A horizontal pipe of diameter 20 cm carries water. The pipe then narrows to connect to a downstream pipe of diameter 5 c

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A Horizontal Pipe Of Diameter 20 Cm Carries Water The Pipe Then Narrows To Connect To A Downstream Pipe Of Diameter 5 C 1 (40.78 KiB) Viewed 13 times

A horizontal pipe of diameter 20 cm carries water. The pipe then narrows to connect to a downstream pipe of diameter 5 cm. A U-tube manometer, that reads 7 cm of mercury, is connected between the pipes upstream and downstream of the narrowing section, as shown in Fig. A1. The flow speed and gauge pressure in the upstream pipe are respectively 1 m/s and 30 kPa. Assume water to behave as an incompressible ideal fluid. Take the density of water to be 1000 kg/m³, density of mercury to be 13,600 kg/m³, and acceleration due to gravity to have the value 10 m/s². U₁-1 m/s P₁-30 kPa 5 cm 20 cm 7 cm mercury Figure A1 (0) Determine the pressure in the downstream small-diameter pipe. (4 marks) (ii) Determine the flow speed in the downstream small-diameter pipe. (4 marks) (iii) Determine the magnitude and direction of the force experienced by the pipe walls in the narrowing section. (13 marks) (iv) If in the above system, the upstream pressure was 300 kPa instead of 30 kPa, suggest a simplified analysis that would give a reasonable engineering estimation of the force experienced by the narrowing section of the pipe. Justify your answer. (4 marks) €