General Information Lab -3 Bernoulli Equation Worksheet and Spreadsheets due Thursday by 12 noon Lab Reports due Tuesday by 4.00 pm

Objectives To investigate the validity of Bernoulli’s equation as applied to a tapering horizontal tube To determine if the variations in Static pressure head can be predicted by Bernoulli’s equation for tapering horizontal tube

Figure1: Test Section and Manometer tubes

Theory Bernoulli’s Equation: pressure head or static head = hs …………………….(1) If horizontal tube leveled correctly, then z1= z2, and equation 1 is then simplified to …………..(2) pressure head or static head = hs velocity head = hv = Total head =hT = hs + hv

Assumptions Bernoulli made some assumptions for his equation to work: Inviscid (no shear stress) Flow is steady Points 1 and 2 which you are comparing are in the same streamline Density of the fluid is constant System is not accelerating

Tube diameter (mm) a 25.0 b 13.9 c 11.8 d 10.7 e 10.0 f 25.0 76.08 55.46 15.8 7.4 2.9 5.0 f b c d e a Tube diameter (mm) a 25.0 b 13.9 c 11.8 d 10.7 e 10.0 f 25.0

Main Objective: Is Bernoulli’s equation validated? Why/ Why not? Any assumptions violated?   In the Data Sheet: hsm = static head measured and hTm = total head measured Measurement Points: Converging Diverging Static probe / Piezometer: measures static heads or pressure heads Pitot Probe: total head

Analysis Determine three flow rates ( High / Medium / Low) Calculate the velocity head at each cross section Calculate the best estimate of the total head hT in the tube Predict the variation of static pressure head hSc along the length of the tube - Compare measured static head to calculated static head value Graph values of hT htm hSm hsc hvc as a function of position along the tube Discuss the converging and diverging section and how the values change within them Discuss the effect of change in flow rate on observations Comment on validity of B.Eq. for convergent and divergent flows