1. CHE315 2.7 Overall Energy Balance Overall Energy Balance Objectives 1.To be able to derive overall energy balance from the 1 st law of thermodynamics 2.To apply the OEB on engineering problems. 3.To be able to derive mechanical energy balance (MEB) from the 1 st law of thermodynamics 4.To apply the MEB on engineering problems 1 st Law of Thermodynamics:The Total Energy

2. CHE315 2.7 Overall Energy Balance Overall Energy Balance Rate of Output – Rate of Input + Rate of Accumulation = 0

3. CHE315 Overall Energy Balance 2.7 Overall Energy Balance  is usually 0.5 for laminar flow and close to 1.0 for turbulent flow (for more details, see section 2.7D)

4. Mechanical Energy Balance Equation But, the first law of thermodynamics gives: Substituting in the overall energy balance equation and replacing V with 1/  : Enthalpy is equal to: For incompressible liquids:

5. CHE315 2.7 Overall Energy Balance Overall Energy Balance Group Activity: Starting with the MEB equation, proof that, for a static incompressible fluid, the pressure difference can be expressed as: (P 2 -P 1 ) =  g (Z 1 -Z 2 ) =  gh

6. CHE315 2.7 Overall Energy Balance Overall Energy Balance For incompressible Fluids: For incompressible Static Fluids:

7. CHE315 2.7 Overall Energy Balance Overall Energy Balance For compressible Static Fluids:

8. CHE315 2.7 Overall Energy Balance Overall Energy Balance For compressible Static Fluids: Ideal Gas: pV = nRT  p/  = RT/M

9. CHE315 2.7G Bernoulli Equation Overall Energy Balance  No mechanical energy is added (Ws = 0)  No friction (  F = 0)  Turbulent flow  Incompressible fluid NNo mechanical energy is added (Ws = 0) NNo friction (  F = 0) TTurbulent flow IIncompressible fluid

10. CHE315 Mechanical Energy Balance MEB Equation: http://www.youtube.com/watch?v=e4uEFCtuNic

11. Example 2.7-4: Example 2.7-5: Example. 2.7-6: Example. 2.7-7:

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15. CHE315 Mechanical Energy Balance 2.6D Average Velocity 1. Define the average velocity mathematically. 2. Apply it to the following: A) v (x) = 5x + 2 B) v (r) = v max (1-(r/R) 2 )  (eq. 2.6-18) Where V max is the maximum velocity and R is the full radius of the pipe (take v and R as constants). 2.7D Kinetic Energy Velocity Correction Factor,  : 3. Integrate the kinetic energy, KE, to express KE in average velocity. 4. What is  ? 5. Prove that  equals 0.5 for laminar flow. 6. What is the value of  for turbulent flow? 2.7G Bernoulli Equation for MEB 7. State the Bernoulli Equation (BE). 8. In which case (conditions), the BE is applied?