Download Pitot and Toricelli

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.
Pitot tube
h2
Figure 1
h1
liquid flow
Therefore the dynamic pressure = total pressure - static pressure.
Now from Bernoulli's equation:
Total pressure = P + ½ v2
Therefore:
dynamic pressure = ½ v2
and the velocity v may be found from the equation:
Fluid velocity (v) = √2/[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
taking v1 = 0 in the Bernoulli equation and equal pressures at
liquid
the top and the hole.
h
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.
v
Figure 2
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:
Fluid velocity (v) = √2gh