Steady Flow Energy Equation for Nozzle

Steady Flow Energy Equation (Bernoulli's):

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

Enthalpy at Point 1 (h₁):

BTU/lb

Velocity at Point 1 (V₁):

ft/s

Elevation at Point 1 (z₁):

Enthalpy at Point 2 (h₂):

BTU/lb

Velocity at Point 2 (V₂):

ft/s

Elevation at Point 2 (z₂):

Equation Balance:

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1. What is the Steady Flow Energy Equation?

Definition: The Steady Flow Energy Equation (SFEE), also known as Bernoulli's equation for nozzles, describes the conservation of energy for fluid flow between two points in a system.

Purpose: It's used in thermodynamics and fluid mechanics to analyze energy changes in nozzles, diffusers, turbines, and other flow devices.

2. How Does the Equation Work?

The equation is expressed as:

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

Where:

\( h \) — Specific enthalpy (BTU/lb)
\( V \) — Velocity (ft/s)
\( g \) — Gravitational acceleration (32.174 ft/s²)
\( z \) — Elevation (ft)
Subscripts 1 and 2 refer to two points in the flow

Explanation: The equation states that the total energy (enthalpy + kinetic + potential) remains constant in steady flow.

3. Importance of the SFEE

Details: This equation is fundamental for designing and analyzing nozzles, determining exit velocities, and understanding energy transformations in fluid systems.

4. Using the Calculator

Tips: Enter values for any five parameters to solve for the sixth. The calculator will show the balance between both sides of the equation (should be zero for perfect energy conservation).

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Use consistent units: BTU/lb for enthalpy, ft/s for velocity, and ft for elevation.

Q2: When can I neglect elevation terms?
A: For horizontal flows or when elevation differences are small compared to other energy terms.

Q3: What does a non-zero balance indicate?
A: A non-zero result suggests either measurement errors, unaccounted losses, or invalid assumptions in your system.

Q4: How is this different from Bernoulli's equation?
A: This is the more general form that includes enthalpy, while Bernoulli's equation is specific to incompressible, isothermal flows.

Q5: What if my velocities are in different units?
A: Convert all velocities to ft/s before entering them into the calculator.