Quiz 2 – 2013.11.27

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!!!

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

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.%.

Outline Mass Balance Energy Balance Momentum Balance

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

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

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

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)

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

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

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

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

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?

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

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

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

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

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