Ch. 4 The first law of thermodynamics: Control Volume

4.1 Thermodynamic analysis of control volumes Control Surface Steady: No change with time  Unsteady, Transient Uniform: No change with location

Thermodynamic analysis of control volumes Conservation of Mass Principle Mass and Volume Flow Rates Mass Flow Rate: Amount of mass flowing through a cross section per unit time Total mass entering CV mass leaving Net change In mass within - =

Mass Flow Rate It is proportional to the cross-sectional area A, the density , the velocity V of the fluid. Vn: Velocity component normal to dA Vav : Average fluid velocity normal to A

Volume Flow Rate Volume of the fluid flowing through a cross-section per unit time The mass and volume flow rate:

Conservation of Energy Principle In closed system Net heat(Q) – Work(W) = Energy change(E) When mass enters or leaves a control volume, the energy increase or decrease within the control volume.

Conservation of Energy Principle The conservation of energy equation for a control volume The energy required ot push fluid into or out of a control volume is called the flow work, or flow energy.

Flow Work If the fluid pressure is P and the cross-sectional area of the fluid element A, the force applied on the fluid element by the imaginary piston F = PA. The work done in pushing the fluid element Wflow = FL = PAL =PV

Total Energy of a Flowing Fluid Three Parts of total energy of a simple compressible system: Internal, Kinetic, and Potential energies. On a unit mass basis, Total energy of a flowing fluid on a unit mass basis ()

Total Energy of a Flowing Fluid By the definition of enthalpy (h = u + Pv): : Methalphy Metaenthalpy, which means beyond enthalphy

Steady Flow Process Process during which a fluid flows through a control volume steadily Steady flow devices: Turbines, compressors, and nozzles operating for long periods of time under the same conditions Steady means no change with time.

Steady Flow Process No properties (volume, mass, total energy) within the control volume change with time. The boundary work is zero for steady flow systems since Vcv is constant. No properties change at the boundaries of the control volume with time. The mass flow rate of the fluid at an opening must remain constant during a steady flow process. The heat and work interactions between a steady flow system and its surrounding do not change with time

Conservation of Mass During a steady flow process, the total amount of mass in CV does not change with time. (Entering Mass = Leaving Mass)

Conservation of Energy Water Heater under steady operation: The water stream will experience an increase in its total energy as it flows through the water heater, which is equal to the electric energy supplied to the water minus the heat losses.

Conservation of Energy  = h + ke + pe

Single-Stream Steady-Flow Systems One inlet and one exit Mass flow rate through the entire CV remains constant For unit-mass basis

Single-Stream Steady-Flow Systems If Then Rate of heat transfer b/w CV and its surroundings = Power (work done per unit time)

Some Steady-Flow Engineering Device Nozzles and Diffusers Jet engines, rockets, spacecraft, garden hoses Nozzle: Device to increase the velocity of a fluid Diffuser: Device to increase the pressure of a fluid by slowing it down.

Some Steady-Flow Engineering Device Turbines Steam, gas, hydroelectric power plants As the fluid passes through the turbine, work is done against the blades which are attached to the shaft. Compressors Device to increase the pressure of a fluid

Some Steady-Flow Engineering Device Throttling Valves Adjustable valves, capillary tubes, porous plugs Any kind of flow-restricting devices that cause a significant pressure drop in the fluid.

Some Steady-Flow Engineering Device Heat Exchangers Devices to exchange heat with mixing of two moving fluid streams. Double-tube (tube and shell) heat exchanger

Some Steady-Flow Engineering Device Pipe and Duct Flow Transport of liquids or gases Flow through a pipe or a duct usually satisfies the steady flow conditions except the transient start-up and shut-down periods