Question

Water is flowing through a horizontal pipe with diameter, D1, at a velocity, V1, and under a pressure, P1. It enters a 900 reducing bend (Shown in grey in Fig 2) that connects to a vertical pipe of diameter, D2. The inlet of the bend is 50 cm above the exit of the bend (as shown in Fig 2). Axes for positive directions of x and z coordinates are provided. Figure 2 Side view of reducing bend from horizontal to vertical pipe The following dimensions apply: D1 = 25 cm; D2 = 15 cm; V1 = 8 m/s; P1 = 300 kPa The flow is steady and incompressible. Frictional effects are negligible in the calculation of the pressure drop as well as any local losses. The weight of the elbow and the water in it can be disregarded since the gravitational effects are negligible. In your exam booklet determine the following: a) What is the velocity, V2, of the vertical pipe? [2 marks] b) Draw the streamline that you will use to solve the problem [2 marks]. c) What is the pressure, P2, at the exit of the bend? [3 marks] d) What is the Horizontal force, Fx, of the 900 reducing bend on the water (make sure to include the correct sign and/or indicate direction and note what is asked for). To guide your answer, draw the control volume you will use to solve the problem. Label all the forces acting on the control volume. [10 marks]. e) If the water exits the pipe and then hits an incline plane (40 degree incline), what is the vertical force required to hold the plane in place. The mass of the plate is 5kg. (make sure to include the correct sign and/or indicate direction and note what is asked for). [8 marks]

50 cm Fz 40° orizontal to vertical pipe Figure 2 Side vi reducing bend from h

Answer 1

d) gyapplagng Continu vity equah ur) 사 point D en-/ @ 4 05)

pressure at oni+ 0.3 bend applaing Beanoyss equahun uに souro 10o0x98 x9.8 5 0.5入10, 9-3 2. 12= (300 +4.9-210) χιο Pa,

ΙΧ 42 ½ ns eo,vis toooritas).g·n2.5 18//seer 392 ore Amp one 392.5 ( 8) = 300 X10 玩ー -17853-75N

㎡ 312-513 レ