First Law of Flow Close to Nozzle

Energy Conservation Equation:

\[ h_1 + \frac{V_1^2}{2} + g \times z_1 = h_2 + \frac{V_2^2}{2} + g \times z_2 \]

Initial Enthalpy (h₁):

BTU/lb

Initial Velocity (V₁):

ft/s

Initial Elevation (z₁):

Final Enthalpy (h₂):

BTU/lb

Final Velocity (V₂):

ft/s

Final Elevation (z₂):

Energy Balance:

Definition: This equation applies the first law of thermodynamics (energy conservation) to fluid flow near a nozzle.

Purpose: It helps engineers analyze energy changes in fluid systems, particularly in nozzles, diffusers, and other flow devices.

The energy conservation equation:

\[ h_1 + \frac{V_1^2}{2} + g \times z_1 = h_2 + \frac{V_2^2}{2} + g \times z_2 \]

Where:

Explanation: The total energy (enthalpy + kinetic + potential) remains constant in steady flow without heat transfer or work.

Details: Proper energy analysis ensures efficient nozzle design, predicts flow behavior, and verifies system performance.

Tips: Enter values for initial and final states. The calculator shows the energy difference (should be zero for ideal conservation).

Q1: What does a non-zero balance indicate?
A: It suggests energy losses (friction, heat transfer) or gains (work input) in the system.

Q2: Why is elevation often negligible?
A: For small height differences, the g×z term is typically much smaller than enthalpy and kinetic terms.

Q3: What units should be used?
A: Consistent units are critical - BTU/lb for enthalpy, ft/s for velocity, and ft for elevation.

Q4: How does this apply to nozzles?
A: Nozzles convert enthalpy to kinetic energy (velocity increases while pressure decreases).

Q5: What if I only know some parameters?
A: You can solve for unknowns by setting other terms to zero or making reasonable assumptions.