From TecQuipment TE93 User Guide (2009) | Source: TecQuipment Ltd User Guide, Experiment 1
Tags: pitot tube, upstream velocity, pressure drop, air valve calibration, dynamic pressure, velocity head, air density, ideal gas law, mean velocity, blockage ratio, TE93
Experiment 1 calibrates the air valve by measuring upstream pressure and pressure drop across the rods at different valve settings (100 % down to 30 %). The results yield a linear relationship between velocity head and pressure drop, which can then be used to estimate upstream pressure at very low flow rates where direct measurement is unreliable.
Upstream velocity (V₁)
The air velocity measured before the rods, derived from the difference between pitot total pressure and upstream static pressure.
Downstream velocity (V₂)
The air velocity measured after the rods, derived from the difference between pitot total pressure and downstream static pressure.
Mean velocity through the rods (V)
The average velocity of air passing between the rods, accounting for the area blocked by the rod cross-sections. Equal to 2V₁ for a full set of rods, or 1.11V₁ for a single rod.
Velocity head
The dynamic pressure component (p_t − p_u), representing the kinetic energy per unit volume of the flow. Measured as ΔP1 on the Control and Instrumentation Unit display.
Pressure drop (Δp)
The difference between upstream and downstream static pressures (p_u − p_d), caused by resistance from the rods. Measured as ΔP2 on the display.
Blockage ratio
The fraction of the working section inlet area blocked by the rods. Five rods of 12.5 mm diameter across a 125 mm high section block exactly half the area (62.5 / 125 = 0.5). A single rod blocks 1/10 of the area.
Determine pressure losses created by the rods and plot pressure drop against upstream pressure
Calculate inlet velocity and mean velocity through the rods at each air valve setting
Establish a calibration gradient that relates velocity head to pressure drop
The fundamental equation linking pitot and static pressure with velocity:
p_t − p₀ = ρv² / 2
For the TE93 apparatus specifically:
p_t − p_u = ρV₁² / 2
Air density comes from the ideal gas law:
ρ = p_A / (R × T₁)
Where R = 287 J/kgK.
Combining these gives the working equations:
Upstream velocity: V₁ = √(2(p_t − p_u) × 287 × T₁ / p_A)
Downstream velocity: V₂ = √(2(p_t − p_d) × 287 × T₁ / p_A)
The mean velocity depends on how much area the rods block.
All rods fitted: five rods of 12.5 mm diameter occupy 62.5 mm of the 125 mm working section height. That is exactly half the inlet area. By continuity, V = 2V₁.
One rod fitted: a single rod blocks 12.5 mm out of 125 mm, which is 1/10 of the inlet area. The remaining area is 9/10, so V = (10/9) × V₁ = 1.11V₁.
Fit all aluminium rods into the working section (no Heated Rod needed)
Connect pipework: upstream static tapping to T-piece, one side to ΔP2 (+), other to ΔP1 (−); downstream static tapping to ΔP2 (−); pitot probe to ΔP1 (+)
Pitot Assembly in the upstream position, probe pointing upstream, centred in the working section
Zero the pressure readings before starting the fan
Record (p_t − p_u) as ΔP1 and (Δp) as ΔP2 at each valve setting: 100 %, 90 %, 80 %, 70 %, 60 %, 50 %, 40 %, 30 %
The same procedure is repeated with only one rod in the centre of column 1, blanking plugs in all other positions.
Plotting velocity head (p_t − p_u) on the vertical axis against pressure drop (Δp) on the horizontal axis gives a straight line through the origin. The gradient x gives:
p_t − p_u = x × Δp
Sample results from the guide:
All rods fitted: gradient ≈ 0.22
One rod fitted: gradient ≈ 4.59
This relationship is the calibration tool for low-flow conditions. At 20 % and 10 % valve openings, upstream pressure is too small to measure reliably, so you calculate it from the (more robust) pressure drop reading using this gradient.
All rods, 100 % valve: mean velocity ≈ 27.3 m/s
One rod, 100 % valve: mean velocity ≈ 23.5 m/s
Results are from a 50 Hz unit; a 60 Hz unit gives slightly lower velocities but the same trends
Air density:
ρ = p_A / (R × T₁)
Upstream velocity:
V₁ = √(2(p_t − p_u) × 287 × T₁ / p_A)
Downstream velocity:
V₂ = √(2(p_t − p_d) × 287 × T₁ / p_A)
Mean velocity (all rods):
V = 2V₁
Mean velocity (one rod):
V = 1.11V₁
Calibration relationship:
p_t − p_u = x × Δp
⚠️ The factor of 2 in V = 2V₁ comes directly from the blockage ratio (rods block half the area). Be prepared to derive this from first principles using continuity.
⚠️ The velocity equations require T₁ in Kelvin, not Celsius. A common slip.
⚠️ Below 20 % valve opening, use the calibration gradient to find upstream pressure from the pressure drop. Direct pitot readings are unreliable at very low flows.
⚠️ The pressure-drop-vs-velocity-head plot should be linear through the origin. A non-linear result or a non-zero intercept suggests experimental error (rod misalignment, air leaks, or inaccurate valve positioning).
Q: Why is the mean velocity through all the rods equal to twice the upstream velocity?
A: Five rods of 12.5 mm diameter block 62.5 mm of the 125 mm working section height, which is exactly half the inlet cross-sectional area. By the continuity equation (constant mass flow rate), halving the available area doubles the velocity.
Q: A student measures p_t − p_u = 80 Pa at an ambient temperature of 293 K and barometric pressure of 101,325 Pa. What is the upstream velocity?
A: V₁ = √(2 × 80 × 287 × 293 / 101,325) = √(13,438,480 / 101,325) = √(132.63) ≈ 11.5 m/s.
Q: If the calibration gradient for all rods is 0.22 and the measured pressure drop is 300 Pa, what is the estimated upstream velocity head?
A: p_t − p_u = 0.22 × 300 = 66 Pa.
Q: Why might results at 10 % valve opening be unreliable when measured directly with the pitot probe?
A: At very low flow rates, the dynamic pressure (velocity head) is extremely small, often only a few pascals. This approaches the resolution and noise floor of the pressure transducer, leading to large relative errors.
pitot tube velocity, upstream static pressure, downstream static pressure, pressure drop across rods, dynamic pressure, velocity head, air valve calibration, blockage ratio, continuity equation, mean velocity, ideal gas law for air, TE93 Experiment 1, air density calculation, flow measurement