Fluid Mechanics · Integral mass, momentum, and energy balances
A vertical pipe of interior diameter D = 100 mm discharges water (ρ = 998 kg/m³)…
Problem
A vertical pipe of interior diameter D = 100 mm discharges water (ρ = 998 kg/m³) downward to the atmosphere through an open end. The discharge speed is V = 8.0 m/s, uniform across the exit. A control volume is drawn from an upstream flange (section 1), where the pipe is still full and the gage pressure is p_1 = 25 kPa, down to the free exit (section 2), which is 1.20 m below section 1. The contained water volume between the two sections is the interior volume of a right circular cylinder of diameter D and length 1.20 m. Take +x horizontally (unused) and +y vertically upward, so the exit velocity is in the −y direction and gravity is in the −y direction, g = 9.81 m/s². The pipe is stationary. Define F_y as the vertical force that the upper flange and any hangers apply to the pipe-and-water control volume, positive in the +y direction (tension in hangers is therefore positive). Include the weight of the contained water; omit the metal weight. The exit is at atmospheric pressure. Neglect interior shear. Determine F_y.
Hint
Constant diameter and a full pipe mean the y-momentum flux does not change between flange and exit.
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