Measuring Flow Rates with a Pitot Tube
Measuring Flow Rates with a Pitot Tube
A pitot tube determines the velocity of a fluid by measuring the fluid's stagnation pressure. In this demonstration, stagnation pressure is measured with a manometer. The height differential in the manometer 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.
Details
Details
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:
P
1
1
2
2
v
1
z
1
P
2
1
2
2
v
2
z
2
All terms on the left side represent the stagnation point (entrance of the pitot tube); here is the stagnation pressure and =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 and drop out. Thus we obtain the simplified form of Bernoulli's equation:
P
1
v
1
z
1
z
2
P
1
P
2
1
2
2
v
2
The equation for the difference in pressure in a manometer is substituted into the simplified Bernoulli equation:
ΔP=gΔh(-ρ)
ρ
m
1
2
2
v
2
ρ
m
This equation can be rearranged and used to solve for fluid velocity or difference in height of the fluids in the manometer:
Δh=
ρ
2
v
2
2g(-ρ)
ρ
m
v
2
2gΔh(-ρ)
ρ
m
ρ
Where is the static pressure of fluid in the pipe, and are the densities of the fluid in the pipe and manometer fluid, is specific gravity of fluid in the pipe, is the gravitational constant, and is the difference in height of the manometer fluid.
P
2
ρ
ρ
m
γ
g
Δh
External Links
External Links
Permanent Citation
Permanent Citation
Jon Barbieri, Rachael L. Baumann
"Measuring Flow Rates with a Pitot Tube" from the Wolfram Demonstrations Project http://demonstrations.wolfram.com/MeasuringFlowRatesWithAPitotTube/
Published: September 26, 2014