Prelab

1. Print this data page and bring it to the lab.

Purpose

The general purpose of this lab is to demonstrate the application of the Continuity principle and Bernoulli's equations. Specifically, to help understand the relationship between pressure and velocity in flow systems, learn to calibrate and use orifice and nozzle flow meters and to become familiar with the use of spreadsheets in engineering applications, including plotting and regression of experimental data.

Theory

Application of the continuity and Bernoulli's equations to either of the above setups will result in the following theoretical formula (ideal flow conditions):

Q_{ideal =} A₂ √ [(2 g ΔP )/γ / (1- (D₂ / D₁ )^4 ) ]

where:

Q_ideal is the ideal flow rate (m³/s)

A₂ is the area of the orifice or nozzle opening at point 2 (m²)

g is the acceleration of gravity (m/s²)

P₁ is the pressure at point 1 (upstream) (kN/m²)

P₂ is the pressure at point 2 (downstream) (kN/m²)

γ is the specific weight of the flowing fluid (water) (kN/m³)

D₁ is the diameter of the pipe (m)

D₂ is the diameter of the orifice or nozzle opening (m)

For non-ideal flow conditions (found in the real world), the correction factor "C" may be used. Q_Real is the product of the above expression and the "C" factor.

Procedure

Part 1: Experimental Setup

1. Choose two obstructions (orifice and nozzle) and measure the diameter of the openings.
2. Measure the inside diameter of the pipe for the experiment.
3. Place one of the obstructions between the pipes making sure it is in the correct way (as in pictures, orifice and nozzle are in the upstream section of the pipe)
4. Connect the ends of the pipe with the bolts. (Three evenly spaced bolts will work, six are better.)
5. Connect the Differential Pressure Gage with the high-pressure side on the portion closer to the pump, and the low-pressure side on the open end.
6. Tighten the brass fittings on the pressure gauge by HAND only. (Using a wrench can over-tighten them and damage the compression seal.)
7. When the water is not running the (raw) pressure reading should be zero (or less than 0.2). If it is not, click on the Pressure Offset Zero button.
8. Click on the Start button and the 4 traces will move across the graph area. You will only see one though because they are all 0 before the pump is turned on.
9. On the graph below you will see two thin bumpy traces and two thick smooth traces.
10. The thick traces are color coded with the numeric displays. The Filtered Pressure and Filtered Flow are green.
11. The pressure reading is in inches of water.
12. The flow reading is in US gallons per minute.

Part 2: Pump Control

1. Turn the water pump on and make sure there are no leaks before proceeding.
2. Set the flow control (valve at table top height) for full flow.
   • You will want to take 5 sets of readings for flows that are (more or less) equally spaced from full flow to 3 US GPM.
   • Note: The stainless steel pumps have two control valves that need to be adjusted for the full range of flows.
     • The two valves being the flow control valve (at the table top) and a bypass valve (the smaller ball-valve underneath with the pump).
       • The bypass valve diverts some water back into the pump instead of the obstruction meter.
       • Use the bypass valve for course adjustments and the flow control valve for fine adjustments.
   • For maximum flow through the obstruction meter the bypass valve must be closed (handle is at a right angle to the pipe)
   • For minimum flows, it must be partially or fully open. If it is not open enough for low flows, the pump will cycle on and off.
     • This will cause turbulence and not provide a smooth flow of water.

Part 3: Data Collection

1. Reset the program filters.
2. Record the pressure drop across the obstruction and the flow from the program.
3. Adjust the valve on the table to change the flow rate. (Remember you want 5 evenly spaced flows from maximum down to 3 US GPM.)
4. Repeat until you have values for the five different flow rates. The flow rate values are not so important as having a range of values to graphically solve later.
5. Record the values on the datasheet that you printed off before the lab.
6. With the pump off, be sure to tilt the pipe to allow the water to drain from it before opening.
7. Repeat with the other obstruction.

Results

1. Plot flow rate (US GPM) against pressure drop (inches of water) (use log-log scale) for each obstruction.
2. Do a power regression (choose "Power" type trendline in Excel) of your data to obtain an empirical formula.
   • This should be in the form Q=a(∆P)^b, where a and b are the regression constants.
3. Compare Q_Real and Q_Ideal and calculate the experimental coefficient of discharge for the orifice and nozzle.

Questions

1. Explain what cavitation is, and why it would be a concern in pumps and turbines that experience changing flows or pressures.
2. Would the theoretical and real flow rates be closer with a denser or lighter fluid? Why?