ES 202 Fluid and Thermal Systems Lecture 8: Application of Bernoulli’s Equation (12/17/2002)

Assignments Reading: Homework: Cengel & Turner Section 12-1, 12-2, 9-4 11-43, 11-45, 11-63, 11-70 in Cengel & Turner

Road Map of Lecture 8 Quiz Review on Lecture 7 Some insights into Bernoulli’s equation Examples and applications Pitot-static tube Lift on airfoil, tennis ball Modified Bernoulli’s equation

Quiz True/False When a fluid is in static equilibrium, the only force acting on the fluid is pressure. Explain your answer. Explain with clarity the cause of buoyancy force on an object immersed in a fluid

Review on Lecture 7 Energy carried by a fluid element can be classified into: mechanical energy thermal energy List the difference(s) between mechanical and thermal energy: mechanical energy can freely change its form among various components mechanical energy can be converted to work completely thermal energy cannot be converted to work completely In what form(s) can mechanical energy exist? flow work ( P / r ) kinetic energy ( V2 / 2 ) potential energy ( g z ) Mechanical Energy Mechanical Work Thermal Energy

Review on Lecture 7 (cont’d) Write down the (steady) Bernoulli’s equation. Describe your interpretation of the equation. mechanical energy can be freely interchanged among its various forms as the fluid element moves along its path Name some assumption(s) behind the Bernoulli’s equation. steady no shaft work or friction small change in thermal energy constant density along flow direction

Some Insights From statics to dynamics Similarity and difference between solid and fluid in addition to K.E. and P.E., there is a flow work component in a fluid system In compressible flow, there is interchange between thermal and mechanical energy (appreciable temperature change)

Different Forms of Bernoulli’s Equation Pressure form definition of stagnation pressure “Head” form (dimension of length)

Pressure Variation Along Flow Direction Consider the following convergent flow device: air air d1 d2 d1 d2 Dh Dh Picture (a) Picture (b) Which configuration represents the correct physics? Explain your choice. If d1 = 10 cm, d2 = 5 cm and air is going at 0.1 m3/sec, determine the value of Dh. What kind of flow device is it? If the flow direction is reversed, what do you expect to be the difference?

Pitot-Static Tube Principle behind a Pitot-Static tube: V d Dh A B fluid column A measures the stagnation pressure (why?) fluid column B measures the static pressure (why?) according to the Bernoulli’s equation, their difference equals the dynamic pressure: Pass out hardware of Pitot-static tube and describe position of holes

Lift on Airfoil and Tennis Ball destroy the flow symmetry between the lower and upper surfaces show visualization Spin on a tennis ball what does the spin do to the tennis ball? Show visualization of flow over airfoil from MMFM. Slowly increase angle of attack. Point out regions governed by Bernoulli’s and regions violating Bernoulli’s

“Modified” Bernoulli’s Equation What if fluid friction causes some losses in the system, can I still apply the Bernoulli’s equation? Recall the “conservation of energy” concept from which we approach the Bernoulli’s equation Remedy: introduce a “head loss” factor