Question

Water flows through the pipe as shown in the below figure. Determine the net tension in the bolts if minor losses are neglected and the wheels on which the pipe rests are frictionless. Please clearly show the steps of the trial & error method. Bolts 50 mm 10 m Cast Iron 20 m 30 m

Answer 1

1 A 50 mm Cast Iron 10 m EBolts B of 2om 3om + t + 3 Bt he equivalent roughness of Cast Iron is Sol " for Water, f = 1000 kg Im?, M = 103 Ns / m Apply Bernoulli's equation at point A and B , .+ ZA Po V8² pg ag fg ag PA=Pg= Patmo VAZO oth h₂= fLv2 ago ag 2g v² 2x9.81 v?( 17 1000f): 196.2 - lis from table equivalent roughness of pipes, the here, O + + o+ 10 = or v² 2g 10 V? ag 10- v2 1 + 10 بے [ 2+ fx son 1=1 É = 0.26mm

Relative Roughness is 2 - 0.26 so 0.0052 . By Iteration Method, we can calculate velocity in the bike. First Iteration :- f = 0.03 Then, from equation (is, we get V?(1+ 1000 X 0.03) = 196• 2 Assume, Va 2.52 m/s Re 1000 X 7.52X 0.05 SVD = M 10-3 126000 Re= at from Moody's Chart Re = 126000, and relative roughness & 2 0.0052 the fruction factar 0.03 15. The obtained value of friction factor and assumed Values are not equal then go for next iteration

Second I toration 3 Assume, f= 0.0315 Then, vX (1+ 1000X 0.0345 ) = 156.2 V= 2.46 m/s Re= DVD = 1000 X 2.46X 0.05 123000 u 10-3 from Moody's Chart at Re= 123000 and $20.0052 the friction factor is 0.0315. So, the assumed value and the value obtained from Moody's Chart are equal . Then, the velocity in the kipe is V=2.46 m/s point A and c. Apply cele t Bernoulli's equation Between VA2 Pc V² + ZA- ag - Sg 29 Here, V=Vc +3c the 0 + 0 + 10 Pc & va (27$5.) 89 29 (² Pc 89 10 - 2.462 + Y 1+ 0.0315 X 20 OOS 315* 20 ) 2x9.81 Pc= 56950 N/m2

ܠܛ The pressure force acts on the bolts is, Pc XA f= PcX ( to ) A 56950X ( IX 0-05) f= 111.82 N 124.82 N. .. Net Tension in the bolts is