1. Fluid Friction

2. Outline Bernoulli ’ s Equation The Pressure-Drop Experiment Laminar Flow Turbulent Flow The Three Friction Factor Problems Computer Methods

3. Outline (Continued) Fitting Losses Enlargement and Contractions More Complex Problems Economic Pipe Diameter Flow Around Submerged Objects

4. Objectives Know the different types of flow. Calculate fluid friction and apply Bernoulli ’ s equation to calculate pressure drop. Formulate flow problems in complex piping systems.

5. Objectives (Continued) Estimate the Economic Pipe Diameter. Solve flow problems around submerged objects.

6. Summary Laminar flow: Re<2100 (momentum transport by molecular motions) Turbulent flow: Re>4000 (sufficiently far from the walls, momentum transport is mainly by eddies) Bernoulli ’ s equation

7. Summary (Continued) Total friction loss The economic pipe diameter is determined by minimizing the total cost. For complex systems, Bernoulli ’ s equation is applied for each section, along with the continuity equation for each node.

8. Summary (Continued) Calculations are in general by trial-and- error, requiring the use of computers. Drag force The velocity of the particle is calculated by making a force balance.