1. Elementary Mechanics of Fluids CE 319 F Daene McKinney Momentum Equation

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

3. Ex (6.3) Given: Figure Find: (a) Force acting on bottom of the tank and (b) the force acting on the stop block. Solution: d=30 mm v=20 m/s Tank m=20 kg V o =20 L T=15 o C W N F

4. Ex (6.3) W N F

5. EX (6.5) Given: Figure Find: Horizontal force required to hold plate in position Solution: T=15 o C Q=0.4 m 3 /s p A =75 kPa F B

6. HW (6.12)

7. Ex (6.17) Given: Figure Find: External reactions in x and y directions needed to hold fixed vane. Solution: V 1 =28 m/s V 2 =27 m/s Q=0.20 m 3 /s FxFx FyFy

8. Ex (6.17) V 1 =28 m/s V 2 =27 m/s Q=0.20 m 3 /s FxFx FyFy

9. Ex (6.34) Given: Figure Find: Force applied to flanges to hold pipe in place Solution: Continuity equation Momentum D=30 cm Q=0.60 m 3 /s P=100 kPa, gage Vol=0.10 m 3 W=500 N p1A1p1A1 p2A2p2A2 V1V1 V2V2 FxFx FyFy W b +W f x y

10. HW (6.37)

11. 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 FxFx FyFy V2V2

12. HW (6.80)

13. HW (6.98)

14. HW (6.101)

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