Control Volume Analysis and Energy Conservation

Reynolds Transport Theorem

Links system analysis to control volume analysis.

Extensive Property

Property changing with system parts considered.

Intensive Property

Property per unit mass in control volume.

Differential Volume (Vd)

Infinitesimal volume within the control volume.

Differential Area (dA)

Infinitesimal area of the control surface.

Unit Vector (n̂)

Outward normal direction to area dA.

Velocity Vector (V)

Fluid velocity relative to control surface.

Mass Flow Rate (ṁ)

Mass passing through a section per time.

Conservation of Mass

Mass in equals mass out for control volume.

Mass Flux

Mass flow rate per unit area.

Volume Flow Rate (VA)

Volume passing through a section per time.

One-Dimensional Flow

Flow with velocity parallel to n̂.

Steady State Operation

Inlet and outlet mass flow rates equal.

Conservation of Energy

Energy in equals energy out for control volume.

Power due to Flow Work

Work done by fluid flow in control volume.

Transient Process

System changes over time, includes time derivatives.

Steady State Assumption

Neglect time derivatives under steady conditions.

Heat Transfer (Q̇)

Energy transfer due to temperature difference.

Work Done (Ẇ)

Energy transfer due to force application.

Control Volume (CV)

Region in space for analysis of fluid flow.

Control Surface (CS)

Boundary of the control volume.

Substantial Derivative

Rate of change of a property in flow.

Net Rate of Flow

Total flow through control surface area.

Differential Area Normal

Direction of dA, crucial for flow calculations.

Mass Rate Balance

Equation relating mass flow rates at inlets and outlets.

Energy Rate Equation

Relates energy inflow and outflow in control volume.

Inlet and Exit Terms

Parameters defining flow entering and leaving CV.

Neglected Terms

Terms omitted under specific assumptions in analysis.