# Pitot Tubes

## Pitot tubes can be used to measure fluid flow velocities by measuring the difference between static and dynamic pressure in the flow.

A pitot tube can be used to measure fluid flow velocity by converting the kinetic energy in a fluid flow to potential energy.

The principle is based on the Bernoulli Equation where each term of the equation can be interpreted as pressure

p + 1/2ρ v^{2}+g hρ

=p + 1/2ρ v^{2}+ γ h

=constant along a streamline(1)

where

p= static pressure (relative to the moving fluid) (Pa)

ρ= density of fluid (kg/m^{3})

v= flow velocity (m/s)

γ=ρg = specific weight (N/m^{3})

g= acceleration of gravity (m/s^{2})

h= elevation height (m)

Each term of the equation has the dimension force per unit area *N/m ^{2 } (Pa) - *or in imperial units

*lb/ft*.

^{2}(psi)### Static Pressure

The first term - *p* - is the static pressure. It is static relative to the moving fluid and can be measured through a flat opening in parallel to the flow.

### Dynamic Pressure

The second term - *1/2* *ρ v ^{2}* - is called the dynamic pressure.

### Hydrostatic Pressure

The third term - *γ h* - is called the hydrostatic pressure. It represent the pressure due to change in elevation.

### Stagnation Pressure

The Bernoulli Equation states that the energy along a streamline is constant - and can be modified to

p_{1}+ 1/2ρ v_{1}^{2}+ γ h_{1}

=p_{2}+ 1/2ρ v_{2}^{2}+ γ h_{2}

= constant along the streamline(2)

where

suffix_{1}is a point in the free flow upstream

suffix_{2}is the stagnation point where the velocity in the flow is zero

### Flow Velocity

In a measuring point we regard the hydrostatic pressure as a constant where *h _{1} = h_{2}* - and this part can be eliminated. Since

*v*is zero,

_{2}*(2)*can be modified to:

p_{1}+ 1/2ρ v_{1}^{2}=p_{2}(3)

or

v_{1}= [2 (p_{2}-p_{1}) /ρ]^{1/2}

=[2/Δpρ]^{1/2}(4)

where

Δp= p_{2}- p_{1}(differential pressure)

With *(4)* it's possible to calculate the flow velocity in point 1 - the free flow upstream - if we know the differential pressure difference * Δp* =

*p*

_{2}*-*

*p*and the density of the fluid.

_{1}It is common to use head instead of pressure. *(4)* can be modified by dividing with specific weight *γ* to

*v _{1} = c [2 g Δh]^{1/2 } (5)*

*where *

*c = coefficient - depending on reference liquid and units used or calculated *

*g = acceleration of gravity *

* Δh* = h

_{2}- h

_{1}= height difference (fluid column)

**Note!** - in the basic equation the head unit is with reference to the density of the flowing fluid. For other units and reference liquids - like *mm Water Column* - check Velocity Pressure Head.

### The Pitot Tube

The pitot tube is a simple and convenient instrument to measure the difference between **static, total **and **dynamic pressure (or head)**.

The head - *Δ**h* - (or pressure difference - *Δp*) can be measured and calculated with the help of u-tube manometers, electronic pressure transmitters or similar instrumentation.

### Air Flow - Velocity and Dynamic Head Chart

The charts below are based on air density *1.205 kg/m*^{3} and water density *1000 kg/m*^{3}.

**Note** that as indicated in the diagram above - pitot tubes are not suited for low velocity flow. Due to low dynamic pressure (head) the readings will be inaccurate.

### Water Flow - Velocity and Dynamic Head Chart

### Flow Metering - Point Velocity Area Method

The point velocities in a duct, channel or pipe can be measured by traversing the cross-sectional area of the conduit. The point velocities can be used to calculate the average velocity that can be used to estimate the flow.

The average velocity can be calculated as

*v _{a} = Σ v_{n} / n *

* = (2 g Σ h _{n} / n )^{1/2} (6)*

*where *

*v _{a} = average velocity (m/s, ft/s)*

*v _{n} = point velocity (m/s, ft/s)*

*h _{n} = point height difference pitot meter (m, ft) *

*n = number of point velocities*

The volume flow in the conduit can be calculated as

*q = v _{a} A (7)*

*where *

*q = flow (m ^{3}/s, ft^{3}/s)*

*A = cross-sectional area (m ^{2}, ft^{2})*

For round ducts larger than 10 inches the average velocity can be calculated as the arithmetic middle of a 10 point traverse from inward side wall with distance

*2%, 8%, 15%, 23%, 34%, 66%, 77%, 85%, 92% and 98%*

For smaller ducts the the average velocity can be estimated to *81%* of centerline velocity.