Question

A pipe system carries water from a reservoir and discharges it as a free jet, as shown. The system consists of piping made from 200-mm diameter commercial steel pipe with two 90 deg elbows with Kı=0.4m and an inlet minor loss Kl = 0.05 1) (4 pts) Assuming ideal fluid model within the reservoir, show that pressure at point A is VÃ Pa = Pamb + y(30 m) р 2 and draw on the diagram the streamline you used. 2) (8 pts) Lay out the energy equation with loss terms from point A to point B and reduce it to a function format of friction factor f and exit velocity VB, i.e. F(f,VB) = 0 3) (6 pts ) Iteration: By guessing a VB to start your calculation of Reynolds number and f , use the energy equation above to update VB. Continue the process until VB converges. Show the final velocity VB and Reynolds number, Re = ? 4) (2 pts) Calculate the flow rate Q in m3/s. 60 m Patm Reservoir K=0.05 MY 30 m 20 m A Datum B 200-mm steel commercial pipe throughout 2.90° elbows K = 0.40 60 m v = .0113 x 10-4 m2/s p= 999 kg/m3

Answer 1

Given: A pipe system carries water from a reservoir and discharge it of a free jet. of pipe is d=-2m K₂ (90 ellow) and inler minor loss (ky) = 0.05 dia. -0.4 y = 0.0113X104 m/s 8 = ggg kg/m3 6om Resevoir streamline som 20ml A patum Gim @ Assuming ided flow pressure or point Air PA = Patm + 8130) - SVA Apply Berouli equation b/w point o hand a. Parm vo Voo PA + 20 = Ig 2g +22 20 30m JS ag 2200 PA = -sv + + Patm + 49 (30) 2 2 ® Energy equation with loss tems from point a to point B Apply Bernoulil equation b/w point A & B. PA Pe VO + 2 + 2B + h 38 Jg 2g VAR + 14 + ܢܰܘ energy egn. Patm 11 VO + PA P5 VA + +0 2g non +20 Ig + Qx0.4) vê + 0.05 Vo 2g 2g + f L VB ago put the value of PA Patm eg +30 VA² + VA Patm 1) 38 +20 + 125 VB? 2g + 10 1.85+ $X120) VB 2 Assume friction factor f = 0.02 put in can 10 (1185+ 0024120 B = 3.72mbs

Reynold no. Vd 66.6x100 - 3.77x.2 0.0113 4154 flow rate 16 = = reet Etex (2) + 2 71 velocity 0.1184 m?la