1. Flow Devices Thermodynamics Professor Lee Carkner Lecture 10

2. PAL # 9 Control Volumes  Air flow through pipe  Find diameter from area, find area from mass flow rate (=  AV)  v = RT/P = (0.287)(350)/(300) =  A = m’ v /V = (18/60)(0.3349)/(25) = 0.004018 m 2  D = (4A/  ) ½ = (4(0.004018) /  ) ½ =

3. PAL # 9 Control Volumes  Rate of flow energy = m’P v  W’ flow = (18/60)(300)(0.3349) =  Energy transport by mass:  E’ mass = m’(h+ke) = m’(c p T + ½V 2 )  E’ mass = (18/60)[(1.008)(350) + (½)(25) 2 (1/1000)] =  Neglecting ke  E’ mass = m’h = m’c p T = (18/60)(1.005)(350) = 105.84 kW 

4. Steady-Flow Devices   E mass,in = E mass,out W’ in + Q’ in + m’ in (h + V 2 /2 + gz) in = W’ out + Q’ out + m’ out (h + V 2 /2 + gz) out   but mass and energy are conserved in each

5. Nozzles  V’ 1 = V’ 2 V 1 A 1 = V 2 A 2 V 1 /V 2 = A 2 /A 1  Velocity changes opposite to pipe diameter change   Small to large opening, velocity decreases, diffuser   But basic idea holds for gases

6. Working With Nozzles  Nozzles increase velocity at the expense of pressure   Other energies usually negligible   Can often use ideal gas law and enthalpy tables to solve problems  n.b.  Simplified nozzle equation  h 1 +½V 2 1 = h 2 +½V 2 2

7. Turbines  The flow work pushes the fluid into a control volume   Change enthalpy into work   Change work into enthalpy   Q ~  PE ~ 0

8. Working with Turbines   but the change in kinetic energy is normally small compared to enthalpy change   Simplified turbine equation:  W’ = m’(  h +  ke)

9. Throttling Valve  A throttling valve restricts flow causing a pressure drop   So conservation of energy gives us h 1 = h 2   A throttling process shifts energy between internal and flow energies   Simplified throttling equation:  u 1 + P 1 v 1 = u 2 + P 2 v 2

10. Mixing Chamber   Usually Q ~ W ~  KE ~  PE ~ 0   Simplified mixing chamber equations:  m’ 1 + m’ 2 = m’ 3  m’ 1 h 1 + m’ 2 h 2 = m’ 3 h 3

11. Heat Exchanger   Generally, W ~  PE ~  KE ~ 0   This means that mass flow and enthalpy are the only important variables

12. Working With Heat Exchangers   Fluid B enters at 3 and exits at 4  Mass conservation:   m’ 3 = m’ 4 = m’ B  Energy conservation   Simplified heat exchanger equation:  m’ A (h 1 -h 2 ) = m’ B (h 4 -h 3 )

13. Unsteady Flow  Unsteady flow involves changes within the control volume  Example:  Mass within the flow volume increases   Deal with changes in properties with time rather than rates 

14. Uniform Flow  If the input and output flow is steady and only the properties of the control volume change, it is a uniform flow process  Q-W = (mh) out – (mh) in + (m 2 u 2 -m 1 u 1 ) system  Where:   mh is the sum of all the enthalpies in or out 

15. Next Time  No class Friday  For Monday:  Read: 6.1-6.4  Homework: tba