CIVE 2010 - Introduction to Water Engineering
CIVE 2010 - Introduction to Water Engineering
FLOW MEASUREMENT EXPERIMENT
INTRODUCTION
The measurement of flow in hydraulic systems may be divided into two broad categories:
flows in pipes or conduits (pressurised), and,
flows in open channel devices (open to atmosphere).
In this experiment four commonly used devices for flow measurement will be calibrated. A range of known flow rates will be passed through each device and the observed pressure difference will be used to determine the differential pressure head, H = (PA-PB) and hence the relationship between head and discharge. Not all devices will give an accurate measurement at all flow rates. The sensitivity of each device determines whether it is more suitable for measuring lower flows or higher flows.
THEORY
The four devices used to illustrate water flow measurement in conduits are:
venturi meter
bend meter
pitot tube
orifice plate.
Each of these devices yields a fixed relationship between discharge, Q, and the differential pressure head, H. The pressure is measured at two points on each device by connecting these two ends to a Bourdon gauge to measure differential pressure, (PA-PB) as shown in the sketch below, which gives a differential pressure:
1536703746500Venturi meter
Pitot tube meter
Magnetic meter
Flow meter test rig experiment
orifice meter
Bend meter
PA-PB
PA-PB
PA-PB
PA-PB aa
3.6 L/s
Venturi meter
Pitot tube meter
Magnetic meter
Flow meter test rig experiment
orifice meter
Bend meter
PA-PB
PA-PB
PA-PB
PA-PB aa
3.6 L/s
Tapping points in the pipes can be connected to the central pressure gauge for measuring the pressure difference between upstream/downstream of the devices. Differential pressure head, H can be found by converting measured differential pressure into a pressure head
H=(PA-PB)gIn all cases, the relationship between Q and H takes the form:
Q=kHnwhere Q is in m3/s
H is pressure head difference measured in m of water
k and n are constants
The power term "n" should take the value 0.5 in each case for closed conduits. The generic constant k in the above equation incorporates several constants that appear in the discharge equation, which is different for each individual device. The full equations and parameters for each device are given in Table 1.
For example, in the case of the Bend meter, by equating the formula to , you should be able to see that n = 0.5 and k = . You need to repeat this for the other devices.
Table 1. Discharge equations and parameters
Device Equation Parameter values
Bend meter
where D = 80 mm
H = observed head difference
Cd = ???Venturi meter
where D1 = 80 mm
D2 = 38 mm
H = observed head difference
Cd = ???Pitot tube meter
where D = 80 mm
H = observed head difference
Cd = ???
Orifice meter
where D1 = 80 mm
D2 = 26 mm
H = observed head difference
Cd = ???
PRACTICAL METHOD
The actual flow rate, Q, is measured using a magnetic flow meter.
The head difference, H, is found measuring differential pressure head using pressure gauge and converting that to a head. There should be two Bourdon gauges one is for measuring small pressure differences (at low flows and/or devices with minimal head difference) while the other is for measuring large differences (at high flows and/or for devices that generate a large head difference).
NOTE: For low flows (less than 1 L/s), ensure orifice plate bypass valve in the closed position, for flows above 1 L/s ensure the bypass valve is fully open!!
STEP 1 Observe that with NO FLOW, there is zero pressure difference indicated by the pressure gauge. If necessary, bleed the tubes to remove any air bubbles trapped in the tubes.
STEP 2 Open the valve to allow a flow to pass through the pipe. Record the flow rate Q using the magnetic flow meter. See Table overleaf for the flow rate ranges to be tested.
STEP 3 For all the devices, observe the pressure differential pressure:
(PA - PB)
(Only record differential pressure for the orifice plate if the orifice bypass valve is closed.)
STEP 4 Repeat STEPS 2 and 3 for four low flows (0-1 L/s bypass valve closed), four medium flows (1-4 L/s bypass valve open) and four high flows (4-16 L/s bypass valve open). Record Q and P in each flow range for the devices indicated in the Table overleaf.
COMPUTATIONS
Enter the flow and measured differential pressure data into Excel. Convert differential pressure into head, H values by dividing by rho x g
Plot Q versus H for each device, and fit a Power-type trendline to the data. This gives an estimate of k for each device.Important: In the trendline options, tick Display Equation on chart and Display R-squared value on chart.
Re-arrange the equations from Table 1 to give Cd in terms of k, and report Cd for each device using the k value from the trendline (step 2).
Calculate Hn for each flow rate and for each device, and plot Q versus Hn. This time, fit a Linear-type trendline (through the origin) to determine an alternate value of k.
Report Cd for each device, based on the new value of k.
Study the Cd values derived from the two sets of trendlines, relative to expected Cd values for the devices being considered.
Study the R-squared values (reflecting how well the equation matches the available data) in each case, in order to comment on the two approaches to calibration.
Comment on the apparent reliability of different devices at different ranges of flow (i.e. which devices are more reliable at low flows, and which ones are more reliable at higher flows, etc.).
IMPORTANT: Your discussion should consider the differences between the results obtained from the two different trendline approaches. It is plausible that the first approach (Q vs H, power trendline) delivers a higher R-squared value, implying less random error. Likewise, the second trendline approach (Q vs Hn, linear trendline) likely delivers less systematic error, but more random error. If so, which result would you consider more reliable?
Flow rate (L/s) Meter differential pressure, P (kPa)
Bend Venturi Pitot Orifice
Low flows (0-1 L/s)
Medium flows (1-4 L/s)
High flows (4-16 L/s)
