TAMU CHEN 304 - L1 (12 pages)

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L1



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L1

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Pages:
12
School:
Texas A&M University
Course:
Chen 304 - Chem Engr Fluid Ops
Chem Engr Fluid Ops Documents

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CBE 341 Lecture 1 9 13 Concept of a fluid fluid accelerating as a rigid body buoyancy Definitions and concepts Elastic solid When an elastic solid is subjected to a small shear force it will deform slightly and assume a new static configuration The shear strain is defined as tan g g for small values of g Fn Ft Ft Fn If A is the area over which the normal and shear forces Fn and Ft respectively are acting then Normal stress Fn A Shear stress t Ft A The shear modulus is defined as Shear modulus Shear stress shear strain t g For a Hookean solid the shear modulus is constant independent of the magnitude of the shear strain or equivalently shear stress 1 Viscous fluid When a fluid element is subjected to the same set of forces as shown above the fluid element will also deform however it will not assume a static configuration at any particular value of strain g Instead the element will continue to deform indefinitely as long as the shear stress is acting on the fluid Hence it is not the deformation g but the dg rate of deformation g dt that is a measure of how a fluid responds to applied shear stress g is called the shear rate or the strain rate or the rate of deformation A typical velocity profile in the fluid element is sketched below The viscosity is defined as Shear stress shear rate t g For Newtonian fluids the viscosity is a constant independent of the shear stress or equivalently the shear rate In this course we will be mostly concerned with Newtonian fluids but will touch upon non Newtonian fluids briefly All gases and common liquids such as water liquid hydrocarbons alcohols glycerol and honey fall in the category of Newtonian fluids In chemical industry we also encounter a large variety of non Newtonian fluids Paints colloidal suspensions and polymer melts are common examples It suffices to say at the present time that for some fluids referred to as shear thinning fluids the viscosity decreases with increasing shear rate while for others it increases with shear rate shear thickening fluids 2 Units and dimensions M L and t denote units of mass length and time Shear or normal stress force area F L2 units M L t2 Shear strain rate units 1 t Viscosity common symbols or h F t L2 units M L t Note that viscosity has the same units as rV where r is the density V is velocity and denotes a length Kinematic viscosity n r units L2 t Note that kinematic viscosity has the same units of V SI Units of viscosity 1 N s m2 1 Pa s 1 pascal second CGS units of viscosity 1 dyne s cm2 1 Poise 1 Pa s 10 Poise Typical values to remember Viscosity of water 1 centipoise CP 10 2 Poise 1 mPa s mPa millipascal Viscosity of air 10 2 CP 10



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