CBE 150A – Transport Spring Semester 2014 Macroscopic Mechanical Energy Balance

CBE 150A – Transport Spring Semester 2014 Macroscopic Energy Balance Assume: Energy is conserved Steady State Accumulation = In – Out + {Generation – Consumption}

CBE 150A – Transport Spring Semester Via Mass Flow KE PE Int. Energy 2.Heat Transfer (Q) Conduction Radiation 3.Work on or by System (W) Pumps Compressors Macroscopic Energy Balance How may Energy enter System? Note: Q and W positive for energy into system

CBE 150A – Transport Spring Semester 2014 Energy Transferred via Mass Flow Convective Term Internal Energy Kinetic Energy Potential Energy Flow Work Term Pressure work required to push fluid through system

CBE 150A – Transport Spring Semester 2014 Overall Mechanical Energy Balance

CBE 150A – Transport Spring Semester 2014 Mechanical Energy Balance

CBE 150A – Transport Spring Semester 2014 Variable Velocity at Cross Section Again integrate across cross section and introduce correction factor, , to allow use of average velocity.

CBE 150A – Transport Spring Semester 2014 Variable Velocity at Cross Section Laminar Flow Parabolic Flow α =α = Turbulent Flow Plug Flow α ≈α ≈ 2

CBE 150A – Transport Spring Semester 2014 MEB with Correction for Variable Velocity Historical Note : Though this result is often called the Bernoulli equation, Bernoulli actually only considered W = h f = 0. ˆ Daniel Bernoulli ( )

CBE 150A – Transport Spring Semester 2014 Example 1 Determine the sign of the individual contributions to the MEB for the following:

CBE 150A – Transport Spring Semester 2014 Cessna 172 Example 2 - Bernoulli and the airplane

CBE 150A – Transport Spring Semester 2014 Cessna 172 Data Gross weight = 2300 lbsGross weight = 2300 lbs Normal cruising speed = 65 mphNormal cruising speed = 65 mph Wing surface area = 160 ft 2Wing surface area = 160 ft 2 Upper wing path length = X lower wing path lengthUpper wing path length = X lower wing path length

CBE 150A – Transport Spring Semester 2014

Mechanical Energy Balance 10 minute problem Water with a density of 998 kg/m 3 is flowing at a steady mass rate through a uniform diameter pipe. The Reynolds number in the pipe is approximately The pump supplies J/kg of fluid flowing through the pipe. Given the other conditions shown on the diagram, calculate the viscous dissipation, h f, in the pipe system.