Wind Tunnel Lab — Variable Cross-Section

Before you begin

What this activity develops, and why it matters beyond this module.

Industry-relevant skill

You will develop the ability to read, interpret, and sanity-check live sensor output — the same manometer and pitot-static instrumentation used in wind-tunnel testing, HVAC balancing, and energy-audit fieldwork. Employers consistently rank this ahead of raw calculation: a technician who can record a number is replaceable; an engineer who can judge whether that number is physically plausible, and diagnose it when it isn’t, is not.

By the end of this activity you will be able to:

Apply the continuity equation and Bernoulli’s principle to predict how pressure and velocity change through a duct of varying cross-section.
Relate pitot-static pressure readings to local flow velocity in a real physical device, not just on paper.
Evaluate whether Bernoulli’s principle holds in practice, by comparing total pressure at multiple measurement stations.
Recognise where the same energy-conversion principles govern efficiency in engineered systems — HVAC ducting, wind-turbine diffusers, low-drag nozzle design — where getting this right reduces energy waste.

Step 2 — Record static pressure readings

Read the gauge static pressure (mmH₂O) at each wall tapping point and enter the values below. The chart will appear once you have worked through the reflection questions.

Tapping points P1–P3: contraction · P4–P6: constant throat section · P7–P11: diffuser.

Static pressure readings mmH₂O — as displayed by the manometer

P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

P11

Fills P1–P11 with example readings for demonstration

Step 3 — Record pitot tube readings

Record the pitot tube pressures at three positions along the duct: first at the inlet (near P1), then at the constant-area throat, then close to P7 in the diffuser.

Pitot Tube — Inlet

Pitot Readings Close to P1 (mmH₂O gauge)

Total pressure P₀

Static pressure Ps

Direct velocity (m/s)

Pitot Tube — Throat

Pitot Readings at Throat (mmH₂O gauge)

Total pressure P₀

Static pressure Ps

Direct velocity (m/s)

Pitot Tube — Diffuser

Pitot Readings Close to P7 (mmH₂O gauge)

Total pressure P₀

Static pressure Ps

Direct velocity (m/s)

Reflect

Is Bernoulli’s principle valid here?

Look at the total pressure P₀ you recorded at the throat and at the second position close to P7. Is Bernoulli’s principle valid in this wind tunnel?

A Yes — the total pressure is close to zero at both locations in the wind tunnel B No — the total pressure reading varies significantly between the two locations, suggesting Bernoulli’s principle is not valid

Calculate

The total pressure P₀ at every tapping in this tunnel is 0 mmH₂O (gauge). The static pressure at P3 is shown below. Using Bernoulli’s principle, estimate the velocity the pitot tube would read at position P3.

Static pressure at P3 (from your readings): — (enter P3 in Step 2 first)

Estimated velocity at P3 (m/s)

m/s

Step 3 — Estimate the Dynamic Pressure

You know the throat velocity from the pitot tube. Using the continuity equation and the cross-sectional area at each tapping, estimate the dynamic pressure at every position along the duct.

Tapping point locations on the variable cross-section duct

Cross-sectional dimensions at each tapping point. Use these areas together with the throat velocity to calculate velocity and dynamic pressure at each position via continuity.

Calculate

Estimate the dynamic pressure at each tapping (Pa)

The velocity at the throat measured by the pitot tube is —. Using the continuity equation and the dimensions in the figure above, calculate the dynamic pressure in Pascal at each position along the duct. Once the first value (P1) is calculated correctly, the remaining 10 will fill in automatically.

Pitot at throat — P₀: — · Ps: —

Point	Zone	Dynamic pressure q (Pa)

Results — Flow Energy at Each Tapping

The three components of flow energy — static pressure, dynamic pressure, and total pressure — are plotted below for all 11 tapping points.

Static, dynamic and total pressure along the duct (Pa gauge)

Static pressure Ps Dynamic pressure q Total pressure P₀ = Ps + q

Static pressure falls in the contraction and recovers in the diffuser. Dynamic pressure does the opposite. Their sum — total pressure — should remain approximately constant if losses are small.

Observe

Q1 — Pressure Recovery

Observe the static pressure readings plotted above. Compare P1 (inlet) and P11 (diffuser exit) — they have roughly the same cross-sectional area, so in an ideal frictionless flow they would have the same static pressure. What does your data show, and why?

A P11 is the same as P1 — the flow is ideal and fully recovers pressure in the diffuser B P11 is slightly lower than P1 — viscous friction along the duct walls dissipates some mechanical energy as heat, so full pressure recovery is not achieved C P11 is higher than P1 — the diffuser amplifies pressure above the inlet value D The comparison is not meaningful because the areas are not exactly equal

Explain

Q2 — Velocity at the Wind Tunnel Inlet

If the pitot tube is placed at the inlet of the wind tunnel, what velocity will it read?

Hint: outside the tunnel the air is still. Think about what the static pressure equals when there is no flow, and what the total pressure equals in still air.

A The same velocity as at the throat — the fan drives the same speed everywhere B 0 m/s — the static pressure equals atmospheric pressure so the dynamic pressure (ΔP = P₀ − Ps) is zero, giving zero velocity C Half the throat velocity — the inlet area is about twice the throat area

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Discuss with your colleagues

Talk through each question with your group, then click Show guidance when you are ready.

2

In the throat (P4–P6) static pressure is at its lowest and dynamic pressure is at its highest. If you doubled the fan speed, how would the shape of the three curves change — and how would their magnitudes change?

By the end of this activity you will be able to:

What is the sign of the static pressure?

Interpret the pressure distribution

Pitot Readings Close to P1 (mmH₂O gauge)

Pitot Readings at Throat (mmH₂O gauge)

Pitot Readings Close to P7 (mmH₂O gauge)

Is Bernoulli’s principle valid here?

Pitot readings — inlet and diffuser

Static, dynamic and total pressure along the duct (Pa gauge)