A pitot tube determines the velocity of a fluid by measuring the fluid’s
stagnation pressure. The stagnation pressure is measured with a manometer.
The manometer height differential is a function of the manometer fluid
density, and the flowing fluid’s kinetic energy. Bernoulli’s
equation relates these terms, and is used to solve for velocity. Vary the
manometer fluid (green) height or the velocity of the fluid in the pipe
(blue) to see how each variable is related. Also, use a slider to vary the
density of the fluid in the manometer.
Pitot tubes are used to measure the velocity of a fluid moving through a
pipe by taking advantage of the fact that the velocity at the height of the
bend in the tube (stagnation point) is zero. Some kinetic energy density of
the fluid flowing through the pipe is converted into pressure, resulting in
a change in manometer height. Bernoulli’s equation is used to
calculate the velocity of the bulk fluid in the pipe by using this pressure
difference in the pitot tube:
P1
+
12
ρ v12
+
γ z1
=
P2
+
12
ρ v22
+
γ z2
All terms on the left side represent the stagnation point (entrance of
the pitot tube); here P1 is the
stagnation pressure and v1 = 0
is the velocity of fluid in the pipe at point 1. All terms on the right side
refer to point 2, a point upstream from the pitot tube. The two points that
are being evaluated are at the same height, so
z1 and
z2 drop out. Thus we obtain the
simplified form of Bernoulli’s equation:
P1
−
P2
=
ΔP
=
12
ρ v22
The equation for the difference in pressure in a manometer is substituted
into the simplified Bernoulli equation:
ΔP
=
g Δh
(ρm
− ρ)
12
ρ v22
=
g Δh
(ρm
− ρ)
This equation can be rearranged and used to solve for fluid velocity or
difference in height of the fluids in the manometer:
Δh
=
ρ v22
2 g (ρm − ρ)
v2
=
\( \sqrt{ \frac{2g \Delta h (\rho_m - \rho)}{\rho} } \)
Where P2 is the static pressure of
fluid in the pipe, ρ and
ρm are the densities of the fluid
in the pipe and manometer fluid, γ is
specific gravity of fluid in the pipe, g is the
gravitational constant, and Δh
is the difference in height of the manometer fluid.
This simulation was created in the
Department of Chemical and Biological Engineering
at University of Colorado Boulder for
LearnChemE.com
by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a
Mathematica simulation
by Jon Barbieri and Rachael L. Baumann. It was prepared with financial support
from the National Science Foundation (DUE 2336987 and 2336988) in collaboration
with Washington State University. Address any questions or comments to
LearnChemE@gmail.com.