Question

The "double nozzle lying in a horizontal plane discharges water (p = 1000 kg/m) into the atmosphere at a rate of 0.50 m/s. Jet A is 10 cm in diameter, jet B is 12 cm in diameter, and the pipe is 30 cm in diameter. Assume the water speed in each jet to be the same. Calculate the force component (E. and F.) acting through the flange bolts required to hold the nozzle in place? Jet Water

Answer 1

Sohn let l be the pressure in larger pipe. P2. be the pressure in smalles dio pipes. v=Yz= V₂ = velocity in smaller pipes. Via velocity is larges pipe. da = diameter of smalles pipes. A= 10 m di : diamets of large pipe. = 30 cm d3= diameter of smaller pipe B = 12um. prea of smaller pipec Az 1 = 1 | 10:1272 Az = 0.0113 m2 prea of larga. pipes = Ag = Adg² = 7 (0:30)? = 0.0706m² Area of Somallea pipe A = A2- ūden 4 (0-10) 20.0078m2 Apely continuity equation at joint Рg, = P9, + PQ, og Jet B A, Bio - Palm Horizontal pipe Jep . A, B, Scanned with CamScanner

0.50 > Aq V2 + A3 V3 0-50 = 0.0078 XV + Ou0113 XV 23V i V2=Vg ginen. W > 4,139 misi celovity in larger V, - pipe .050 AL 020706 |v, = 6.59 m/s Scanned with CamScanner

Since. these is not - negligible mention or auge ne the pressure press so considerin pressure condihan. [P, = P2 = 8/20 Now FBD 14: 134 mis, 12 P2 - 4.139 nfs G. 57m's Scanned with CamScanner

.: We know that force in pipe is given by Fnet - Rate of Change of momentum ดุสรา ๆ geris of fluid along that anykers axi Newton's second law of motion. Now Efq = (mil),- (mv) ix =) Piarsih So + Fe-BZ =-pQ, Va - PQ, vi singo. a. fx = -p (@z v to, w ) Fe = -1060 (0.0078 x4,139 +0.5*6.57) X Singer Fa - - KN 22 1-674 sfy = (rövby - (ov)y -) PACOs30° + Fy - PZA3 = PQ3V3 - P Q yuos 30° Fy = loro 10.0113 x 4.139-0.5*6.57 XC60930') -2.798 KNI ce Scanned fit fy = CamScanner And

Sor th components are fp = - ] 674 KN Fy = -2.798 KAT CS Scan Scanned with CamScanner

Her the effect of pressure can be neglected as no data is given related to that is given so we can apply Bernauli's to get that. Rest I explain all the steps cleary . Please forgive for calculation mistake if any doubt please comment.

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