1. Quiz 2 –

2. TIME IS UP!!! Questions What is the Reynolds number?
Differentiate the flow patterns observed in laminar flow from those in turbulent flow.
How does temperature affect the dynamic viscosity of a fluid?
TIME IS UP!!!

3. Overall Balances

4. Outline
Mass Balance
Energy Balance
Momentum Balance

5. Mass Balance
For an overall mass balance, no mass is being generated. Why?

6. Mass Balance
Imagine the control volume as having infinitesimal surfaces dA. We need to find the net outflow of mass across the control surface.

7. Mass Balance
For every dA element, a streamline of velocity vector v passes through it.

8. Mass Balance
For every dA element, a unit normal vector n exists.

9. Mass Balance
The component of velocity vector v in the direction of the unit normal vector n is given by:

10. Mass Balance
The rate of mass efflux through dA:

11. Mass Balance
What do we get when we integrate over the entire control surface?

12. Mass Balance POSITIVE: net outflow of mass
NEGATIVE: net inflow of mass
ZERO: ?

13. Mass Balance
Rate of mass outflow across control surface (and control volume):
Rate of mass accumulation in control volume:

14. Mass Balance

15. Overall Mass Balance

16. Overall Mass Balance
A well-stirred storage vessel contains kg of dilute methanol solution (xMetOH = 0.05). A constant flow of 500 kg/min of pure water is suddenly introduced into the tank and a constant rate of withdrawal of 500 kg/min of solution is started. These two flows are continued and remain constant. Assuming that the densities of the solutions are the same and that the total contents of the tank remain constant at 10,000 kg of solution, calculate the time for the alcohol content to drop to 1.0 wt.%.

17. Outline
Mass Balance
Energy Balance
Momentum Balance

18. Forms of Energy Possessed/Carried by fluid
Internal Energy
Potential Energy
Kinetic Energy
PV-work
Transferred between system and surroundings
Heat
Shaft work

19. Internal Energy (U) Intrinsic property of the fluid
Molecules in random motion

20. Potential Energy (mgz)
Position of the fluid with respect to an arbitrary reference plane

21. Kinetic Energy (mv2/2α) Due to fluid motion Correction factor, a
To account for velocity distribution
Ranges from 0.5 (laminar) to 1.0 (turbulent)

22. PV Work (PV)
Work done by surroundings to push the fluid into the system P S d

23. Heat (Q) Net heat passing through the boundary of the system
Positive if heat is transferred to the system from the surroundings
Negative if system to the surroundings
Excludes heat generated by friction

24. Shaft Work (Ws) Net work done on the system by the surroundings
Convention (IUPAC)
Positive if work done on the system
Negative if work done by the system

25. Total Energy Balance Energy balance from point 1 to point 2:
U1, v1, P1, V1, S1 Q z1
U2, v2, P2, V2, S2 Ws z2
Datum/reference plane

26. Total Energy Balance
Energy balance from point 1 to point 2:

27. Total Energy Balance
Water at 93.3°C is being pumped from a large storage tank at 1 atm abs at a rate of m3/min by a pump. The motor that drives the pump supplies energy at the rate of 1.49 kW. The water is pumped through a heat exchanger, where it gives up 704 kW of heat and is then delivered to a large open storage tank m above the first tank. What is the final temperature of the water to the second tank?

28. Mechanical Energy Balance
A modification of the total energy balance
- shaft work
- kinetic energy
- potential energy
- flow work (PV)
Does not include heat and internal energy.
- Why?
Energy converted to heat is lost work
- loss of mechanical energy by friction

29. Ideal Fluids Bernoulli Equation No shear stress; zero viscosity
For isothermal flow and Q=WS=0,
Bernoulli Equation

30. Bernoulli Equation Restrictions: Valid only for incompressible fluids
No devices that add/remove energy should be between points 1 and 2
No heat transfer occurring in the system
No loss of energy due to friction

31. Real Fluids Friction losses: SF (energy dissipation)
Total heat absorbed by the fluid
Total work done by fluid,
-W = -WS + SF
Additional work must be done by the fluid to overcome fluid friction

32. Real Fluids Note: energy per mass units kJ/kg or ft-lbf/lbm
For incompressible flow:
Derivation for incompressible flow energy balance skipped