The Pitot static tube

This is a device for measuring the velocity of a moving fluid - Figure 1 is a simplified diagram.



The total pressure within the moving fluid can be considered to have two components:
(a) the static pressure which it would have if the fluid was at rest, and
(b) the dynamic pressure which is the pressure equivalent of its velocity.






Therefore the dynamic pressure = total pressure - static pressure.

Now from Bernoulli's equation:

Total pressure = P + ½ρv²

Therefore: dynamic pressure = ½ρv²

and the velocity v may be found from the equation:

Fluid velocity (v) = √2/ρ[total pressure – static pressure]

The total pressure is measured by the pressure head h₂ and the static pressure by pressure head h₁. Therefore the formula may be written:

Fluid velocity (v) = √2g[h₂ – h₁]

Torricelli's theorem

This theorem applies to a fluid flowing from a drum with a horizontal opening near the base (Figure 2). It states that, if the difference in levels between the hole and the upper liquid surface is h, then:


v₂² = [2gh]^1/2

taking v₁ = 0 in the Bernoulli equation and equal pressures at the top and the hole.

This theorem applies to the flow of fluid from a drum with a horizontal opening near the base. The relation may be deduced from Bernoulli's equation by taking the velocity v₁ to be zero and assuming equal static pressures at the top of the fluid and outside the hole.


If the difference in levels between the hole and the upper liquid surface is h, then the velocity (v) with which fluid emerges from the hole is given by: