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 you should use this calculator?

Use this calculator to easily calculate how:

Stream properties are going to change when flow conditions are changing,
Static pressure is going to change when fluid flows through pipes with different internal diameters,
Pressure is going to change when flowing fluid changes its elevation,

Calculator description

Bernoulli equation is the most important equation for engineering analysis of flow problems. You can resolve many practical tasks by the direct implementation of the Bernoulli equation.

The equation represents the balance of fluid energy associated with its static energy (pressure), kinetic energy (velocity) and energy of the height of the fluid (gravity).

Bernoulli equation

Every single member, in Bernoulli equation on the left side of the above equation, represents specific energy contained in the unit of mass in the fluid stream. The first member is static energy (pressure), the second one is the kinetic energy (velocity), and the third one is potential energy (gravity). The constant on the right side of the above equation means that the sum of all three members is constant at any point in the fluid stream.

This behavior is Bernoulli's principle that states that when flow velocity is increasing, static pressure or potential energy is going to decrease.

Bernoulli's principle has application in wing design where the shape of a wing makes flow velocity change. As a result, a pressure difference is created on the upper and bottom surface area of the wing, resulting in the force pointing up, for airplanes (lifting up the plane), or down for racing cars (adding to the gravity in additional downforce for better grip).

How is the calculation executed?

With this calculator, you can calculate flow parameters like pressure, velocity, height, and diameter at any point of a stream if you know parameters in some other point of a stream.

The point of streamline where stream parameters are known is marked as position one (left side of the calculator), and the point in which you want to calculate stream parameters is marked as two (right side of the calculator). Parameters in point two that you can calculate are:

Pressure
Flow velocity
Stream diameter
Height (geodetic position)

If you select to use volume flow rate in calculations, you can select to calculate between:

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

When is this calculator not relevant?

This calculator is only valid for inviscid flow and non-conducting fluid flow.