Venturi Flow Rig Experiment r5y6w

A. SUMMARY: The topic investigated in this experiment was the venturi Flow Rig. This is very significant in chemical engineering because the venturi meter offers the best means of measuring the flowrate of fluids out of all the other means. The major objectives of this lab was to; compare the behaviour of real and ideal fluids using a venture meter, to record the head loss profile through a venturi meter at different flowrates and to estimate the coefficient of discharge of a venturi meter. In the course of the experiment, the following equipments were used; a Perspex venture meter having eleven (11) manometric tubes to measure the static head of the fluid, a water supply tank, a pump, a level control device, a stop-clock to take readings of the time it took the water to discharge and a lever system to measure the weight of water discharge. From the experiment, it was found out that the Bernoulli's theorem only applies to ideal fluids. That is fluids that are incompressible (constant density), irrotational (smooth flow or laminar flow), non-viscous (fluid without internal friction) and finally a steady flow (one with constant velocity at each point. It was also found out that the head loss across different sections of the Venturi meter were minimal when compared to that involved in other flow-measuring device such as an orifice. From the plots of various graphs at different flowrates, it was also found out that the static head, the velocity head and the total head are directly related (direct proportionally) to the flowrates. Also there is a direct relationship between pressure drop and flowrate. One other important finding from the experiment was that the coefficient of discharge of a venturi was higher due to the fact that the head loss is small. Therefore, it can be inferred that the smaller the head loss, the greater the coefficient of discharge when measuring the flow of fluids. It was found out also that the theoretical flow of fluid through venture is slightly higher than the actual value. Also the coefficient of discharge for the venture was estimated to be 0.95 ± 0.03. From the experiment, it can be concluded that the ventrui meter is suitable for both compressible and incompressible fluids. This is true because when it comes to measuring the flow of compressible fluids or real fluids, the mass flow rate for a compressible fluid can increase with increased upstream pressure, which will increase the density of the fluid through the constriction even though the velocity will remain constant (Holland, 1986). Finally, it can also be concluded that for higher flow rates where power loss could become significant; the venturi meter could be very suitable.

B.

INTRODUCTION: Page 1 of 15

There were three major objectives of this experiment. These are; to compare the behaviour of real and ideal fluids using a venture meter, to record the head loss profile through a venturi meter at different flowrates and to estimate the coefficient of discharge of a venturi meter. Venturi meters are used to accurately measure fluid flow in a pipe for both compressible and incompressible fluid. This is true because the head loss when using a venture meter is minimal when compared to other devices for measuring fluid flow. For an incompressible fluid, its behaviour may be explained or predicted by Bernoulli’s equation. This can be done by considering it in of the total head. The total head can be calculated as: pρg + v22g + z = H

(1)

Where: pρg is the static or pressure head (m) v22g is the velocity head (m)

z is the elevation head (m) H is the total head (m) For a horizontal venture (that is one without height), the equation becomes: pρg + v22g = H

(2) This means that for an incompressible fluid, the pressure head or static head plus the velocity head is constant or equal to the total head. It is noteworthy to mention here that the total head (H) should have remained constant at all points along the tube, but due to the effect of friction, some head losses were experienced. Though, these head losses were minimal in this case since we are using a venturi meter. If the flow rate (Q) was measured, then from the continuity equation, the velocity of at each position along the duct can be calculated.

The continuity equation is: Q= A1 V1 = A2 V2

(3)

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Where: Q is the flow rate

(m3/s)

A1 is the area at the inlet section of the venturi

(m2)

V1 is the velocity at the inlet section of the venturi (m/s) A2 is the area at the throat of the venturi

(m2)

V2 is the velocity at the throat of the venturi

(m/s)

Note: the above equation can be extended to other sections of the tube The above equation can be transposed for the velocity at each section as: Vn = Qan

(4)

Where: Vn is the velocity at each section of the tube

(m/s)

Q is the flow rate

(m3/s)

an is the area at each section of the tube

(m2)

By determining the velocities at each sections of the duct together with the peizometric heads, the behaviour of real fluids (compressible fluids) can be compared with that of ideal fluids (incompressible fluids) as predicted by Bernoulli. For the latter (that is for compressible fluids), the density would not be constant. It will vary from the density ρ1 at the venturi inlet to the density ρ2 at the venturi throat. (Douglas, Gasiorek and Swaffield 2001). As mentioned earlier, for a compressible fluid the mass flow rate would increase with increased upstream pressure, which will increase the density of the fluid through the constriction (though the velocity will remain constant). The reverse is the case for an incompressible fluid or ideal fluid. By measuring the pressure drop across the venturi meter, we can also calculate the value of the coefficient of discharge ( Cd ). This can be expressed in of the flow rate (Q) as: Q= Cd * at * [(2∆p/ρ(1-m2)

(5)

Where:

Page 3 of 15

Q is the flowrate

(m3/s)

Cd is the coefficient of discharge

(dimensionless)

at is the area of the throat of the venturi

(m2)

∆p is the pressure drop across the venturi

(Nm-2)

∆p is the density of water

(100 kgm-3)

m is the ratio of the area of the throat of the venturi ( at) to the area at the approach duct ap

Thus, m= atap (6) Where: at is the area of the throat of the venturi

(m2)

ap is the area at the approach duct

(m2)

The coefficient of discharge is introduced to for the fact that the theoretical flow of a fluid is slightly greater than the actual or measured flow. Equation (5) above can be transposed for Cd as: (7)

Cd= Qat*2∆pρ(1-m2)

Note: all the parameters are as explained above in the previous equations (5) and (6). Having known the coefficient of discharge Cd, the theoretical flow can also be estimated and compared with the actual flow using: Qactual= Cd * Qtheoritical

(8)

Where: Qactual is the actual or measured flow

(m3/s)

Cd is the discharge coefficient

(dimensionless)

Qtheoritical is the theoretical flow

(m3/s) Page 4 of 15

The theoretical values of the static heads can also be compared with its experimental static heads by calculating the theoretical heads as: hn

= h1 - [vn22g - v122g] (9)

Where hn is the theoretical static head at various sections of the tube

(m)

h1 is the static head at the inlet of the tube

(m)

Vn is the velocity at various sections of the tube

(m/s)

V1 is the velocity at the inlet of the tube

(m/s)

One important relationship that can be shown when using a venturi meter to measure fluid flow is the direct relationship between the pressure drop and the flowrate. This can be shown by calculating the pressure drop across the venturi and then plotting a graph of the square-root of the pressure drop against the flowrate. The pressure drop can be calculated as: (10)

∆p= ρg∆h

Where: ∆p is the pressure drop across the venturi

(Nm-2)

ρ is the density of water

= 1000 kgm3

∆h is the head loss across the venturi

(m)

The energy loss can also be calculated in of the power consumption as: (11)

Power consumption=Q*∆P

Where: Q is flowrate

(m3/s)

∆P is the pressure drop across the venturi

(Nm-2) Page 5 of 15

C.

EXPERIMENTAL EQUIPMENT:

The main experimental equipment used in this experiment is a Perspex venturi meter having eleven manometric tubes to measure the head loss across the venturi. Other equipments include; a lever system to measure the weight of the water discharged, a stopwatch to measure the time needed for a certain volume of water to be supplied; in order to then calculate the actual rate of flow. Other equipments are; water supply tank, a pump and a level control device. A Venturi Meter consists of a short converging conical tube leading to a cylindrical portion, called the throat, of smaller diameter of that of the pipeline, which is followed by a diverging section in which the diameter increases again to that of the main pipeline (Douglas, Gasiorek and Swaffield 2001). The geometry of the venturi meter is designed to reduce head losses to a minimum. This is accomplished by providing a relatively streamlined contraction (which eliminates separation ahead of the throat) and a very gradual expansion downstream of the throat (which eliminates separation in the decelerating portion of the device. Thus most of the head losses that occurs in a well-designed venturi meter is due to friction losses along the walls rather than losses associated with separated flows ( Munson, Young and Okiishi 2002). The diagram of a venturi meter used in this experiment can be seen in figure 1 below.

manometric tubes

Venturi tube

Figure 1: Diagram of a venturi meter Page 6 of 15

Taken from http://www.cs.cdu.edu.au/homepages/jmitroy/eng243/VenturiMeter.pdf

The venturi tube has a converging conical inlet, a cylindrical throat, and a diverging recovery cone. It has no projections into the fluid, no sharp corners, and no sudden changes in contour. In Figure 3 showing the venturi tube, the inlet section decreases the area of the fluid stream, causing the velocity to increase and the head loss to decrease. The low pressure is measured in the centre of the cylindrical throat since the pressure will be at its lowest value, and neither the pressure nor the velocity is changing. The recovery cone allows for the recovery of head such that total head loss is minimal only about 10%. The working principle of the venturi meter can be explained using a schematic diagram of the venturi metre on the next page:

Figure 2: Schematic diagram of a venturi meter

Taken from www.icaen.uiowa.edu/~fluids/Posting/Home/EFD/EFD.../lab2_lecture.ppt

For ideal fluids, the velocity V1 and V2 are uniform and steady at the points A1 and A2. For real fluids, this would not be the case. The pressure would fall where the liquid velocity increases in the constriction, thus the greater the velocity change the greater the pressure drop. As the fluid moves from point 2 to point 3, the velocity is decreased and the pressure is increased. The slow rate of change creates a small energy loss; most of the energy is changed back to pressure. It is this relatively small loss that allows the venturi meter’s use in low pressure pipes. This small loss is also what makes the use of the Venturi meter attractive for flow measurements. (Watson 1998). There is a gain in kinetic energy resulting from the increased linear velocity in the throat. This is been balanced by the decrease of pressure in the throat. This reduction in pressure which occurs when the fluid flows through the throat is called the venturi effect (Coulson & Richardson, 1999). Page 7 of 15

D.

EXPERIMENTAL PROCEDURE AND OBSERVATIONS:

The procedures undertaken in this experiment was in two (2) stages. First, the pump was switched on, and the rotameter adjusted to ensure that water flows through the venturi. During this process, it was ensured that no air was induced into the system via the throat of the venturi. After establishing a steady flow, the static heads at each manometric tube were measured. Also with the weigh bench, the weights of water discharged by the system per unit time were measured. This together with the volume of water discharged was then used to calculate the flowrate (Q). With the dimensions of the essential parts of the venturi meter that were given in a table behind the venturi tube, the velocity and the velocity heads were also calculated. Using the head difference between the manometer tube 1 h1 (approach duct) and the manometer tube in the venturi throat position ht, the pressure drop across the venturi for the different flow rates were also calculated. The experiment was repeated for two other flowrates. For full list of measurements taken and for calculated data, see table 1-6. For graphs showing relationship between different parameters (both experimental and calculated), see figures 3-6

E.

RESULTS AND CALCULATIONS:

The results (both experimental and calculated results) obtained in the experiment are represented in table 1-4 below. The graphs of static head h, the velocity head hv and the total head H across the venture at each flowrate are shown in figure 3-5.

Tub e1 (m) 0.26 9 0.25 3

Tub e2 (m) 0.25 4 0.24 2

0.24

0.23

Tub e3 (m) 0.15 6 0.16 5 0.17 4

Tub Tube e 5 4 (m) (m) 0.01 0.002 9 0.049 0.09

0.06 0.09 7

Tube 6 (m) 0.10 8 0.12 7 0.14 6

Tube 7 (m)

Tube Tube 9 8 (m) (m)

0.157

0.186

0.205

0.165

0.188

0.203

0.173

0.19

0.2

Tube 10 (m) 0.22 0.21 4 0.20 9

Tub e 11 (m) 0.22 8 0.22 0.21 2

Tim e (s) 12.2 4 13.9 5 16.6 3

Flowr ate (m3/s) 0.0004 9 0.0004 3 0.0003 6

Static heads gotten from the experiment

Page 8 of 15

Table 2: Calculated Results for the velocity heads (Vh) across the venturi meter Tube 1 (m) 0.043 14 0.033 47 0.023 59

Tube 2 (m) 0.068 58 0.053 08 0.036 86

Tube 3 (m) 0.172 56 0.133 90 0.092 98

Tube 4 (m) 0.303 45 0.233 65 0.163 47

Tube 5 (m) 0.248 93 0.192 02 0.133 90

Tube 6 (m) 0.170 69 0.132 25 0.091 61

Tube 7 (m) 0.120 88 0.092 98 0.065 15

Tube 8 (m) 0.087 47 0.067 47 0.047 02

Tube 9 (m) 0.065 08 0.050 01 0.035 15

Tube 10 (m) 0.048 95 0.037 73 0.026 45

Tube 11 (m) 0.043 14 0.033 47 0.023 59

Flowrate 0.00049 0.00043 0.00036

Veocity heads (Vh) across the venturi meter calculated from equation (1)

Tube 1 (m/s) 0.92

Tube 2 (m/s) 1.16

Tube 3 (m/s) 1.84

Tube 4 (m/s) 2.44

Tube 5 (m/s) 2.21

Tube 6 (m/s) 1.83

Tube 7 (m/s) 1.54

Tub e8 (m/s ) 1.31

0.81

1.02

1.62

2.14

1.94

1.61

1.35

1.15

0.99

0.86

0.81

0.68

0.85

1.35

1.79

1.62

1.34

1.13

0.96

0.83

0.72

0.68

Tube 10 (m) 0.268 95 0.251 73 0.235 45

Tube 11 (m) 0.271 14 0.253 47 0.235 59

Tube 1 (m) 0.312 14 0.286 47 0.263 59

Tube 2 (m) 0.322 58 0.295 08 0.266 86

Tube 3 (m) 0.328 56 0.298 90 0.266 98

Tube 4 (m) 0.305 45 0.282 65 0.253 47

Tube 5 (m) 0.267 93 0.252 02 0.230 90

Tube 6 (m) 0.278 69 0.259 25 0.237 61

Tube 7 (m) 0.277 88 0.257 98 0.238 15

Tube 8 (m) 0.273 47 0.255 47 0.237 02

Tube 9 (m/s ) 1.13

Tube 10 (m/s) 0.98

Tube 11 (m/s) 0.92

Tube 9 (m) 0.270 08 0.253 01 0.235 15

Flowra te 3 (m /s) 0.0004 9 0.0004 3 0.0003 6 Flowrat e (m3/s) 0.0004 9 0.0004 3 0.0003 6

Table 3: Calculated Results for the total heads (H) across the venturi meter

Table 5: Calculated Results for Theoretical values of hn Table 4: Calculated Results for Velocity ( Vn) across the venturi meter Page 9 of 15

Tube Tube Tub Tube Tube 4 5 Tube e7 2 (m) 3 (m) (m) (m) 6 (m) (m) 0.24 0.13 0.00 0.02 0.19 0.269 4 9 9 4 0.141 1 0.23 0.15 0.05 0.09 0.16 0.253 3 3 3 5 0.116 6 0.22 0.17 0.10 0.13 0.19 0.24 7 1 3 1 0.172 9 Theoretical values of hn was calculated using equation (9)

Tube 1 (m)

Tube 8 (m) 0.22 5 0.21 9 0.21 7

Tub e9 (m)

Tube 10 (m)

Tube 11 (m)

Flowrate (m3/s)

0.24 0.23 7 0.22 9

0.263

0.269

0.00049

0.249

0.253

0.00043

0.232

0.24

0.00036

Table 6: Calculated Results Pressure drop and square-root of pressure drop across the venturi for different flowrates. Pressure drop (∆p) (Nm-2)

Flowrate (m3/s) (m3/s)

P

Nm-2 38.868238 1510.74 0.00049 96 33.733662 1137.96 0.00043 71 28.706096 824.04 0.00036 91 Pressure drop calculated using equation (10)

Figure 3: Graph of Static heads against Tube no. for different flowrates Q1, Q2 and Q3

Figure 4: Graph of velocity head hv against Tube no. for different flowrates Q1, Q2 and Q3

Figure 5: Graph of total head, H against Tube no. for different flowrates Q1, Q2 and Q3 Page 10 of 15

Figure 5: Graph of hn against tube no. for different flowrates Q1, Q2 and Q3 comparing experimental and theoretical hn

Figure 6: Graph of p against flowrate showing the relationship between pressure drop, ∆P and flowrate, Q.

SAMPLE CALCULATIONS: (A) Sample calculation for velocity across each section of the venturi

Using equation (4): Vn = Qan Velocity across the first section; Where Q = 0.00049 m3/s, A1 = 530.9mm2 = 0.0005309m2

Page 11 of 15

Therefore, V1 = 0.000460.0005309 = 0.92 m/s

(B) Sample calculation for total head across the venturi

Using equation (2): pρg + v22g = H Total head across the first section of the venturi; Where = pρg = static head h = 0.269m,

v22g = 0.9222*9.81 = 0.04314m

Therefore, total head (H) across first section of the venturi = 0.269m + 0.04314m = 0.31214m (C) Sample calculation for velocity heads (hv) across the venturi

From equation (1) v22g = velocity head Velocity head across the first section of the venture; Where v2 = 0.922 = 0.8464 m2/s2 2 * g = 2 * 9.81 = 19.62 m/s2 Therefore, Velocity head across the first section of the venturi = 0.8464 19.62 = 0.04314 m (D) Sample calculation for theoretical values of hn across each section of the venturi

Using equation (9): hn = h1 - [vn22g - v122g] Theoretical hn across the second section of the venture; Where v222* g = 1.16219.62 = 0.06858m v122g

= 0.92219.62 = 0.043139m

and h1 = 0.269m

Therefore theoretical hn across the first section of the venture = 0.269 – [0.06858 – 0.043139] = 0.2435 m

(E) Sample calculation for pressure drop (∆p) the venturi for flowrates Q1, Q2 and Q3

Using equation (10): ∆p= ρg∆h For flowrate Q1: Where: ρ=1000 kgm3, g=9.81 m/s2 ∆h= h1 - ht = (0.156 m – 0.002) = 0.154 m

Therefore , ∆p = 1000 * 9.81 * 0.154 = 1510.74 Pa For flowrate Q2: Where ρ=1000 kgm3, g=9.81 m/s2 ∆h= h1 - ht = (0.165 m – 0.049m) = 0.116 m

Therefore , ∆p = 1000 * 9.81 * 0.154 = 1137.96 Pa Page 12 of 15

For flowrate Q3: Where ρ=1000 kgm3, g=9.81 m/s2 ∆h= h1 - ht = (0.174 m – 0.09) = 0.084 m

Therefore , ∆p = 1000 * 9.81 * 0.084 = 824.04 Pa

(F) Sample calculation for estimation of the energy loss

Using equation (11): Power consumption=Q*∆P Where total pressure loss (∆P) = (1510.74 + 1137.96 + 824.04) Pa = 3472.74 Pa Also total flowrate (Q) = Q1 + Q2 + Q3 = (0.00049 + 0.00043 + 0.00036) m3/s = 0.00128 m3/s Therefore, Power consumption = 0.00128 * 3472.74 = 4.45W

(G) Sample calculation for the coefficient of discharge( Cd ):

From equation (7): Q= Cd * at * [(2∆p/ρ(1-m2) Transposing the above equation for Cd : Cd= Qat*2∆pρ(1-m2) m = at /ap = 2.011*10-42.659*10-4 = 0.7563

Therefore, m2 = (0.7563)2 = 0.5719 = 0.001282.659*10-4*2*3472.741000(1-0.5719)

= 0.95

Therefore, the coefficient of discharge ( Cd ) = 0.95 This is in line with the theoretical value of Cd ( 0.98 ) gotten from textbooks. (H) Sample calculation for the theoretical flow:

Using equation (8): Qactual= Cd * Qtheoritical Therefore, Qtheoretical = QactualCd = 1.28*10-30.95 = 1.35*10-3 m3/s

C.

DISCUSSION OF RESULTS: The graph in figure 3 shows the relationship between the static heads and the flowrates at each section of the venture meter. It shows that, the higher the flowrate, the higher the static head, Page 13 of 15

except for the manometric tubes with smaller area where the head loss was small because of the small cross-sectional area (for example tube 2). The graph in figure 4 shows the relationship velocity heads and flowrates across the venturi. This shows that the higher the flowrate, the higher the velocity head. As it can be seen from figure 4, the highest flowrate correspond to the highest velocity head while the lowest flowrate corresponds to the lowest velocity head. The graph in figure 4 shows that the higher the flowrate, the higher the total head. As such, at flowrate (Q1), we had higher total head (H) followed by flowrate (Q2) and lastly flowrate (Q3) Also from the graph in figure 5, it shows that the theoretical values of hn at different flowrates is slightly higher than the experimental values, except for h1 were it was assumed that the theoretical values were the same with the experimental values. From the graph of the square-root of pressure drop p against flowrate, Q in figure 6, it can be inferred that there is a direct relationship between the square-root of the pressure difference; hence the graph is a straight line graph. This means that if there is a tenfold increase in the flowrate, there must be a one hundred increase in the pressure difference. From the calculation of the theoretical flow, it can be seen that the theoretical flow is slightly higher than the actual or measured flow. This is in line with the theory. It is because of this slight difference that a coefficient of discharge was introduced. It is noteworthy that this coefficient of discharge varies with the rate of flow. This can be explained by equation (6) and (7). From table 2, it shows that there is a linear increase in velocity at the throat of the venturi. This increase leads to a gain in kinetic energy and at the same time, this increase is been balanced by a decrease of pressure in the throat. This explains why the velocities at tube 4 (section D of the venturi meter) which is the throat were all higher than the velocities at other sections of the venturi meter. The velocities at tube 4 were 2.44 m/s, 2.14 m/s and 1.79 m/s at different flowrates respectively. Other velocities were below these ones.

D.

CONCLUSIONS: From the experiment, the following conclusions can be drawn. Page 14 of 15

(i)

The venturi meter is indeed the most accurate method of measuring fluid flow both incompressible and compressible fluid because the head losses recorded in using it is minimal compared to other measuring devices.

(ii)

Contrary to what we know from the idea of an ideal fluid, where the velocity is constant at each point, in the case of the venture, the velocity is high at the throat, though this is balanced by a reduction in the pressure at the throat too due to venturi effect.

(iii)

The theoretical discharge was slightly higher than the actual or measured discharge. This slight difference was ed for by the coefficient of discharge.

(iv)

The head loss, the velocity head and the total head all depends on the rate of flow. The higher the rate of flow, the higher the head loss, the higher the velocity head and the higher the total head too.

(v)

There exist a direct relationship between the pressure drop across the venturi and the flowrate. This can be seen when the square-root of the pressure drop, P was plotted against the flowrate, Q. This gave a straight line graph.

References: Coulson, J.M. and Richardson, J.F. (1999) Coulson & Richardson’s Chemical Engineering. 6th ed. Oxford: Elsevier Science, Volume 1, Chapter 5. Douglas, J.F. Gasiorek, J.M and Swaffield, J.A. (2001) Fluid Mechanics. 4th ed. London: Prentice Hall, Chapter 6 & 17. Holland, F. (1986) Fluid Flow for Chemical and Process Engineers. 2nd ed. Oxford: Butterworth-

Heinemann. Munson, B.R. Young, D.F and Okiishi, T.H. (2002) Fundamentals of Fluid Mechanics. 4th ed. New York: John Wiley & Sons, Inc., Chapter 8. Mitroy, J. Lab note on Engineering Mechanics (2009) Charles Darwin University [online] Available from: http://www.cs.cdu.edu.au/homepages/jmitroy/eng243/VenturiMeter.pdf [ accessed 07 March 2011 ]. Watson, K.L. (1998) Foundation Science for Engineers. 2nd ed. London : Macmillan Press Ltd, Chapter 20. http://www.icaen.uiowa.edu/~fluids/Posting/Home/EFD/EFD.../lab2_lecture.ppt [ accessed 07 March 2011 ]

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