular Blume Manning's. coefficient (n) slope (s) Depth of -Z100 lys = 0.001 Q = 4 m/s 2 y ty b breadth ob fiangular plume (6) ay Perimeter of riangular plume P = 252 y. Area (A) 1 x bh. 1x (24) x y y 2 using Discharge A 12/3 equation (9)%* se x A 4 = 1/2 x (0.001)94xy ? 0.014 After Solving we get y = 1.6068 m (6) Halt angle ot the Mach cone d - Söt (ta) sin' ( ) 30° = 30 Given :-) Francis turbine N = His 30 ft P = 150 HP 75 rpm o. lm3/s Qis H2 = Isft laws using turbine gH N²D² constant HON? 1/2 NI Ne ( #2) (39) 12 75 N2 N2 = 53.03 rpm Rotation of turbine a²aH 1/2 Qi 2 (H) (38) 1/2 Q2 Q2 = 0.0707 m3/s For power PI P2 (#2) 3/ HI H2 3/2 ISO 30 is P2 P2 = 53.03 HP