# Pitot Tubes

## Pitot tubes can be used to indicate fluid flow velocities by measuring the difference between the static and the dynamic pressures in fluids

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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}+ γ h = constant along a streamline(1)

where

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

ρ= density (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

Since the Bernoulli Equation states that the energy along a streamline is constant, *(1)* 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}(4)

where

p_{2}- p_{1}= dp (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 *dp = **p _{2}*

*-*

*p*and the density of the fluid.

_{1}### 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 - *h* - (or pressure difference - *dp*) can be measured and calculated with 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}.

### Water Flow - Velocity and Dynamic Head Chart

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