# Bernoulli Equation Calculator

Bernoulli Equation Calculator may be quite useful when comparing two points on a streamline and calculating elevation, flow speed, and pressure at any of them. All you have to do is enter the necessary parameters into the application, and the unknown parameter will be discovered quickly.

### Equation of Bernoulli

A steady flow of an incompressible fluid is described by the Bernoulli equation. It signifies that the fluid's properties (such as density) do not vary over time. According to the Bernoulli principle, regardless of changes in the surroundings, the overall pressure of such a fluid (both static and dynamic) remains constant along the streamline.

This principle can be mathematically represented as follows **p + 0.5ρv² + ρhg = constant**

- where, p = pressure at the chosen point;
- ρ = density of the fluid (constant over time),
- v = flow speed at the given point,
- h = elevation of the chosen point, and
- g = acceleration due to gravity (on Earth typically taken as 9.80665 m/s²).

The terms 0.5v^2 and hg stand for kinetic energy per unit volume and hydrostatic pressure, respectively.

### Using a Streamline to Compare Two Points

To compare two points on a streamline, we can utilise Bernoulli’s Equation. We can write the expression as p₁ + 1/2ρv₁² + ρh₁g = p₂ + 1/2ρv₂² + ρh₂g because the overall pressure on a fluid is constant. If you know one of the five criteria, you can simply figure out the others.

### How to Calculate Flow Rate?

Using the Bernoullis Equation, you can quickly determine the volumetric and mass flow rates of a fluid. The flow rate is the number of cubic metres or kilogrammes that pass through one point of streamline in one hour.

You must first understand the area of a cross-section through which the fluid is flowing before you can calculate the flow rate. We need to know the diameter of pipes since we use them. The formula q = π * (d/2)² * v * 3600 can be used to compute the volumetric flow rate.

- Where, q = volumetric flow rate in m
^{3}/h, - d = pipe diameter in metres, and
- v = flow speed in m/s
- Because the flow rate is constant along the streamline, we can compare two places.
- q₁ = q₂ or π * (d₁/2) ² * v₁ = π * (d₂/2) ² * v₂

You may also compute the mass flow rate by multiplying the volumetric flow rate and the fluid density i.e. m = q * ρ

### Incompressible and Compressible Fluids

This Bernoulli equation calculator can only be used to study the flow of an incompressible fluid, as previously stated. It denotes that the fluid's density remains constant and that it cannot be squeezed under pressure. Nonetheless, compressible fluids can be represented by a similar equation. The effect of elevation change is ignored in this situation. The flow, however, is then influenced by a second parameter: the fluid's specific heat.

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### FAQs on Bernoulli Equation

**1. What is the most effective illustration of Bernoulli's principle?**

The form of an aeroplane wing, causes air to flow for a longer duration on top of the wing, causing air to travel faster, reducing air pressure and providing lift, when compared to the distance travelled, airspeed, and air pressure experienced beneath the wing.

**2. Is it possible to use the Bernoulli equation to describe rotating flow?**

In rotating flow, Bernoulli's equation works perfectly. Bernoulli's equation holds along a streamline and in the absence of significant viscosity dissipation.

**3. What are Bernoulli's equation's assumptions?**

The following conditions must be met to apply Bernoulli's equation: The flow has to be consistent. (Velocity, pressure, and density are constant at all times.) The flow must be incompressible - even if the pressure changes, the density along the streamline must remain constant.

**4. Is Bernoulli applicable to laminar flow?**

The total quantity of energy in a laminar flow is always the same, according to Bernoulli's principle for an ideal fluid. Potential energy owing to gravity, potential energy due to fluid pressure, and kinetic energy due to flow speed are the three components of this energy.