Question 2 of 13: Pitot-Static Tube in an Air Duct

Question 2: Pitot-Static Tube in an Air Duct (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — Sketch and explanation. A pitot-static tube carries two concentric passages: the central, forward-facing tip senses the stagnation (total) pressure where the flow is brought to rest, while a ring of small side ports further back on the probe senses the undisturbed static pressure of the duct flow. Each passage is piped to one leg of a U-tube manometer containing water; because the duct fluid (air) is far less dense than the manometer fluid (water), the manometer deflection is small but readable, and the deflection is driven purely by the dynamic pressure of the flow.

Approach for (b) and (c). The manometer reading converts to the true dynamic pressure via Δp = (ρwater − ρair)gΔh, and that same dynamic pressure equals ½ρairV² by the pitot-static (Bernoulli) relation — so a direct-reading pressure gauge would show exactly the same Δp, just without the density-difference amplification a liquid column provides.

1. Part (b): dynamic pressure from the manometer reading. With Δh = 24 mm = 0.024 m: $$ \Delta p = (\rho_w-\rho_{air})g\,\Delta h = (1000-1.19)(9.81)(0.024) \approx 235.2\ \text{Pa} $$
2. Solve for velocity. Setting Δp equal to the dynamic pressure of the duct air: $$ V = \sqrt{\frac{2\Delta p}{\rho_{air}}} = \sqrt{\frac{2(235.2)}{1.19}} $$ $$ \boxed{V \approx 19.9\ \text{m/s}} $$
3. Part (c): the same velocity read on a differential pressure gauge. A gauge measures the stagnation–static difference directly, with no manometer-fluid amplification factor, so it reads the dynamic pressure itself: $$ \Delta p_{gauge} = \tfrac{1}{2}\rho_{air}V^2 = \tfrac12(1.19)(19.9)^2 $$ $$ \boxed{\Delta p_{gauge} \approx 0.235\ \text{kPa}} $$ This numerically equals the Step 1 result — the manometer and the gauge report the same physical dynamic pressure, the manometer simply displays it magnified into a visible liquid-column height.