In order to test the theory on the bench, I gather data from actual laboratory experiments and correlate the data with model predictions. To calibrate the equipment, I first run some tests on very simple devices. The first device is a simple round orifice normal to a flat wall in a plenum. The second device is an extension of the first device that also includes an additional plate, close up against the orifice so as to restrict flow.

Air flows through the flow meter, then past the pressure meter, and finally into the plenum and out through the orifice. I run this test with orifice sizes of 1/16" and 1/8". I vary the plenum pressure by adjusting the pump (not shown) and I measure the mass flux through the orifices. Interestingly, basic Fluid Mechanics texts do not give formulas or tables for this particular setup.

Air enters the plenum through the hose and exits through the orifice. The plenum is a cylinder about an inch long and 1/4" in diameter. The orifice diameters, [D] for the two tests are 1/8" and 1/16". The pressure varies from zero to about 60 psig. The device is  smooth acrylic plastic.

Column

Description

1

Gauge psig (pounds per square inch, gauge) - reading directly from pressure gauge.

2

Gauge k-pa (kilo-pascals) - gauge psig times 6895 k-pa/psi.

3

Density - 1.2 kg/m³ times (11.6/14.6 + gauge k-pa / 78.91)

4

1/16" diam. Gauge - numerical reading directly from flow meter for 1/16" diameter orifice.

5

1/18" diam. Gauge - see directly above.

6

Where Pg is the operating pressure + 11.6 psi, Ps is the scale pressure (100 psi) + 11.6 psi, Ts is the scale temperature (70F) + 460F and Tg is the operating Temperature, (50F) + 460F. Example, the factor for 5 psig at 50F, f = sqrt(16.6/111.6 * 530/510) = .39316.

7

1/16" Std. Flux (scfm) - gauge reading times adjustor gives the flow at standard conditions (70 deg. F and 14.6 psi)

8

1/8" Std Flux (scfm) - see directly above.

9

1/16" Flux (kg/sec) - std flux (scfm) times 4.5 nt/lb times .07849 lb/scfm / 9.81 m/s² / 60 s/min.

10

 1/8" Flux (kg/sec) - see directly above.

Problem #2: A circular plate over the orifice creates a ring-shaped "valve" at the center and changes the flows.

Find M-dot; Mo-dot; and Te-dot.

Problem #3: Air leaving the valve area continues to experience skin-friction drag.

Find drag as a function of U, p and d.

To do: Create control volumes from concentric rings of thickness dR, radiating out from the orifice between the plates, like nested bicycle tires. (The rings in this panel appear on their sides.) During the traverse across dR, within a control volume, Mo and Te change slightly as a function of drag and pressure gradient across dR. For control volume[r], write equations for these small changes.

Continued ...

There is (1) a pressure gradient from the inside to the outside and (2) some skin friction across the top and the bottom. These act to change the momentum and thermal energy of the air passing through.

Very small section of a ring showing direction of mass flux. Width (w) is actually curved slightly and continues around as the circumference of the ring.

States

Symbol

Units

Notes

Mass

M

Kg

Air: d ~ 1.2 kg/m3

Momentum

Mo

Kg-m/s

Mo = M * U

Thermal Energy

Te

Kg-m²/s²

Te = PV = NRT

Rates and Flows

Mass Flux

M-dot

Kg/s

 M-dot = dM/dt

Momentum Flux

Mo-dot

Kg-m/s²

 Mo-dot = dMo/dt

Thermal Energy Flux

Te-dot

Kg-m²/s³

 Te-dot = dTe/dt