Velocity At Section 1 From Bernoulli Equation Calculator

Bernoulli Equation:

\[ V_1 = \sqrt{2 \cdot g \cdot \left( \frac{P_2}{\gamma_f} + 0.5 \cdot \frac{V_2^2}{g} + Z_2 - Z_1 - \frac{P_1}{\gamma_f} \right)} \]

Pressure at Section 2 (P₂):

Specific Weight of Liquid (γ_f):

N/m³

Velocity at Point 2 (V₂):

m/s

Datum Height at Section 2 (Z₂):

Datum Height at Section 1 (Z₁):

Pressure at Section 1 (P₁):

Velocity at Point 1 (V₁):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Bernoulli Equation?

The Bernoulli Equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a flowing fluid. It states that for an incompressible, inviscid fluid, the total energy along a streamline remains constant.

2. How Does the Calculator Work?

The calculator uses the Bernoulli Equation:

\[ V_1 = \sqrt{2 \cdot g \cdot \left( \frac{P_2}{\gamma_f} + 0.5 \cdot \frac{V_2^2}{g} + Z_2 - Z_1 - \frac{P_1}{\gamma_f} \right)} \]

Where:

\( V_1 \) — Velocity at Point 1 (m/s)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( P_2 \) — Pressure at Section 2 (Pa)
\( \gamma_f \) — Specific weight of liquid (N/m³)
\( V_2 \) — Velocity at Point 2 (m/s)
\( Z_2 \) — Datum height at Section 2 (m)
\( Z_1 \) — Datum height at Section 1 (m)
\( P_1 \) — Pressure at Section 1 (Pa)

Explanation: The equation calculates the velocity at point 1 based on energy conservation principles, considering pressure energy, kinetic energy, and potential energy differences between two points in the flow.

3. Importance of Velocity Calculation

Details: Accurate velocity calculation is crucial for designing fluid systems, analyzing pipe networks, determining flow rates, and ensuring proper system performance in various engineering applications.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Pressure in Pascals, specific weight in N/m³, velocity in m/s, and height in meters. Ensure all values are positive and specific weight is greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the Bernoulli Equation?
A: The equation assumes steady flow, incompressible fluid, inviscid flow, and flow along a streamline.

Q2: When is this equation not applicable?
A: Not applicable for compressible fluids, viscous flows, flows with significant energy losses, or across streamlines.

Q3: What is specific weight and how is it different from density?
A: Specific weight is weight per unit volume (N/m³), while density is mass per unit volume (kg/m³). They are related by γ = ρ·g.

Q4: Can this be used for gases?
A: Only for low-speed gas flows where compressibility effects are negligible (Mach number < 0.3).

Q5: What are typical velocity ranges in pipe flow?
A: Typically 1-5 m/s for water systems, but varies based on application and pipe size.