Question

solve all parts please! thank you

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) 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

Date.... ly 45° B Gixen, Moming Coefficient, Ņ= 0.014 slope flow Q 4 m3/sec 0.ool 7 Area of flow, Az 1 XACXAD 2 the figure 30 CA= y ton 450 AC = 20D ay So, sor A = 1X2yxy Area of flow, wetted perimeter, P= AB + BC P = 2(AB) P = 2(AB) p. = 2 (12) P = 252 212 y AB=BC P = 252 y

22 ma A Р 252 Hydraulic Mean depth 2524 Now, using manning's formula Ca I m16 16 yl ( 2 ) 1 ca (60.060) yve C ₂ y 252 0.014 0.014 TITUT Now, Discharge, Q = AC Smi y² x y V (60.068) ten) 40.001) Q Q 2 yob x 60.068 y x 0.001 252 Q 101294 x y 16/6 2 X 11294 3.5417 Q. 1.1294 x 4 (6/6) 4 years 41266) Depth of flow, y = 1.6086 m so Depth of flow is 1.6086m

Date.. b Giren Mach Number, M = 2 Elevation H = 2ooom we Know that Half Angle of MACH CONE Sint 2 Sinc 2 30 Giren, N=75 орт H = 30 ft P = 150 hp Q = 0.1 m3/sec H₂ 15 ft Now, we know that N₂ JH2 So 75 √30 vis N₂ = 53.03 8pm lo Speed af turbine at 15 ft Head is 53.037pm

ALSO we know that turbine P P 4,312 H 3/2 150 P2 (30)312 (15) 3/2 P2 = 53.03 hp 53.03 power output at 15 ft head is hp IN