Prandtl probe calculator

Description

p_t - total (stagnation) pressure

Measured pressure of the stream when flow velocity is brought to zero isentropically, in the center of the Prandtl probe

p_d - dynamic pressure

Differential pressure calculated as the difference between the total (stagnation) and the static pressure.

p - static pressure

Measured pressure of the flow without the affect of the fluid movement (kinetic) energy

ρ - fluid density

Mass per unit of volume

R - gas constant

Gas constant in terms of energy per unit of mass and temperature, for gas density calculation using ideal gas state equation

κ - isentropic coefficient

Specific heat ratio

T - temperature

Fluid temperature for gas density calculation based on the ideal gas state equation

q - volumetric flow rate

Fluid flow rate in terms of units of volume per unit of time

ṁ - mass flow rate

Fluid flow rate in terms of units of mass per unit of time

V - velocity

Flow velocity in terms of units of distance per unit of time

c - speed of sound

Sound speed for given gas and actual conditions in terms of pressure, density and temperature

M - Mach number

Flow velocity and actual speed of the sound ratio

D - internal diameter

Internal circular pipe diameter

A - area

Internal pipe cross section area

h - channel height

Height of the channel for rectangled closed pipe line

w - channel width

Width of the channel for rectangled closed pipe line

Calculation setup

Select value to input. You should enter selected one. The other one will be calculated.

p_t

total (stagnation) pressure

p_d

dynamic pressure

Select value to input. You should enter selected one. The other one will be calculated.

ρ

fluid density

T

temperature

Select pipe shape

round pipe

full cross section fluid flow

rectangular duct

for rectangle channels and full cross section flow

Why Prandtl probe?

You can use a Prandtl probe as flow velocity metering instrument mainly for open flow around solid bodies. However, it is also suitable for velocity measurement of air flow in a rectangle and round channels.

What has to be understood to perform the calculation?

With a Prandtl probe, you can measure flow velocity indirectly, by measuring a difference between stagnation pressure and static pressure of flow in a single point of a flow streamline.

A Prandtl probe measures stagnation pressure in the central part of a Prandtl probe, where flow velocity equals zero. When flow velocity is zero at some point of streamline, measured pressure in that point equals total pressure.

On the outer part of the Prandtl probe where flow streamlines are tangent to the Prandtl probe, the flow velocity is unimpaired, and the pressure measured at that part of streamline is called static pressure.

The difference between stagnation and static pressure in one point of flow streamline is called dynamic pressure. Dynamic pressure represents kinetic energy, and flow velocity can be calculated using this calculator.

What about Pitot tube?

You can use the calculator for Pitot tube as well. A Pitot tube metering instrument is measuring stagnation pressure in one point of a streamline. After you measure static pressure by some other instrument like a barometer, you can compute dynamic pressure, and the flow velocity using this calculator.

When is this calculator suitable?

You can use this calculator for incompressible flow of liquids and compressible flow of ideal gases.