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Transport Process
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Uploaded: 6 years ago
Category: Chemical Engineering
Type: Lecture Notes
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Filename: 03.pptx
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Transcript
Quiz 2 – 2013.11.27
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!!!
Overall Balances
Outline
Mass Balance
Energy Balance
Momentum Balance
Mass Balance
For an overall mass balance, no mass is being generated. Why?
Mass Balance
Imagine the control volume as having infinitesimal surfaces dA. We need to find the net outflow of mass across the control surface.
Mass Balance
For every dA element, a streamline of velocity vector v passes through it.
Mass Balance
For every dA element, a unit normal vector n exists.
Mass Balance
The component of velocity vector v in the direction of the unit normal vector n is given by:
Mass Balance
The rate of mass efflux through dA:
Mass Balance
What do we get when we integrate over the entire control surface?
Mass Balance
POSITIVE: net outflow of mass
NEGATIVE: net inflow of mass
ZERO: ?
Mass Balance
Rate of mass outflow across control surface (and control volume):
Rate of mass accumulation in control volume:
Mass Balance
Overall Mass Balance
A well-stirred storage vessel contains 10000 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.%.
Overall Mass Balance
Outline
Mass Balance
Energy Balance
Momentum Balance
Possessed/Carried by fluid
Internal Energy
Potential Energy
Kinetic Energy
PV-work
Transferred between system and surroundings
Heat
Shaft work
Forms of Energy
Intrinsic property of the fluid
Molecules in random motion
Internal Energy (U)
Position of the fluid with respect to an arbitrary reference plane
Potential Energy (mgz)
Due to fluid motion
Correction factor, a
To account for velocity distribution
Ranges from 0.5 (laminar) to 1.0 (turbulent)
Kinetic Energy (mv2/2?)
Work done by surroundings to push the fluid into the system
P
S
d
PV Work (PV)
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
Heat (Q)
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
Shaft Work (Ws)
Energy balance from point 1 to point 2:
Datum/reference plane
U1, v1, P1, V1, S1
U2, v2, P2, V2, S2
z1
z2
Q
Ws
Total Energy Balance
Energy balance from point 1 to point 2:
Total Energy Balance
Water at 93.3°C is being pumped from a large storage tank at 1 atm abs at a rate of 0.189 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 15.24 m above the first tank. What is the final temperature of the water to the second tank?
Total 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
Mechanical Energy Balance
No shear stress; zero viscosity
For isothermal flow and Q=WS=0,
Bernoulli Equation
Ideal Fluids
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
Bernoulli Equation
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
Real Fluids
Note: energy per mass units
kJ/kg or ft-lbf/lbm
For incompressible flow:
Real Fluids
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