Piping Networks and Pressure Losses

1. Fabrication of piping system (see schematic and photograph, Fig. 2)

1. Affix (tape or glue) a small plastic water reservoir to the work surface. If it is a covered container, drill holes in the lid for the inlet and outlet water lines and pump power cable.
2. Mount the small submersible pump in the reservoir.
3. Mount the rotameter (water flow meter) vertically in the work area. It may help to strap the rotameter to a small vertical beam or L-bracket to keep it upright. Connect a flow tube from the pump outlet to the rotameter inlet (lower port).
4. Connect plastic compression fitting tees to both ends of a section of rigid plastic tube (recommend length L ~ 0.3 m, inner tube diameter D ~ 6.4 mm). Mount the tees on pipe clamps. Connect rubber tubing from one tee (inlet) to the rotameter outlet. Connect rubber tubing from the other tee (outlet) to the reservoir.
5. Construct a second assembly with two mounted tee fittings. Wrap a length of soft plastic tubing coiled helically around a cylindrical core (recommend cardboard tube, R ~ 30 mm and ~5 tubing wraps). Zip ties or clamps may help keep the tubing coiled. Install the two free ends of the tubing to the tee fittings.
6. Construct a third assembly with two mounted tee fittings. Connect four (or more) elbows with short lengths of rigid plastic tube between the tees. Using multiple elbows amplifies the pressure drop reading, improving measurement accuracy.
7. Install clear rigid plastic tubes (~0.6 m) to the open ports on the six tee fittings. Use a level to ensure that the tubes are vertical. These tubes will be the manometers (pressure measurement devices).
8. Fill the reservoir with water.

2. Operation

1. Straight tube: Turn on the pump, and adjust the rotameter valve to vary the water flow rates. For each case, record the water flow rate and the vertical water level in each manometer tube. Record the pressure drop based on the difference in manometer levels (Eqn. 1).
2. Coiled tube: Connect the coiled test section inlet to the rotameter outlet, and the test section outlet to the reservoir. As in Step 2.1, record the water flow rate and pressure drops for a number of flow rates.
3. Elbow fittings: Connect the elbow fitting test section to the rotameter and reservoir. Collect a set of flow rate and pressure measurements, as in Step 2.2.

3. Analysis

1. For the straight tube case, evaluate the Reynolds number and friction factor f (Eqn. 2). Evaluate the Reynolds number and friction factor uncertainties (Eqn. 6). Here e_ΔP is the uncertainty in pressure measurements (, is uncertainty in manometer level), and e_U is the uncertainty in average channel velocity (from rotameter data sheet, with typical uncertainty of 3 - 5% of range). For water at room temperature (22°C), ρ = 998 kg m^-3 and µ = 0.001 kg m^-1 s^-1.
   (6)
2. Compare the friction factor results from Step 3.1 with the analytic models (Eqn. 3).
3. Repeat Step 3.1 for the coiled tube case. This time, subtract the predicted pressure drop (Eqns. 2-3) for the straight portion of the test section from ΔP. Here we assume the uncertainty in the straight-length pressure correction is negligible. Compare measured friction factors with values from the correlation (Eqn. 4).
4. Repeat Step 3.2 for the elbow fitting case. Subtract the predicted pressure drop for the straight lengths of tubing between the elbow fittings to obtain a corrected pressure loss . Evaluate the equivalent length and uncertainty for each elbow. Here, N_e is the number of pipe elbows.
     (7)
5. Compare the equivalent length result (L_e/D) with the typical reported values (~30).