Internal flow · ME 347 · Cal Poly

Mapped how airflow pressure shifts through a 90° turn.

Every bend in a duct costs energy. With a team of four, I measured pressure at 30 points around a bend, compared it with two textbook models, and quantified exactly how much the turn costs.

Role: Testing & analysis
Team: 4 students
Equipment: Airflow bench, manometer
Course: ME 347, Cal Poly

Airflow box feeding a rectangular duct with pressure taps around a 90-degree bend

The problem

Bends in ductwork waste energy, but how much, and why?

What I did

Read 30 pressure taps with a manometer and compared the results to one- and two-dimensional flow models.

The result

The bend lost about 3× the pressure of an equivalent straight duct (78.33 vs. 25.75 Pa), a loss coefficient of K = 0.112.

30pressure taps measured

~3×loss of a straight duct

34m/s airflow

2flow models compared

How I did it

01
Measure
Recorded pressure along the inner wall, outer wall, and across the bend.
02
Map
Showed how the turn pushes pressure up outside and down inside.
03
Compare
Checked the data against two ideal-flow models.
04
Quantify
Calculated the extra energy loss caused by the bend.

Skills I used

Pressure measurement
Manometry
Flow modeling
Loss analysis
Data visualization

Full engineering write-up

Worked with a team of four on this lab, and I measured how a 90-degree turn redistributes pressure across a rectangular duct. We compared the experiment with one- and two-dimensional ideal-flow models and quantified the additional loss caused by the bend.

Apparatus and reduction

Thirty pressure taps across one curved flow path

An airflow box supplied steady flow through a contraction and into the rectangular bend. An inclined water manometer recorded differential pressure at ten inner-wall taps, ten outer-wall taps, and ten taps across the bend radius.

Ambient pressure and temperature established air density. The airbox-to-inlet pressure difference gave an average duct velocity of 34.16 m/s. A separate estimate from the inner-to-outer pressure difference and the free-vortex model gave 32.17 m/s.

34.16 m/sVelocity from the inlet contraction

32.17 m/sVelocity from the free-vortex estimate

30 tapsInner, outer, and radial measurements

Pressure through the bend

Curvature creates the pressure gradient that turns the flow

Pressure separated sharply between the two walls near the middle of the bend. At tap 5, the inner wall reached -611.90 Pa while the outer wall reached 350.01 Pa. The profiles returned toward similar values near the outlet.

The higher pressure at the outer wall supplies the radial pressure gradient required for centripetal acceleration. The inner and outer curves therefore form opposite peaks around the center of the turn.

Gauge pressure along the duct bend, with inner-wall pressure falling below negative 600 pascals and outer-wall pressure rising above 300 pascals near the middle — Measured gauge pressure along both walls. Tap 5 lies near the middle of the 90-degree bend.

Tap	Inner wall	Outer wall	Pressure separation
1	53.85 Pa	85.67 Pa	31.82 Pa
3	-210.49 Pa	198.26 Pa	408.75 Pa
5	-611.90 Pa	350.01 Pa	961.91 Pa
7	-308.40 Pa	188.46 Pa	496.86 Pa
10	-24.48 Pa	-2.45 Pa	22.03 Pa

Angular model comparison

The two-dimensional model captured the shape

The normalized inner-wall pressure difference rose through the bend, peaked near its midpoint, and fell toward the outlet. The experiment followed the two-dimensional inviscid model closely in shape.

The measured values deviated where the ideal model could not represent viscosity, wall shear, losses, secondary flow, or local separation.

Experimental and two-dimensional model values for normalized pressure difference along the inner wall of the bend — Experimental points follow the model’s rise and fall through the bend, with smaller departures near the inlet and outlet.

Radial pressure gradient

Pressure increased from the inner radius to the outer radius

The radial taps showed a monotonic pressure increase toward the outer wall. That trend matched the free-vortex model and the expected balance between pressure force and centripetal acceleration.

The one-dimensional model consistently overpredicted the normalized pressure difference. The idealized model captured the direction and curvature of the result but omitted the losses and three-dimensional flow structures present in the apparatus.

Experimental normalized radial pressure data increasing from the inner radius to the outer radius below the one-dimensional model prediction — The measured radial pressure rise stayed below the ideal one-dimensional prediction across the bend.

Bend loss and takeaway

Turning the flow cost more pressure than wall friction alone

The measured bend-loss coefficient was K = 0.112, corresponding to a 78.33 Pa pressure drop. The lab-manual chart gave K ≈ 0.12 and 83.41 Pa, a close independent check.

An equivalent length of straight commercial-steel duct produced an estimated 25.75 Pa drop. The bend loss was about three times larger because the turn introduced secondary flow, greater turbulence, and possible separation in addition to ordinary wall friction.

K = 0.112Experimentally calculated loss coefficient

78.33 PaCalculated pressure loss through the bend

25.75 PaEstimated loss for equivalent straight duct

Engineering takeaway: both ideal models explained the dominant pressure pattern, but their residual error contained useful information about real losses and secondary flow.