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Submitted By dino1985
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Objective:

a) To determine the coefficient of discharge for a Venturi meter.

b) To investigate the variation of piezometer (or static) head along the length of the Venturi meter.

Theory:

A venturi is a short tube with a constricted throat used to determine fluid pressure and velocities by measurement of differential pressures generated at the throat as fluid transverses the tube. It was by this method the venturi meter was develop by a scientist known as Clemens Herschel.
[pic]
Venturi meters can pass 25 – 50% more flow than an orifice meter. In a Venturi meter setup, a short, smaller diameter pipe is substituted into an existing flow line. In the Venturi Tube the fluid flow-rate is measured by reducing the cross sectional flow area in the flow path, generating a pressure difference. After the constricted area, the fluid is passes through a pressure recovery exit section, where up to 80% of the differential pressure generated at the constricted area, is recovered. By Bernoulli’s principle the smaller cross-sectional area results in faster flow and therefore lower pressure. The Venturi meter measures the pressure drop between this constricted section of pipe and the non-constricted section.

[pic]

The discharge coefficient for the Venturi meter is generally higher than that used for the orifice, usually ranging from .94 to .99. Due to simplicity and dependability, the Venturi tube flow-meter is often used in applications where higher turndown ratios or lower pressure drops than orifice plates can provide are necessary. With proper instrumentation and flow calibrating the venturi meter flow-rate can be reduced to about 10% of its full scale range with proper accuracy. This provides a turndown ratio of around 10:1.

Consider the flow of an incompressible fluid through the Venturi tube shown in the figure below. The cross-sectional area of the upstream section is A1; at the throat section 2 is A2 and at any other arbitrary section n is An, piezometer tubes at these sections register h1, h2 and hn respectively above the arbitrary datum.

[pic]

u12/2g + h1 = u22/2g + h2 = un2/2g + hn

where u1, u2, and un, are the flow velocities at sections 1, 2, and n.
The equation of continuity is: u1A1 = u2A2 = unAn = Q

Where Q denotes the volume flow rate.
Substituting for u1 in terms of u2: u22/2g (A2/ A1)2 + h1 = u22/2g + h2

Hence the velocity at the throat is: u2 = √ [(2g (h1 - h2)/ (1-(A2/ A1)2]

The ideal rate of flow is: Q = A2 u2 = A2√ [(2g (h1 - h2)/ (1-(A2/ A1)2]

Allowing for “losses” and variation of velocity across the cross-section, the actual flow rate is: Q = CDA2√ [(2g (h1 - h2)/ (1-(A2/ A1)2]
Where Cd is the coefficient of discharge for the Venturi meter.

The ideal variation of piezometer head along the meter can be expressed solely in terms of the geometry of the meter. u12/2g – h2 = un2/2g - hn

The change in piezometer head relative to the inlet is: hn - h1 i.e. hn - h1 = u12/2g - un2/2g = u22/2g [(u1/u2) 2 – (un/u2) 2]
Since: u1/u2 = A2/ A1 = (d2/d1)2
Then: u1/u2 = (d2/d1)2
Therefore: hn - h1 = u12/2g [(d2/d1)4 - [(d2/dn)4]

Once the value for Q has been calculated and measured, the measured value can be divided by the
Calculated value to determine the value of Cv , the discharge coefficient (typically between 0.90-0.99). Qmeasured = C* Qcalculated

Apparatus:

Venturi Apparatus by Norwood Instruments Ltd.
TecQuipment Hydraulic Bench (H1)
Stop watch

Hydraulics bench H1
The hydraulics bench provides facilities for performing a number of experiments in hydraulics at laboratory bench scale. A small centrifugal pump, drawing water from a sump which lies below the bench, delivers to apparatus place on the bench top. The flow rate is controlled by a valve in the supply line, and it is measured by collection of the discharge from the apparatus before return to the sump for circulation. The discharge is weighed in a weigh tank. Around the edge of the bench there is a raised lip, so that any water leaking from the equipment does not spill over the edge, but drains back to the sump through a waste hole provided for the purpose.
The weigh tank is supported beneath the bench, to one end of a weigh beam. The other end of the weigh beam projects slightly from the bench support, and carries a weight hanger, sufficient to balance the dry weight of the tank, plus a small amount of water. An operating lever, adjacent to the weight hanger, acts directly to open and shut a drain valve, so allowing the contents to be emptied back to the sump. To find the rate of discharge, the drain valve is closed. Water then starts to accumulate steadily in the weigh tank, so there comes a time when the weigh beam rises to its upper stop. A stop watch is started at this instant. A known weight is then added to the hanger, so returning the beam to its lower position. The stopwatch is stopped when the beam rises to its upper stop for a second time. The lever ratio of the weigh beam is 3:1, so the weight of water collected in the timed interval is three times the added weight. The drain valve is then opened to empty the weigh tank into the sump.

The Norwood Venturi apparatus
Fig. 2 shows the arrangement of the Venturi meter, which is manufactured in clear plastic material. Water from the bench supply valve flows through a flexible hose to the inlet tank upstream of the meter. The flow rate of water through the meter is controlled by a gate valve at the exit end of the meter, from which another flexible hose leads the water to the measuring tank. Several piezometer tappings, positioned along the length of the Venturi, are connected to vertical manometer tubes, which are mounted in front of a scale that is graduated from 150-516 mm. The whole assembly is supported on a base.
Fig 3 gives the dimension of the Venturi meter, and the positions of the 11 piezometer tappings (A-L) along its length. In accordance with B.S 1042, the converging section has a taper angle in the range 15-200 whilst the longer diverging section has a taper in the range 5-71/20.

Diameter at inlet, d1 = 25.4mm
Diameter at throat, d2 = 15.9mm
Length of converging section = 26mm
Length of throat section = 12mm
Length of diverging section = 80mm
Overall length = 118mm

Location of piezometer tappings are given in the following table:
|Piezometer |A(1) |B |
|Mass ( Kg) |t/(s) |Average Time |H1/ (mm) |H2 (mm) |Q / (m3/s) |(h1 – h2) /(mm) |√(h1 – h2) / |
| | | | | | | |(m1/2) |
|13.57 |28.90 |- |
|5.05 ×10-4 |4.78 ×10-4 |0.947 |
|4.87 ×10-4 |4.61 ×10-4 |0.947 |
|4.68 ×10-4 |4.43 ×10-4 |0.947 |
|4.48 ×10-4 |4.24 ×10-4 |0.946 |
|4.27 ×10-4 |4.04 ×10-4 |0.946 |
|4.03 ×10-4 |3.82 ×10-4 |0.948 |
|3.39 ×10-4 |3.21 ×10-4 |0.947 |
|3.32 ×10-4 |3.15 ×10-4 |0.949 |
|3.17 ×10-4 |2.99 ×10-4 |0.943 |
|2.87 ×10-4 |2.71 ×10-4 |0.944 |

a) Variation of Piezometric head and Piezometer tappings.

Table 3 piezometer reading and location.

|Piezometer |A(1) |B |C |
|B |13 |6 |23.2 |
|C |13 |19 |18.46 |
|D |13 |33 |15.90 |
| | | |[x = 20Tan 10.350] → dn = [x*2] + d2 mm |
|E |38 |47 |16.9 |
|F |38 |60 |18.51 |
|G |38 |73 |20.05 |
|H |38 |86 |21.58 |
|J |38 |99 |23.12 |
|K |38 |112 |24.66 |

At (A) dn = 25.4 mm
Therefore (d2/dn)4 = (15.9/25.4)4 = 0.153 mm

Table 5 showing the values for (d2/dn) 4th pwr. for each point labeled.

Piezometer |A(1) |B |C |D(2) |E |F |G |H |J |K |L | |dn(mm) |25.4 |23.2 |18.46 |15.9 |16.90 |18.51 |20.05 |21.58 |23.12 |24.66 |25.4 | |(d2/dn)4 |0.153 |0.221 |0.550 |1 |0.784 |0.544 |0.395 |0.295 |0.224 |0.173 |0.153 | | Qty = 30 lb v = m/ρ » 13.57 kg/ 1000 kg/m3 = 13.57x10-3 m3 t = 50.46 s Q = v/t » 13.57x10-3 m3 /50.46 = 2.69x10-4 m3/s therefore: u22 = Q/A2 » 2.69x10-4/1.985 x10-4 = 1.355 m/s

Therefore hB - h1 = u12/2g [(d2/d1)4 - [(d2/dn)4] = (0.531)2/19.62 [0.153-0.221] = 0.014 [-0.289]*1000 = -4.046 mm
N.B. all calculations are rounded off to 3 significant figures.

Table 6 theorectical values

hA-h1
(mm) |hB-h1
(mm) |hC-h1
(mm) |hD-h1
(mm) |hE-h1
(mm) |hF-h1
(mm) |hG-h1
(mm) |hH-h1
(mm) |hJ-h1
(mm) |hK-h1
(mm) | |0 |-4.05 |-5.56 |-11.86 |-59.31 |-36.75 |-22.75 |-13.35 |-6.67 |-1.88 | |

Graph:

Figure 1 showing the graph of discharge [part A]

[pic]

Figure 2 showing graph for (hn-n1 vs Xn) actual values.

[pic]

Figure 3 showing graph of (hn-h1 vs Xn) for theoretical values.

[pic]
Discussion:

.

Conclusion: http://www.engr.iupui.edu/me/courses/me310lab/experiment12.pdf http://controls.engin.umich.edu/wiki/index.php/FlowSensors#Venturi_Meter

-----------------------
12.7

4.75

12.7

4.75

26

7.5

7.5

80

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