2. اگر حجم کنترل در حال حرکت بود چه سرعتی در فرمول؟ + –

3. بقای جرم Incompressible Fluids Steady, Compressible Flow فرض یکنواخت و یک بعدی بودن سرعت در هر مقطع

4. An unsteady situation: dm C.V. /dt >0 Mass flow into control surface, kg/s Mass in system,m(t) Control surface Control Volume

5. A steady situation: dm C.V. /dt =0Massoutflow Massinflow Control surface Control Volume

6. An unsteady situation: dm C.V. /dt >0Massoutflow Massinflow Control surface Control Volume

7. EXP1)The balloon is being filled through section 1, where the area is A1, velocity is V1,and fluid density is ρ1. The average density within the balloon is ρb(t). Find an expression for the rate of change of system mass within the balloon at this instant.

8. EXP2) با توجه به پروفیل سرعت داده شده برای جریان درون لوله، سرعت متوسط را محاسبه کنید.

9. EXP3) Use the triangular control volume in Fig., bounded by (0, 0),(L, L), and (0, L), with depth b into the paper. Compute the volume flow through sections 1, 2, and 3, and compare to see whether mass is conserved.

10. V = Ui; U=30 m/s. The boundary-layer thickness at location d is δ=5 mm. The fluid is air with density ρ=1.24 kg/m3. Assuming the plate width perpendicular to the paper to be w=0.6 m, calculate the mass flow rate across surface bc of control volume abcd.

12. هر یک از سرعت ها چه مفهومی دارند؟

14. Typical Momentum Applications Fluid Jets Nozzles Vanes Pipe Bends

15. EXAMPLE : Momentum Application A 15 m/s jet of water (diameter 30 mm) is filling a tank. The tank has a mass of 5 kg, and contains 20 liters of water as shown. The water temp is 15 deg C. Find: ‐ Force acting on the stop block. ‐ Force acting on the bottom of the tank

17. SOLUTION………….cont.

18. EXAMPLE: Momentum Application-Vane A horizontal jet strikes a vane that is moving at a speed v v = 7 m/s. Diameter of the jet is 6 cm. Speed of the fluid jet is 20 m/s, relative to a fixed frame. What components of force are exerted on the vane by the water in the x and y directions? Assume negligible friction between the water and the vane.

19. SOLUTIONS پره

20. SOLUTIONS cont……..

21. معادله برنولی

22. Restrictions on Bernoullis’ Equation  Valid only for incompressible fluids  No energy is added or removed by pumps, brakes, valves, etc.  No heat transfer from or to liquid  No energy lost due to friction

23. Torricelli’s Theorem For a liquid flowing from a tank or reservoir with constant fluid elevation, the velocity through the orifice is given by: where, h is the difference in elevation between the orifice and the top of the tank Example: If h = 3.00 m, compute v 2 h

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