Flow Measurement

ME313L Fluid Mechanic Lab Manual (DRAFT)

Flow Measurement Experiment Object: Several types of flowmeters flowmeters will be studied for their characteristics including accuracy and head loss. Calibration of a flowmeter will also be performed. Equipment:

Safety valve

Manomete Rotameter

Gate valve

Elbow

Manometer tappings

Venturi meter

Orifice meter

I Rotameter Wide angle diffuser Manometer tappings Flow

A

Venturi meter B

Orifice meter

D

E

H F

G

C 51.9 51.9 mm

26 mm 16 mm

Figure 1

26 mm

20 mm

Flow measurement measurement apparatus

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ME313L Fluid Mechanic Lab Manual (DRAFT) The flow measurement apparatus consists of a water loop as shown above figure. The supple line is connected to a gravimetric hydraulic bench. The flow rate controlled by a gate valve located at the discharge side of the hydraulics bench. A venturi meter, wide-angled diffuser, orifice meter and rotameter are arranged in series. Pressure taps across each device are connected to vertical manometer tubes located on a panel at the rear of the apparatus. The discharge from the apparatus is returned to the hydraulics bench. Procedure:

1) Ensure that the hydraulic bench valve and the flow control valve on the apparatus are both closed. 2) Turn on the pump in the hydraulic bench and open the valve on the bench fully. 3) Slowly open the flow control valve to allow any trapped air to escape. Continue opening the valve until the rotameter reading reaches its maximum or the water manometers reach their readable limit, whichever happens first. 4) Record all the pressure readings from the manometers and the flow rate data from the gravimetric bench (see the Gravimetric Bench Operations handout). 5) Repeat the procedure of step 4 for flow rates of approximately 85%, 70%, 55%, 40% and 25% of full flow. Use the flow control valve to adjust the flow rate. 6) Fully close the flow control valve and the hydraulic bench valve. After both valves have been closed, shut the pump off. Theory:

A) Calculation of Discharge 1) Venturi meter Apply the continuity equation and the conservation of energy equation across the venture meter (pressure taps  A to  B). Neglect the head loss across the meter. Assume  za-  zb is zero. The density of water can be taken as 1000 kg/m 3. From the continuity   A A ρ V A

= ρ V B  A B

The discharge 2g

•

m = ρ Q = ρ V B  A B = ρ  A B

1

−

 A B  A A

2

P A ρ g

−

P B ρ g

12

2

ME313L Fluid Mechanic Lab Manual (DRAFT) Considering the geometry of the Venturi , the mass flow will be •

m = 0.962 h A − h B

12

kg/s

2) Orifice Meter Apply the continuity equation and the conservation of energy equation across the venture meter (pressure tappings  E  to F ). The head loss ∆ H  across the orifice meter cannot be neglected. In the energy equation the terms P E ρg

−

PF  ρ g

− ∆ H 

can be replaced by

 P   P   2  K    E  − F    ρ  g  ρ  g  The effect of the head loss across the orifice is to make the difference in the manometer heights less than it would otherwise be. The coefficient of discharge K  for this particular orifice geometry has been found to be 0.601. Again assuming that  z E  - zF  is zero and the density of water is 1000 kg/m 3 gives that 2g

•

m = ρ V F  A F  = ρ K A F 

1

−

 A F  A E 

2

P E  ρ g

−

PF  ρ g

12

Considering the geometry of the Orifice, the mass flow will be •

m = 0.846 h E 

−

h F 

12

kg/s

B) Calculation of Head Loss The head loss is the non-recoverable pressure drop across each meter, that is, the orifice, venturi and rotameter. for the venturi

∆ H = h A - hC 

for the orifice

∆ H = h E  - hF 

for the rotameter ∆ H = h H  - h I 

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ME313L Fluid Mechanic Lab Manual (DRAFT) C) Calculation of Minor Loss Write the energy equation across the wide-angled diffuser (from C  to  D ) and include the minor loss term, KV 2/2g, where K is the minor loss coefficient of the diffuser. Results:

The results can be presented as 1 ) From the gravimetric bench data, determine the mass flow rates through the apparatus for the six runs. 2) In tabular form compare the theoretical to the actual mass flow rates of  the venturi meter and the orifice meter and determine percent errors. 3) Determine the actual head loss (mm water) for the rotameter, venturi meter and the orifice meter and plot the results as a function of actual flow rate through the meter (plot both curves on the same graph). 4 ) Plot a calibration curve for the rotameter (volumetric flow rate liters/min as a function of rotameter reading). 5) For the wide-angled diffuser plot a curve of the K-value (minor-loss coefficient) as a function of flow rate. Compare the experimental value of  K  to the published value of  K  and find the percent error. The diffuser has a cone angle of 100 o

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