In this Bernoulli calculator, we will show you how to find pressures and velocities in a fluid in just a few seconds.
We will also help you understand what Bernoulli’s equation is, and break down each part of the formula while we’re at it.
What is Bernoulli’s principle?
How does it relate pressure, velocity, and height in a fluid?
How can you apply it to real-world problems? We will also show you practical examples to make it super easy to understand.
Bernoulli Calculator (ΔP, v₁, v₂)
Understanding Bernoulli’s Equation
Bernoulli’s equation is one of the most important principles in fluid dynamics. It relates the pressure, velocity, and height of a fluid in steady, incompressible, and frictionless flow. The equation is written as:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Explanation of Terms
- P → Pressure in the fluid (Pa or kPa)
- ρ → Density of the fluid (kg/m³)
- v → Velocity of the fluid (m/s)
- g → Acceleration due to gravity (9.81 m/s²)
- h → Height or elevation of the fluid (m)
This equation states that the total energy (pressure energy + kinetic energy + potential energy) of the fluid remains constant along a streamline.
Real World Applications of Bernoulli’s Equation
| Application | Description |
|---|---|
| Aircraft Wings (Lift) | Faster air above the wing reduces pressure, creating lift that allows planes to fly. |
| Venturi Meters | Used to measure flow rate by comparing pressure difference in a narrowed section. |
| Carburetors | Fuel mixes with air in engines because of pressure drop in the venturi section. |
| Blood Flow in Arteries | Bernoulli’s principle helps explain variations in blood pressure in constricted vessels. |
| Chimneys | Wind moving over the chimney top reduces pressure and helps draw smoke upward. |
Example Problem: Water Flow Through a Pipe
Problem: Water flows through a horizontal pipe. At point 1, the pressure is 200 kPa and velocity is 2 m/s. At point 2, the pressure drops to 150 kPa. The fluid density is 1000 kg/m³. Find the velocity at point 2.
Step-by-Step Solution
- Step 1: Given Data
P₁ = 200 kPa, P₂ = 150 kPa, v₁ = 2 m/s, ρ = 1000 kg/m³, h₁ = h₂ (horizontal pipe → no height difference). - Step 2: Apply Bernoulli’s Equation
P₁ + ½ρv₁² = P₂ + ½ρv₂² - Step 3: Rearrange for v₂
v₂ = √[(2/ρ)(P₁ – P₂) + v₁²] - Step 4: Substitution
v₂ = √[(2/1000)(200,000 − 150,000) + (2²)]
v₂ = √[(2/1000)(50,000) + 4]
v₂ = √[100 + 4] = √104 - Step 5: Final Answer
v₂ ≈ 10.20 m/s
✅ This example shows how Bernoulli’s principle predicts the increase in velocity when pressure decreases in a fluid system.
Limitations of Bernoulli’s Equation
Incompressible Flow
Bernoulli’s equation assumes fluid density is constant. It’s not valid for compressible fluids at high velocities (like gases).
No Viscosity
The equation ignores fluid friction. It’s inaccurate for flows with significant viscous effects or turbulence.
Steady Flow Only
Bernoulli’s equation is only valid for steady flow, where velocity and pressure at a point do not change with time.
Along a Streamline
The equation applies along a single streamline. It may not hold between streamlines in rotational or complex flows.
Neglects Energy Losses
It does not account for energy losses due to friction, heat, or pumps. Real systems often require corrections.
FAQs
What is Bernoulli’s equation?
In this Bernoulli calculator, we will show you how pressure, velocity, and height in a fluid are connected. It helps you see how energy moves along a streamline in seconds.
What is the difference between pressure, velocity, and elevation head?
Pressure head comes from the fluid’s pressure, velocity head from its speed, and elevation head from its height. Together, they show the total energy of the fluid.
Can Bernoulli’s equation be used for all fluids?
No. It works only for incompressible, non-viscous fluids in steady flow along a streamline.