Applied Hydraulics Module 3 Impact of Jets

As per The Mumbai University Syllabus
MGMCET Kamothe Navi Mumbai


Prepared by
Asst.Prof. Niranjan Dilip Patil

1. APPLIED HYDRAULICS IMPACT OF FREE JETS (OPEN CHANNEL FLOW AND HYDRAULIC MACHINERY) module – III NIRANJAN DILIP PATIL Assistant Professor Department of Civil Engineering MGM’s College of Engineering & Technology, Navi Mumbai

2. Pelton Wheel Vane or Bucket

3. Pelton wheel

4. T op i cs Impulse-Momentum Principle Hydrodynamic Force of Jets Work done and Efficiency Angular Momentum Principle Applications to Radial Flow Turbines Layout of Hydropower Installation Heads and Efficiencies

5. Introduction Analysis and Design of Hydraulic Machines (Turbines and Pumps) is essentially based on the knowledge of forces exerted on or by the moving fluids. Learning Objective: Evaluation of force, both in magnitude and direction, by free jets (constant pressure throughout) when they impinge upon stationary or moving objects such as flat plates and vanes of different shapes and orientation.

6. Force exerted by the jet on a stationary plate Impact of Jets The jet is a stream of liquid comes out from nozzle with a high velocity under constant pressure. When the jet impinges on plates or vanes, its momentum is changed and a hydrodynamic force is exerted. Vane is a flat or curved plate fixed to the rim of the wheel Force exerted by the jet on a stationary plate Plate is vertical to the jet Plate is inclined to the jet Plate is curved 2. Force exerted by the jet on a moving plate Plate is vertical to the jet Plate is inclined to the jet Plate is curved

7. Impulse-Momentum Principle From Newton's 2 nd Law: F = m a = m (V 1 - V 2 ) / t Impulse of a force is given by the change in momentum caused by the force on the body. Ft = mV 1 – mV 2 = Initial Momentum – Final Momentum Force exerted by jet on the plate in the direction of jet, F = m (V 1 – V 2 ) / t = (Mass / Time) (Initial Velocity – Final Velocity) = (ρQ) (V 1 – V 2 ) = (ρaV) (V 1 – V 2 )

8. Force exerted by the jet on a stationary plate Plate is vertical to the jet F =  aV 2 If Plate is moving at a velocity of ‘U’ m/s, F =  a(V-U) 2

9. Problems: A jet of water 50 mm diameter strikes a flat plate held normal to the direction of jet. Estimate the force exerted and work done by the jet if The plate is stationary The plate is moving with a velocity of 1 m/s away from the jet along the line of jet. The discharge through the nozzle is 76 lps. 2. A jet of water 50 mm diameter exerts a force of 3 kN on a flat vane held perpendicular to the direction of jet. Find the mass flow rate.

10. A jet of water strikes with a velocity of 35 m/s a flat plate inclined at 30° with the axis of the jet. If the cross-sectional area of the jet is 25 cm2, determine: ( i ) The force exerted by the jet on the plate, (ii) The components of the force in the direction normal to the jet (iii) The ratio in which the discharge gets divided after striking the plate

11. A 75 mm diameter jet having a velocity of 30 m/s strikes a flat plate, the normal of which is inclined at 45° to the axis of the jet. Find the normal pressure on the plate, ( i ) When the plate is stationary; (ii) When the plate is moving with a velocity of 15 m/s in the direction of jet, away from the jet. Also determine the power and efficiency of the jet when the plate is moving

12. Force exerted by the jet on a stationary plate Plate is inclined to the jet F N =  aV 2 sin  F x = F N sin  F x = F N cos 

13. Force exerted by the jet on a moving plate Plate is inclined to the jet F N =  a(V-U) 2 sin  F x = F N sin  F x = F N cos 

14. Problems: A jet of data 75 mm diameter has a velocity of 30 m/s. It strikes a flat plate inclined at 45 to the axis of jet. Find the force on the plate when. The plate is stationary The plate is moving with a velocity of 15 m/s along and away from the jet. Also find power and efficiency in case (b) A 75 mm diameter jet having a velocity of 12 m/s impinges a smooth flat plate, the normal of which is inclined at 60 to the axis of jet. Find the impact of jet on the plate at right angles to the plate when the plate is stationery. What will be the impact if the plate moves with a velocity of 6 m/s in the direction of jet and away from it. What will be the force if the plate moves towards the plate.

15. Force exerted by the jet on a stationary plate Plate is Curved and Jet strikes at Centre F =  aV 2 (1+ cos  )

16. Force exerted by the jet on a moving plate Plate is Curved and Jet strikes at Centre F =  a(V-U) 2 (1+ cos  )

17. Problems: A jet of water of diameter 50 mm strikes a stationary, symmetrical curved plate with a velocity of 40 m/s. Find the force extended by the jet at the centre of plate along its axis if the jet is deflected through 120 at the outlet of the curved plate A jet of water from a nozzle is deflected through 60 from its direction by a curved plate to which water enters tangentially without shock with a velocity of 30m/s and leaver with a velocity of 25 m/s. If the discharge from the nozzle is 0.8 kg/s, calculate the magnitude and direction of resultant force on the vane.

18. Force exerted by the jet on a stationary plate (Symmetrical Plate) Plate is Curved and Jet strikes at tip F x = 2  aV 2 cos 

19. Force exerted by the jet on a stationary plate (Unsymmetrical Plate) Plate is Curved and Jet strikes at tip F x =  aV 2 (cos  + cos  )

20. Problems: 1. A jet of water strikes a stationery curved plate tangentially at one end at an angle of 30 . The jet of 75 mm diameter has a velocity of 30 m/s. The jet leaves at the other end at angle of 20 to the horizontal. Determine the magnitude of force exerted along ‘x’ and ‘y’ directions.

21. Force exerted by the jet on a moving plate Considering Relative Velocity, If  < 90 F x =  aV r1 (V r1 cos  + V r2 cos  ) OR F x =  aV r1 (V W1 + V W2 )

22. Force exerted by the jet on a moving plate Considering Relative Velocity, If  = 90 F x =  aV r1 (V r1 cos  – V r2 cos  ) OR F x =  aV r1 (V W1 )

23. Force exerted by the jet on a moving plate Considering Relative Velocity, If  = 90 F x =  aV r1 (V r1 cos  – V r2 cos  ) OR F x =  aV r1 (V W1 – V W2 )

24. Impact of jet on a series of flat vanes mounted radially on the periphery of a circular wheel F =  aV (V- U)

25. Impact of jet on a series of flat vanes mounted radially on the periphery of a circular wheel F =  aV (V-U) (1+ cos  )

26. Problems: 1. A jet of water of diameter 75 mm strikes a curved plate at its centre with a velocity of 25 m/s. The curved plate is moving with a velocity of 10 m/s along the direction of jet. If the jet gets deflected through 165 in the smooth vane, compute. Force exerted by the jet. Power of jet. Efficiency of jet. 2. A jet of water impinges a curved plate with a velocity of 20 m/s making an angle of 20 with the direction of motion of vane at inlet and leaves at 130 to the direction of motion at outlet. The vane is moving with a velocity of 10 m/s. Compute. Vane angles, so that water enters and leaves without shock. Work done per unit mass flow rate

27. Force exerted by the jet on a moving plate (PELTON WHEEL) Considering Relative Velocity, F x =  aV r1 (V r1 – V r2 cos  ) OR F x =  aV r1 (V W1 – V W2 ) Work done / sec = F.U Power = F. U F .U ½ mV 2 Efficiency =

28. Problems: 1. A jet of water having a velocity of 35 m/s strikes a series of radial curved vanes mounted on a wheel. The wheel has 200 rpm. The jet makes 20 with the tangent to wheel at inlet and leaves the wheel with a velocity of 5 m/s at 130 to tangent to the wheel at outlet. The diameters of wheel are 1 m and 0.5 m. Find Vane angles at inlet and outlet for radially outward flow turbine. Work done Efficiency of the system

29. Jet Propulsion Jet propulsion means the propulsion or movement of the bodies such as ships, aircrafts, rocket etc. with the help of jet. There are following cases which are used J e t p r o p ulsio n of a t a n k t o w hic h orif i ce is fitted, and Jet propulsion of ships .

30. (a)Jet propulsion of a tank with an Orifice

31. Condition for maximum efficiency and expression for maximum efficiency

32. (b) Jet propulsion of Ships A ship is driven through water, A jet of water is discharged at the back also called stern of the ship, exerts a propulsive force on the ship. The water from the surrounding media is taken by following two ways: Through inlet orifice which are at right angles to the direction of the motion of the ship, and Through the inlet orifices, which are facing the direction of motion of the ship.

33. (1) Through inlet orifice which are at right angles to the direction of the motion of the ship

34. (2) Through the inlet orifices, which are facing the direction of motion of the ship

35. Layout of Hydropower Installation H g = Gross Head h f = Head Loss due to Friction = Where V = Velocity of Flow in Penstock L = Length of Penstock D = Dia. of Penstock H = Net Head = H g - h f

36. Efficiencies of Turbine Hydraulic Efficiency Mechanical Efficiency Volumetric Efficiency Overall Efficiency

37. Ref e ren c e Chapter 17 & 18 A Textbook of Fluid Mechanics and Hydraulic Machines Dr. R. K. Bansal Laxmi Publications

38. Question please ?