# Pitot Tubes

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

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A Pitot-static tube can measure the fluid flow velocity by converting the kinetic energy in the fluid flow into potential energy.

The principle is based on the Bernoulli Equation where each term can be interpreted as a form of 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 this equation has the dimension force per unit area - *N/m ^{2 } *or in imperial units

*psi, lb/ft*.

^{2}### Static Pressure

The first term - *p* - is the static pressure. It is static relative to the moving fluid and can be measured through an 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 the 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, *h _{1} = h_{2}* and this part can be eliminated. Since

*v*is zero, (2) can be modified to:

_{2}

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

Charts 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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