How to Generate A Force in A Fluid Flow

1. How to Generate A Force in A Fluid Flow P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Dicover the mother of Force Vector ……

2. Deformation of Fluid Element : Main Cause Behind Creation of Force

3. The Shocking News • 1 million to 10 million years they might be able to make a plane that would fly ?!?!?! • People had dreamed of flying for many years. • The United States Army was trying to develop an airplane in 1903, but the plane wouldn't fly. • The New York Times wrote that maybe in1 million to 10 million years they might be able to make a plane that would fly. • Only eight days later two men were successful in flying the first manned plane. • Controlled, powered flight had seemed impossible until Orville Wright took off on the 17th December 1903. • They were Wilbur Wright and his younger brother, Orville.

4. Development of an Ultimate Fluid machine

5. The Natural Genius& The Art of Generating Force

6. Hydrodynamics of Prey & Predators

7. The Art of C-Start

9. The Art of Complex Swimming

10. Kate Carew Interviews the Wright Brothers • “Are you manufacturing any racing machines?” • “Not just now, but we intend to.” • “How much can I buy one for?” • “Seven thousand five hundred-dollars.” • “Is that all? It doesn’t seem like an outside price for a perfectly good airship?” • “Airship!” shouted the Wright brothers indignantly. • “Is that the wrong word?” • “An airship,” said Wilbur contemptuously, “is a big, clumsy balloon filled with gas.” • “Well, I don’t see why your biplane shouldn’t be called an airship, too.” • “It’s a flying machine,” said Wilbur. • “The name we prefer is ‘flyer,’” said Orville. • “An airship would cost $50,000,” said Wilbur. • “More like $150,000,” said Orville, and they argued the question.

11. http://www.wrightbrothers.org/History_Wing/Aviations_Attic/Carew_Interview/Carew_Interview.htmhttp://www.wrightbrothers.org/History_Wing/Aviations_Attic/Carew_Interview/Carew_Interview.htm Transformation of an Airship into a Flying Machine

12. The Great Grand Fathers of Modern Flights

13. 19th Century Inventions Otto Lilienthal H F Phillips

14. History of Airfoil Development

15. Which is best for describing how aircraft get the needed lift to fly? Bernoulli's equation or Newton's laws and conservation of momentum?  Can We Identify the Cause?

16. Actions inside a Differential Fluid Volume

17. Cartesian Fluid Element

18. Scalar Product of and a Second Order Tensor

19. Force is an Extensive Property Recognize the intensive cause behind the extensive cause. Step 1: The first index i refers to the axis, to which the fluid element surface is perpendicular. The second index j indicates the direction of the force component.

20. Force contributed by Each Unit Area of A Differential Element • Divide the individual components of the above force vectors by their corresponding area of the fluid element side. • The results of these divisions exhibit the components of a second order stress tensor.

21. Force per unit area : An Important Tensor in Fluid Flows

22. General Stress Condition

23. Force Balance on A Plane Force Balance on Plane x in x direction: Force Balance on Plane x in y direction: Force Balance on Plane x in z direction:

24. The Resultant Force on A Plane The resulting Force on Plane x: The resulting Force on Planey: The resulting Force on Plane z:

25. The total resulting force acting on the entire surface of the element are obtained by considering the nine components. Force Balance on Differential Element Divide the resultant force by dV and obtain intensive equivalent of dF

26. Transpose : A Natural Thinking

27. Stress is the Mother of Force The stress is A tensor It can be easily shown that • The above expression is a scalar differentiation of the second order stress tensor and is called the divergence of the tensor field. • We conclude that the force acting on the surface of a fluid element is the divergence of its stress tensor. • The stress tensor is usually divided into its normal and shear stress parts.