Bernoulli Pressure Calculator

Enter Bernoulli Values

Calculation target

Known pressure

Known pressure unit

Output pressure unit

Fluid density

Density unit

Velocity at point 1

Velocity 1 unit

Velocity at point 2

Velocity 2 unit

Elevation at point 1

Elevation 1 unit

Elevation at point 2

Elevation 2 unit

Gravity

Use m/s².

Head loss

Head loss unit

Added pump head

Added head unit

Formula Used

The calculator uses the extended Bernoulli equation between two stations:

P1 + 0.5ρv1² + ρgz1 + ρghA = P2 + 0.5ρv2² + ρgz2 + ρghL

For pressure at point 2:

P2 = P1 + 0.5ρ(v1² - v2²) + ρg(z1 - z2) + ρg(hA - hL)

For pressure at point 1:

P1 = P2 + 0.5ρ(v2² - v1²) + ρg(z2 - z1) + ρg(hL - hA)

Here, P is pressure, ρ is density, v is velocity, g is gravity, z is elevation, hA is added pump head, and hL is head loss.

How to Use This Calculator

Select whether you want to calculate pressure at point 1 or point 2.
Enter the known pressure and choose its unit.
Add fluid density, velocity values, and elevation values.
Enter gravity, head loss, and added pump head if needed.
Select the output pressure unit.
Press the calculate button to show the result above the form.
Use the CSV or PDF button to save the calculation.

Example Data Table

Case	P1	ρ	v1	v2	z1	z2	Head Loss	Added Head	Purpose
Water pipe	200 kPa	1000 kg/m³	2 m/s	5 m/s	10 m	4 m	0.5 m	0 m	Nozzle pressure check
Pump line	150 kPa	998 kg/m³	1.5 m/s	3 m/s	2 m	15 m	2 m	20 m	Discharge pressure estimate
Oil flow	35 psi	55 lb/ft³	4 ft/s	9 ft/s	12 ft	5 ft	1 ft	0 ft	Pressure drop review

Bernoulli Pressure Calculation Guide

Why Bernoulli Pressure Matters

Bernoulli pressure calculations help estimate how pressure changes along a flowing stream. The method links pressure energy, velocity energy, and elevation energy. It works best for steady flow, nearly incompressible fluids, and points placed on the same streamline. Engineers often use it for water lines, tanks, nozzles, siphons, and simple pipe checks.

Advanced Inputs

This calculator improves the basic equation by allowing unit choices, head loss, and added head. Head loss represents energy removed by friction, bends, valves, entrances, or fittings. Added head represents energy supplied by a pump. Both terms make the result more realistic than a frictionless classroom example.

Input Quality

Use consistent physical assumptions before trusting any answer. The fluid density should match the actual liquid or gas condition. Water near room temperature is often close to 1000 kg per cubic meter. Oil, fuel, and air need different density values. Gravity may also change slightly by location, but 9.80665 m/s² is a common standard value.

Velocity and Elevation Effects

Velocity has a strong effect because it is squared. A small velocity change can create a large pressure change. Elevation also matters. A higher point usually has lower static pressure when other terms stay similar. A lower point can gain pressure from gravity head.

Reading the Result

The result may be positive or negative, depending on the selected reference and output unit. Negative gauge values can occur in suction zones. Absolute pressure should not be allowed below zero in real systems. Check vapor pressure when cavitation is possible.

Accuracy Notes

For accuracy, measure station heights from one common datum. Use centerline elevations for pipes. Use free surface elevation for tanks. Keep pressure types consistent throughout the form. Do not mix gauge pressure at one station with absolute pressure at another. When comparing results, watch unit conversions carefully. Rounded display values may hide small pressure differences, so keep the detailed values for records.

Engineering Use

This tool is useful for first estimates and educational checks. It does not replace detailed pipe network software. Complex systems may require minor loss coefficients, Reynolds number analysis, pump curves, compressibility corrections, and measured field data. Treat the final value as a calculated estimate. Review each input, compare with known limits, and document every assumption for safe engineering decisions.

FAQs

1. What does this calculator find?

It calculates pressure at one point in a flowing system when the pressure at another point is known. It also shows pressure change, pressure head, dynamic term, elevation term, loss term, and total head values.

2. Can I use gauge pressure?

Yes. Gauge pressure can be used if every pressure value in the calculation follows the same reference. Do not mix gauge and absolute pressure in the same Bernoulli setup.

3. What is head loss?

Head loss is energy removed from the flow by friction, fittings, valves, bends, entrances, and exits. It lowers the downstream pressure when flow moves from point 1 to point 2.

4. What is added pump head?

Added pump head is energy supplied to the fluid by a pump. It increases available pressure energy and can offset elevation rise, velocity increase, and friction loss.

5. Why does velocity affect pressure strongly?

Velocity is squared in the dynamic pressure term. Because of that, a small velocity increase can create a significant static pressure decrease, especially in nozzles or narrowed pipe sections.

6. Can this be used for gases?

It can be used for rough checks when density is nearly constant. For high-speed gas flow or large pressure changes, compressible flow methods are more suitable.

7. Why can the result be negative?

A negative gauge result means the calculated pressure is below atmospheric pressure. A negative absolute pressure is not physically valid and indicates wrong assumptions or input values.

8. Is this enough for final design?

No. Use it for estimates, study, and quick checks. Final design may need pipe roughness, minor losses, pump curves, safety factors, codes, and field validation.