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Bernoulli's equation calculator

Basic fluid dynamics

online since 2015

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Bernoulli's principle calculator
Bernoulli's principle calculator

Bernoulli’s Principle Calculator – Analyze Fluid Flow Easily

The Bernoulli equation is one of the most important principles in fluid mechanics, helping engineers and scientists analyze flow problems efficiently. It describes the conservation of energy in a fluid stream, making it useful for a wide range of engineering applications, from aviation and hydraulics to pipe systems and fluid dynamics.

What Can You Calculate with Bernoulli’s Equation?

This is the expression of law of head conservation to the flow of fluid in a conduit or streamline and is known as Bernoulli equation:

Z1 + p1gρ1 + V122g = Z2 + p2gρ2 + V222g

where is: Z1,2 - elevation above reference level; p1,2 - absolute pressure; v1,2 - velocity; ρ1,2 - density; g - acceleration of gravity

With this Bernoulli’s principle calculator, you can determine various flow parameters, including:

  • ✅ Pressure – Measure how pressure changes along a streamline
  • ✅ Velocity – Calculate the speed of fluid at different points
  • ✅ Height (Elevation) – Find the height of fluid at different locations
  • ✅ Diameter – Determine the cross-sectional area of a pipeline

By knowing these parameters at one point in a stream, you can predict how they change at another point.

Understanding Bernoulli’s Equation – The Law of Head Conservation

If we neglect friction losses and assume no external energy is added or removed, the total energy in a fluid streamline remains constant. This means the total head (H)—which includes elevation head (Z), pressure head (p/ρg), and velocity head (v²/2g)—remains unchanged throughout the flow.

Real-World Applications of Bernoulli’s Equation

Bernoulli’s equation is widely used in various engineering fields, such as:

  • 🚀 Aerodynamics – Explains how airplane wings generate lift
  • 🔧 Piping Systems – Helps design water and gas pipelines
  • ⛽ Venturi Meters – Measures flow rates in pipes
  • 🏗 HVAC Systems – Optimizes airflow in ventilation systems

This calculator is also useful for pressure drop calculations, Venturi tube flow rate meters, orifice plate sizing, and more.

Start using the Bernoulli’s principle calculator to solve fluid flow problems with ease!

Action
Calculation setup
Press what to calculate
Conditions at position one
Dimensions at one
Flow rates
Conditions at position two
Dimensions at two
Fluid properties

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Description

p1 – pressure in position one
Static pressure of fluid in the point in which flow parameters are known – referent position
p2 – pressure in position two
Static pressure of fluid in the point in which flow parameters should be calculated
D1 - diameter in position one
Internal pipe or stream diameter in the point in which flow parameters are known
D2 - diameter in position two
Internal pipe or stream diameter in the point in which flow parameters should be calculated
V1 - velocity in position one
Flow velocity where flow diameter is D1 and where flow parameters are known
V2 - velocity in position two
Flow velocity where flow diameter is D2 and where flow parameters should be calculated
z1 – height in position one
Height or elevation of the fluid stream in the point in which flow parameters are known
z2 – height in position two
Height or elevation of the fluid stream in the point in which flow parameters should be calculated
q - volumetric flow rate
Fluid flow rate in terms of units of volume per unit of time. Considered to be constant
ṁ - mass flow rate
Fluid flow rate in terms of units of mass per unit of time. Considered to be constant
ρ - fluid inlet density
Density of fluid in terms of mass per unit of volume. Considered to be constant
Δp - pressure drop
Pressure difference between two points of stream line

Calculation setup

Select value to calculate. You should enter not selected one.
p2
calculate pressure in position two
z2
calculate height in position two
v2
calculate velocity in position two
Available only if "use flow rate q in the calculation" is selected. You should enter values for not selected one.
v1
calculate velocity in position one
D1
calculate diameter in position one
q
calculate flow rate
Available only if v2 calculation is not selected. You should enter values for not selected one.
v2
calculate velocity in position two
D2
calculate diameter in position two

Why Use This Bernoulli’s Principle Calculator?

This Bernoulli equation calculator helps you quickly analyze how fluid flow parameters change under different conditions. Use it to:

  • ✅ Understand stream property variations – See how flow parameters adjust when conditions change.
  • ✅ Calculate static pressure changes – Determine how pressure varies as fluid flows through pipes of different diameters.
  • ✅ Analyze pressure changes with elevation – Evaluate how height differences affect fluid pressure.

How Does This Calculator Work?

The Bernoulli equation is a fundamental tool in fluid mechanics, used to analyze and solve flow problems in engineering. It represents the balance of three types of energy in a fluid:

  • Static energy (Pressure) – The force exerted by the fluid.
  • Kinetic energy (Velocity) – The energy due to fluid motion.
  • Potential energy (Gravity) – The energy due to elevation.

Bernoulli’s Principle Explained

The Bernoulli equation states that the total energy of a fluid remains constant along a streamline, assuming no friction losses and no external energy input. As fluid velocity increases, static pressure or potential energy decreases.

This principle is widely used in engineering, including:

  • ✈ Aerodynamics – Wing design for airplanes to generate lift.
  • 🏎 Motorsports – Creating downforce in race cars for better grip.
  • 🚰 Hydraulics – Designing pipelines and fluid transport systems.

How to Use This Calculator?

This tool helps you calculate key flow parameters at any point in a fluid stream when values at another point are known.

Step-by-Step Calculation Process

  • 1️⃣ Define the known parameters at the first point (left side of the calculator).
  • 2️⃣ Select what you want to calculate at the second point (right side).
  • 3️⃣ Compute one or more of the following:
    • Pressure
    • Flow velocity
    • Stream diameter
    • Height (geodetic position)

Additionally, if volume flow rate is considered, you can determine:

  • Flow velocity at the start of the stream
  • Flow diameter at the start
  • Volume flow rate

When Is This Calculator Not Applicable?

This calculator is only valid for inviscid (frictionless) fluid flow and does not apply to conducting fluid flow, such as electrically conductive liquids.

Use this Bernoulli’s principle calculator to simplify complex fluid flow calculations and gain deeper insights into fluid dynamics!

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