A pitot tube measures flow speed from the difference between total and static pressure. Adjust the differential pressure, fluid and duct diameter to see the Bernoulli-based velocity, volumetric flow and Reynolds number update in real time, and grasp the principle of flow measurement intuitively.
Parameters
Fluid
Sets density ρ and viscosity μ
Differential pressure ΔP (total − static)
Pa
Total-vs-static pressure difference the pitot tube reads
Fluid density ρ (custom)
kg/m³
Used only when the fluid is set to "Custom"
Pitot coefficient Cp
Corrects for tube imperfections. 0.98-1.00 for a standard tube
Duct diameter D
mm
Used for the flow rate and Reynolds number
Results
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Velocity V (m/s)
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Volumetric flow Q (L/s)
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Mass flow (kg/s)
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Reynolds number Re
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Dynamic pressure q (Pa)
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Compressibility
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Pitot tube in duct flow — streamline animation
The stagnation point at the nose taps total pressure, the side hole taps static pressure, and the U-tube manometer shows the height difference proportional to ΔP. Velocity vectors are small near the wall and largest mid-duct.
Flow velocity V [m/s]. p₀ is the total pressure at the tube's stagnation nose, pₛ the static pressure at the side tap, and Δp their difference. ρ is fluid density, Cp the pitot coefficient.
$$Q=V\cdot\frac{\pi D^2}{4},\qquad Re=\frac{\rho V D}{\mu}$$
Volumetric flow Q [m³/s] and Reynolds number Re. D is the duct diameter, μ the viscosity. Re<2300 is laminar, higher is turbulent. Mass flow equals ρQ.
What is the Pitot Tube Velocity Simulator?
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I heard that thin probe sticking out of an aircraft fuselage is a "pitot tube". How can a probe tell you how fast the plane is going?
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Good question. That probe does not measure speed "directly" — it actually measures pressure. The nose of the pitot tube has a forward-facing hole, and when the flow hits it the flow stops in an instant. That spot where the flow stops is the "stagnation point", and the pressure there is the "total pressure". A second hole on the side of the tube reads the undisturbed "static pressure". Measure the difference between those two and the speed comes out of a calculation.
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Speed from a pressure difference... how is that even possible?
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The key is Bernoulli's equation. Roughly speaking, it is energy conservation: where the flow is fast the pressure is low, and where it is slow the pressure is high. The difference between total and static pressure is called the "dynamic pressure", and it is exactly ρV²/2. So if you measure the differential pressure Δp you can back out the speed from V = √(2Δp/ρ). Move the differential-pressure slider on the left — you will see velocity rise as a gentle curve, proportional to the square root of pressure.
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I see! But air and water have wildly different densities. Does the same differential pressure give a different result?
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That is the interesting part. V = √(2Δp/ρ) has ρ in the denominator, so the denser water gives a smaller velocity for the same differential pressure. Put the other way around, a water flow only slightly fast produces an enormous differential pressure. That is why a water-pipe flow meter works in hundreds to thousands of Pa, while HVAC duct measurement is tens to hundreds of Pa — completely different pressure ranges. Switch the fluid and watch the slope of the chart change dramatically.
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There is also a "pitot coefficient Cp" slider. What is that adjusting?
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Cp is a correction factor that makes up for "the imperfections of a real tube". In theory the flow stops perfectly at the nose and the side hole reads the static pressure exactly, but a real tube has a slightly rounded nose, or the tube itself disturbs the flow. A well-calibrated standard pitot-static tube has Cp around 0.98 to 1.00. A cheap or home-made tube can drop to 0.95. For precision work, each tube is calibrated one by one in a wind tunnel.
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Does this formula work at any speed? Even for a very fast flow?
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That needs care. V = √(2Δp/ρ) assumes "constant density", that is, incompressible flow. For water it is always fine. But once air exceeds 30% of the speed of sound (Mach 0.3, about 100 m/s at 20°C), the air itself starts to compress and its density changes, so the formula picks up an error. Then you need a separate formula that accounts for compressibility. This tool warns "compressible correction required" once air goes past Mach 0.3.
Frequently Asked Questions
A pitot tube measures velocity from the difference between the total (stagnation) pressure and the static pressure. A forward-facing hole at the tube nose brings the flow to a complete stop, capturing the total pressure p0 at that point. A side-facing hole captures the static pressure ps along the flow. From the incompressible Bernoulli equation, p0 − ps = ρV²/2, which solves to V = √(2Δp/ρ). This tool multiplies that result by the pitot coefficient Cp to correct for tube imperfections.
Static pressure ps is the true pressure the fluid feels while moving with the flow; dynamic pressure q = ρV²/2 is the kinetic energy of the flow expressed as pressure. Total (stagnation) pressure p0 is their sum, p0 = ps + q, the pressure you get when the flow is brought completely to rest. A pitot tube taps total and static pressure separately and so measures their difference, the dynamic pressure q. Velocity is then recovered from V = √(2q/ρ).
The pitot coefficient Cp corrects for how far a real tube departs from an ideal pitot tube. Nose-shape imperfections, the position and number of static holes, and the disturbance the tube itself causes all shift the measured differential pressure slightly from the theoretical value. For a well-calibrated standard pitot-static tube, Cp is typically 0.98 to 1.00. Cheap or home-made tubes can drop to about 0.95, so calibrate in a wind tunnel when accuracy matters.
V = √(2Δp/ρ) comes from the incompressible Bernoulli equation, so it is accurate only where density is essentially constant. For liquids such as water it always applies. For air, once the velocity exceeds about 30% of the speed of sound (Mach 0.3, roughly 100 m/s at 20°C), density changes can no longer be ignored and a compressible formula is required. Below Mach 0.3 the error stays within a few percent and the incompressible formula in this tool is sufficient.
Real-World Applications
Aircraft airspeed indicators: The most famous use of a pitot tube is on aircraft. A pitot-static probe protruding from the nose or wing leading edge taps total and static pressure, and the airspeed (speed relative to the flow) is computed from the differential pressure. The speed the pilot reads is that differential pressure converted directly. Ice or debris blocking the holes corrupts the speed reading, so heated tubes are standard and the probe is always checked before departure.
HVAC and ventilation duct airflow: In building and factory air conditioning, the duct air velocity is measured with a pitot tube and multiplied by the cross-sectional area to get the airflow. Because the velocity is not uniform across a duct, a "traverse method" divides the section into a grid and averages several measured points. The Reynolds number this tool shows is a guide to whether the flow is laminar or turbulent.
Wind-tunnel testing and research measurement: In wind tunnels for aerodynamic testing of cars and buildings, the pitot tube serves as the reference velocity probe. For detailed mapping of the velocity field around a model, a "pitot rake" of many fine total-pressure tubes, or a multi-hole probe that also resolves direction, is used. A calibrated Cp underpins the reliability of the test data.
Quick pipe flow measurement: When you want to estimate the flow in a water or gas pipe without installing a full flow meter, a pitot tube (or an averaging pitot tube, the Annubar) is inserted to read the differential pressure. Its advantage over an orifice plate is a smaller pressure loss. Being able to obtain velocity, flow rate and Reynolds number from the differential pressure at once, as in this tool, helps with a quick estimate in the field.
Common Misconceptions and Pitfalls
The biggest pitfall is swapping the total and static connections. The forward-facing hole of a pitot tube taps total pressure and the side hole taps static pressure; reverse the tubing or manometer connections and the sign of the differential pressure is wrong, so velocity cannot be computed. Also, if the side static holes are partly blocked by a burr or paint, the static reading runs high or low and the differential pressure is corrupted. Aim the total hole correctly into the flow, and choose a tube with several static holes around the axis. If the differential pressure is nearly zero while flow is present, suspect a swapped connection or a blocked hole first.
Next, treating a single-point reading as representative of the whole duct. The flow rate Q = V·A in this tool assumes the whole section flows at the same velocity V. In a real duct or pipe, however, the velocity is zero near the wall and maximum at the centre, and the profile differs greatly between laminar and turbulent flow. Measuring only at the centre tends to overestimate the flow. An accurate flow rate requires averaging several points by the traverse method, or applying a velocity-profile factor (the ratio of section-mean to centreline velocity) as a correction.
Finally, continuing to use the incompressible formula without checking the Mach number. V = √(2Δp/ρ) assumes constant density and is accurate enough for low-speed air. But in a high-speed air flow the air is compressed at the stagnation point and its density rises, so the incompressible formula underestimates the velocity. The guideline is Mach 0.3 (about 100 m/s for air at 20°C). Beyond it, switch to a compressible stagnation formula. This tool changes the verdict to "compressible correction required" once air reaches Mach 0.3 or above. For liquids the Mach number is effectively meaningless, so they can always be treated as incompressible.
How to Use
Enter differential pressure (ΔP) in Pa from your pitot tube manometer reading—typical range 5–500 Pa for subsonic flow
Set fluid density (ρ) in kg/m³: air at sea level ≈ 1.225 kg/m³, water ≈ 998 kg/m³
Input pressure coefficient (Cp)—use 1.0 for standard pitot-static probes or 0.84–0.98 for hemispherical/conical tips
Specify pipe/duct diameter (d) in mm to calculate volumetric and mass flow rates
Click Calculate to solve Bernoulli equation V = √(2ΔP/(ρ×Cp)) and derive Reynolds number, dynamic pressure, and compressibility correction
Worked Example
Airflow in a wind tunnel: ΔP = 125 Pa, ρ = 1.2 kg/m³ (standard air), Cp = 1.0, d = 80 mm duct diameter. Velocity V = √(2×125/(1.2×1.0)) = 14.43 m/s. Volumetric flow Q = V×A = 14.43×π×0.04² = 0.0729 m³/s = 72.9 L/s. Mass flow = 1.2×0.0729 = 0.087 kg/s. Reynolds number Re = (1.2×14.43×0.08)/1.81×10⁻⁵ ≈ 76,400 (turbulent). Dynamic pressure q = 0.5×1.2×14.43² = 125 Pa (validates pitot reading).
Practical Notes
Pitot tubes require viscous fluid correction below Re ≈ 1,000; add 2–5% velocity loss for laminar effects in thin channels
Compressibility becomes significant above Mach 0.3 (V ≈ 100 m/s in air); simulator flags when ΔP exceeds 5% static pressure