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ME 3834‐Fluid Mechanics Problem 6.68 Given: ‐Water flows through a circular tube of diameter D=50mm ‐Smoothly contoured plug of diameter d=40mm is held in the end of the tube where the water discharges to the atmosphere ‐Frictional effects neglected. ‐Velocity profiles uniform at each section. Find: a) Pressure measured by the gage shown. b) Force required holding plug. Solution: Assumptions: 1) Steady flow 2) Incompressible flow 3) No friction 4) Flow along a streamline 5) ∆z=0 6) We use the pressure gage a) Basic equation: By applying the assumptions, this equation becomes: From continuity for uniform flow, 7 So, 19.4 ⁄ . 999 And, 19.4 . 7 164 . b) To determine the force required to hold the plug, apply the x‐component of the momentum equation to the CV shown. So, 164 10 4 0.05 999 7 4 0.05 19.4 7 322 170 152 .