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

Continuum Hypothesis ,[object Object],[object Object],[object Object],[object Object]

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.

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

Fluid Statics ,[object Object],[object Object],[object Object],[object Object],[object Object],X Y Z  xy  xz  yz  yx  zx  zy

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

Simple Non-trivial Shape of A Fluid Element

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

Pressure Variation with Elevation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1st order Taylor series estimate for pressure variation over dz

[object Object],[object Object],[object Object],[object Object]

Pressure Variation for a Uniform-Density Fluid

Draft Required to Establish Air Flow Air in Flue as out

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

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

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

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

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.

Natural Draft ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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.

PRESSURE ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object]

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

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

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

An important Property of A Fluid

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

Elasticity (Compressibility) ,[object Object],[object Object]

Surface Tension ,[object Object],[object Object],[object Object]

Vapour Pressure ,[object Object],[object Object],[object Object],[object Object]

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