Question

Consider a pipe system as shown in Figure 1. The pipe is connected to a mercury manometer at point 1 and point 2. Prove that the pipe wall between these points is exerting less than 600 N of fluid force. The frictional losses along the pipe is not negligible. Water 1.5 m 1 0.15 m 2 30° 0.15 m Mercury,SG 13.5

Answer 1

т е | Sm 21 4 water. O | ) зоо d= 0.15m n , T о: 15 м) A Sky betweren Pq and P2 finding relation by using pascal law. Р. + Рgя + на 8 (0-15) = PA and Р. + 3 (21) + Рg + 90-10) - PA

00 we get P2 + sah Sug gX(0.15) = P2t 992 + ggn + 39 (0.5) (Ps-Pz) = gx 0:15*(Sng - ) -8921 = (9.8 5.81 X 0.15 (13600-1000))+1000x9.31 of *1.5Ginoo) (P1-P2) 11183.4 Pa O area of biße (A) = x d? - 0.017677 m²

F.B.D of water in section and او 2 PIAL F K 1.5 m ►F 4V F & weight (h: A2 Ffore applied by pipe on fluid. Weight (W) veg (AxL) SX Рx4 N 0-01767x1.5 X 1000 X 9.81 - 260. 0355 N. In direction of flow Net force rate of change in momentum [has - Az + w los bo'] = m [v,-)

and from continuity AVI A2 Vz - V₂ = V₂ LAI - Az = A3 Do, F = (bi- p2) A + W looto 0.017 67 X 13183.4 + 260-03 60060 F = 327. 6294 N 4 force applied by pipe wall on fluid hence, F GooN