CE 319 F Daene Mc Kinney Elementary Mechanics

CE 319 F Daene Mc. Kinney Elementary Mechanics of Fluids Momentum Equation

Momentum Equation • Reynolds Transport Theorem • b = velocity; Bsys = system momentum • Vector equation -- 3 components, e. g. , x

Ex (6. 3) T=15 o. C • • • v=20 m/s Given: Figure Find: (a) Force acting on bottom of the tank and (b) the force acting on the stop block. Solution: d=30 mm W F N Tank m=20 kg Vo=20 L

Ex (6. 3) W F N

EX (6. 5) • • • T=15 o. C Given: Figure Find: Horizontal force required to hold plate in position Solution: Q=0. 4 m 3/s B p. A=75 k. Pa F

HW (6. 12)

• • • Ex (6. 17) Given: Figure Find: External reactions in x and y directions needed to hold fixed vane. Solution: Fy Fx V 1=28 m/s Q=0. 20 m 3/s V 2=27 m/s

Ex (6. 17) Fy Fx V 1=28 m/s Q=0. 20 m 3/s V 2=27 m/s

Ex (6. 34) • • • Given: Figure Find: Force applied to flanges to hold pipe in place Solution: Continuity equation D=30 cm Vol=0. 10 m 3 W=500 N P=100 k. Pa, gage y Q=0. 60 m 3/s • Momentum x p 1 A 1 Fy V 1 p 2 A 2 V 2 Fx Wb+Wf

HW (6. 37)

Ex (6. 72) • • • Given: Water jet, 6 cm diameter, with velocity 20 m/s hits vane moving at 7 m/s. Find: Find force on vane by water. Solution: Select CV moving with the vane at constant velocity. The magnitude of the velocity along the vane is constant V 2 Fy Fx

HW (6. 80)

HW (6. 98)

HW (6. 101)

Sluice Gate • • Find: Force due to pressure on face of gate Solution: Assume: v 1 and v 2 are uniform (so pressure is hydrostatic)