MECE251 Fluids Lesson 8 part II Simple Fluid

Objectives 1. Qualitative - viscosity and shear stress 2. Quantification - shear stress for

Definition of a Fluid When a shear stress is applied: • Fluids continuously deform

Definition of a Fluid Velocity of plate, U y x U denotes the velocity

Viscosity • Newtonian Fluids – Most of the common fluids (water, air, oil, etc.

Non-Newtonian Fluids – Special fluids (e. g. , most biological fluids, toothpaste, some paints,

Couette Flow Velocity of plate, U u(y) = (U/a) y u(y) y R·I·T a

Poiseuille Flow Shear stress distribution within the fluid in a pipe (laminar flow) and

Free-body diagram of a fluid cylinder for flow in a nonhorizontal pipe. R·I·T MECE-251

Entrance region, developing flow, and fully developed flow in a pipe system. R·I·T MECE-251

Pressure distribution along a horizontal pipe including entrance region. R·I·T MECE-251 13

Next Steps L 8 Task 4 B: Please review the example problems on line.

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MECE-251 Fluids, Lesson 8 (part II): Simple Fluid Motion 1 - Read Text Sections 2 - Solve Chapter Problems 3 & 4 – Lectures, Example, and Review Problems 5 - Solve Case Study 6 - Complete On-line Lesson Quiz R·I·T MECE-251 1

Objectives 1. Qualitative - viscosity and shear stress 2. Quantification - shear stress for some simple flows 3. Qualitative - entrance length and developed flow R·I·T MECE-251 2

Stress Field R·I·T MECE-251 3

Definition of a Fluid When a shear stress is applied: • Fluids continuously deform • Solids deform or bend R·I·T MECE-251 4

Definition of a Fluid Velocity of plate, U y x U denotes the velocity of the plate and u(y) is x-component of fluid velocity. The layers (lamina) of fluid move at different speeds, u(y) This velocity difference causes stress analogous to the friction between moving contacting solids. This stress is a function of viscosity and the velocity gradient. R·I·T MECE-251 5

Viscosity • Newtonian Fluids – Most of the common fluids (water, air, oil, etc. ) – “Linear” fluids – Viscosity is constant R·I·T MECE-251 6

Non-Newtonian Fluids – Special fluids (e. g. , most biological fluids, toothpaste, some paints, etc. ) – “Non-linear” fluids R·I·T MECE-251 7

Couette Flow Velocity of plate, U u(y) = (U/a) y u(y) y R·I·T a du/dy = (U/a) = constant MECE-251 8

Poiseuille Flow Shear stress distribution within the fluid in a pipe (laminar flow) and typical velocity profiles. R·I·T MECE-251 9

R·I·T MECE-251 10

Free-body diagram of a fluid cylinder for flow in a nonhorizontal pipe. R·I·T MECE-251 11

Entrance region, developing flow, and fully developed flow in a pipe system. R·I·T MECE-251 12

Pressure distribution along a horizontal pipe including entrance region. R·I·T MECE-251 13

Next Steps L 8 Task 4 B: Please review the example problems on line. L 8 Task 4 C: Then, solve the review problem. L 8 Task 5: L 8 Task 6: Form groups and work on your case study. Take the Lesson 7 quiz. Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M. C. Potter and C. W. Somerton, Mc. Graw Hill Several Images are from Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi R·I·T MECE-251 14