Bernoulli Pressure Calculator

Calculate

Upstream pressure P₁ (Pa)

Fluid density ρ (kg/m³)

Upstream speed v₁ (m/s)

Downstream speed v₂ (m/s)

Enter values above to calculate

Calculate Reset

How it calculates

1

For horizontal flow (h₁ = h₂): P₁ + ½ρv₁² = P₂ + ½ρv₂²

2

P₂ = P₁ + ½ρ(v₁² − v₂²)

3

Faster flow → lower pressure

Formula

P₂ = P₁ + ½ρ(v₁² − v₂²)

Variable Table

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How to Use This Calculator

This bernoulli pressure calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.

Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.

Assumptions and Limits

The formula P₂ = P₁ + ½ρ(v₁² − v₂²) is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.

Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.

Worked Example

Common Mistakes

• Bernoulli assumes incompressible, non-viscous, steady flow
• This form assumes equal heights — add ρg(h₁−h₂) for height changes
• Faster flow means LOWER pressure (the basis of lift and Venturi meters)

Related

Frequently Asked Questions

Why does faster flow have lower pressure?

Energy conservation: as kinetic energy (½ρv²) rises, pressure energy must fall. This explains aerofoil lift and the Venturi effect.

What are Bernoulli's assumptions?

Incompressible, non-viscous (no friction), steady, streamline flow along a single streamline.