ES 202 Fluid and Thermal Systems Lecture 11 Pipe Flow Major and Minor Losses 1 7 2003 Assignments Reading Cengel Turner Section 12 6 Homework 12 72 12 79 in Cengel Turner Lecture 11 ES 202 Fluid Thermal Systems 2 Road Map of Lecture 11 Announcements Recap from Lecture 10 modified Bernoulli s equation concept of viscosity Major losses friction factor Moody diagram flow chart to determine friction factor non circular ducts Minor losses Lecture 11 ES 202 Fluid Thermal Systems 3 Announcements Lab 2 this week in Olin 110 from 7th to 9th period Section 5 meets tomorrow Section 6 meets on Friday Post lab group schedule 2 lab sessions over the 3 hour period 1st session starts at 1 35 pm 2nd session starts at 2 55 pm Homework assigned on Monday and Tuesday will be due on Friday by 5 pm Solutions to all homework sets are available at reserve library under Mayhew Lecture 11 ES 202 Fluid Thermal Systems 4 Introducing the Friction Factor Recall results from dimensional analysis of pipe flow VD l P g1 2 V D D From hindsight cast the above equation as VD P l g 2 2 V D D V 2 l P f 2 D friction factor 2 The friction factor as defined only depends Reynolds number relative roughness Lecture 11 ES 202 Fluid Thermal Systems 5 How to find the friction factor Since the friction factor only depends on two independent groups it is simple to represent its variation with multiple contour lines on a 2D plane Display and describe the Moody diagram representation of two groups partition of different flow regimes independent of surface roughness in laminar regime insensitivity at high Reynolds number in turbulent regime The whole problem of finding the pressure drop across piping system is reduced to finding the friction factor on the Moody diagram Lecture 11 ES 202 Fluid Thermal Systems 6 Flow Chart Find Reynolds number fluid properties geometry D flow speed V Laminar Re 2300 Re V D Turbulent Re 2300 Find relative roughness 64 f Re Look up Moody diagram Lecture 11 ES 202 Fluid Thermal Systems 7 Example on Moody Diagram Example Water flows in a commercial steel pipe pipe diameter 10 cm mean speed 10 m s pipe length 3 m Find the pressure drop between the entrance and exit of the pipe What will be the difference if water is replaced by oil What if the pipe duct is not circular needs a representative length measure of the duct cross section notion of hydraulic diameter example with a rectangular duct 4 Ac Dh perimeter extra factor of 4 recovers the diameter for a circular pipe Lecture 11 ES 202 Fluid Thermal Systems 8 Alternative Method The Moody Diagram is a handy way to represent data on friction factor If reading off the diagram does not seem appealing the same amount of data can be curve fitted to give an explicit functional relationship between friction factor Reynolds number and relative roughness The Haaland formula offers another alternative 1 11 1 6 9 D 1 8 log f Re 3 7 Lecture 11 ES 202 Fluid Thermal Systems 9 Friction Factor Viscous Stress and Head Loss Central question is there a relationship between friction factor viscous stress head loss Consider the following pipe flow problem 1 2 Perform a mechanical energy balance for the above system Perform a momentum balance for the above system What can you conclude from the above analyses If the pipe is tilted at an angle of 30 deg with the horizontal what will be the difference in your analysis Lecture 11 ES 202 Fluid Thermal Systems 10