The document discusses several key properties of fluids relevant for fluid mechanics, including: 1) Fluids can be modeled as continua when the number of molecules is sufficiently large at any point. 2) For static fluids, the only stress is normal stress since shear stress would induce motion. 3) Pressure in static fluids varies only with elevation and is constant at any horizontal plane. 4) Pressure measurement devices like manometers use fluid statics principles to determine pressure differences.

1. Properties of Fluids for Fluid Mechanics P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Basic Steps to Design………….

3. Static Fluid For a static fluid Shear Stress should be zero. For A generalized Three dimensional fluid Element, Many forms of shear stress is possible.

4. One dimensional Fluid Element +X +  +Y u=0 u=U

6. Stress Tensor X Y Z  yy  zz  yz  yx  zx  zy  xx  xy  xz  xz

7. First Law of Pascal Proof ?

8. Simple Non-trivial Shape of A Fluid Element

16. Fluid Statics for Power Generation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Steps for Design of Flow Devices………….

20. Pressure Variation for a Uniform-Density Fluid

23. Pressure Variation for Compressible Fluids Basic equation for pressure variation with elevation Pressure variation equation can be integrated for γ (p,z) known. For example, here we solve for the pressure in the atmosphere assuming ρ (p,T) given from ideal gas law, T(z) known, and g ≠ g(z).

25. Draft Required to Establish Air Flow Air in Flue gas out

26. Natural Draft H chimney T atm T gas A B p A = p ref +  p Z ref, ,p ref

28. H chimney T atm T gas A B p A = p ref +  p Z ref, ,p ref

29. Pressure variations in Troposphere: Linear increase towards earth surface T ref & p ref are known at Z ref .  Adiabatic Lapse rate : 6.5 K/km

30. Reference condition: At Z ref : T=T ref & p = p ref

31. Pressure at A: Pressure variation inside chimney differs from atmospheric pressure. The variation of chimney pressure depends on temperature variation along Chimney. Temperature variation along chimney depends on rate of cooling of hot gas Due to natural convection. Using principles of Heat transfer, one can calculate, T gas (Z). If this is also linear: T = T ref,gas +   (Z ref -Z). Lapse rate of gas,  gas is obtained from heat transfer analysis.

33. Pressure Measurement Another Application of Fluid Statics

34. Pressure Measurement Pressure is an important variable in fluid mechanics and many instruments have been devised for its measurement. Many devices are based on hydrostatics such as barometers and manometers, i.e., determine pressure through measurement of a column (or columns) of a liquid using the pressure variation with elevation equation for an incompressible fluid.

37. Manometers U Tube Inverted U Tube Enlarged Leg Two Fluid Inclined Tube

38. U-tube or differential manometer Right Limb fluid statics : Left Limb fluid statics : Point 3 and 2 are at the same elevation and same fluid

39. Gauge Pressure:

40. Absolute, Gauge & Vacuum Pressures System Pressure Atmospheric Pressure Gauge Pressure Absolute Pressure Absolute zero pressure

41. Absolute, Gauge & Vacuum Pressures System Pressure Atmospheric Pressure Vacuum Pressure Absolute Pressure Absolute zero pressure

42. Stress Tensor for A Static Fluid 0 0 0 0 0 0 X Y Z  yy  zz  xx

43. An important Property of A Fluid under Motion

44. Shear stress (  : Tangential force on per unit area of contact between solid & fluid