Download ME 3834-Fluid Mechanics Problem 6.68 Given:

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
.