change height 
 change fluid velocity 
manometer height (cm)
4.7
density of manometer fluid (kg/L)
7.9
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 difference in height of the fluids (Δh) in the manometer or the fluid velocity (v2):
Δh = ρ v22 2 g (ρm − ρ)
v2 = 2 g Δh (ρm − ρ) ρ
Where ρ and ρm are the densities of the fluid in the pipe and manometer fluid, γ is specific gravity of fluid in the pipe, and g is the gravitational constant.
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). Address any questions or comments to LearnChemE@gmail.com.
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