Fluid Mechanics 2Practical 1- Discharge through an Orifice

Lecturer: Mr. Van WykGroup: 34

Date performed: 14 April 2011Date submitted: 29 April 2011

Group members:Dildar A. 20900360Gumpe S. 20904907Naidoo D. 20920925Neerputh K. 20902223Sunder S. 20921378

1

Table of Contents 1. Introduction page 3 and 42. Aim, Hypothesis and Apparatus page 53. Method page 64. Results and observations page 7,8,9,10 and 115. Discussion and Conclusion page 126. References page 13

2

Introduction:An orifice meter is a type if flow measurement and it consists of a flat orifice plate. This orifice plate has a hole in the middle where fluid flows through. As the fluid flows through the opening in the middle of the orifice plate, there is a change in the velocity and pressure of the fluid.The vena contracta is created as the fluid flows through the hole and it is the narrowest point of the flow of fluid. After the fluid flows past the vena contracta point, the fluid begins to expand and the velocity and pressure of the fluid changes again. The vena contracta produces losses in the orifice. Coefficients of contraction, velocity, and discharge (flow rate) are equations used to express the losses induced in the orifice.Coefficient of contraction:Cc= Avc

Ao

Where:Cc= coefficient of contraction (no units).Avc= ( πDv c2

4)area of the vena contracta (m ).²

Ao= (πDo24

) area of the orifice (m ).²Coefficient of velocity:Cv=Va

Vt

Where:3

Cv= coefficient of velocity (no units).Va= (√2gH) actual velocity of the fluid (m/s).Vt= (√2gHc) theoretical velocity of the fluid (m/s).

Coefficient of discharge (flow rate):Cd=Qa

Qt

Where: Cd= coefficient of discharge (flow rate).Qa= ¿actual flow rate of the fluid (m /s).³

Qt=(Ao√2gH) theoretical flow rate of the fluid (m /s).³

4

Aim:To determine the coefficient values of contraction, velocity and discharge (flow rate) in an orifice and how the different values of heads affect these coefficients.

Hypothesis: It is expected that the velocity of the fluid will increase as the fluid passes through the vena contracta because its area is smaller than the area of the orifice. The pressure of the fluid is assumed to decrease after it passes through the vena contracta point. The actual velocity and flow rate of the fluid will be less than the theoretical values for the velocity and flow rate of the fluid.

Apparatus: An orifice meter attached to a tank containing water. A hydraulic bench. A pitot tube. Orifice plate with a circular opening in the middle which has a diameter of 12.7mm. A piezometer to measure the head values of water in the tank (inches). A calliper to measure the diameter of the fluid flowing from the vena contracta point. A mass of 15 lbs (pounds) attached to the tank containing water. A stopwatch to record the time taken.

5

Method: The tank was allowed to be filled with water so that the level of water in the tank is kept constant as the overflow pipe was taken into consideration. The height of water in the tank (H) was recorded using the left-hand scale of the piezometer (inches). The diameter of the water flowing through the vena contracta point was measures using a calliper. The pitot tube was rotated into the flow of water and the height (Hc) of the water was measured using the right-hand scale of the piezometer. The pitot tube was then rotated back out after the reading was taken. The valve on the tank was closed and the timer was started on the stopwatch. The tank on the lever dropped as the mass of water exceeded the 15 lbs (pounds) of weight. As the weight started to rise, the timing was stopped. The valve for the flow of water into the tank was closed and the flow of water was adjusted so that the inflow and outflow of water was equivalent. The height of the water (H) was recorded using the left hand scale of the piezometer and will be kept constant. This entire procedure was repeated five times.

6

Results and observations:Number of readings

Diameter of vena contracta H Hc t (s)

1 10.5mm 15.4inchesx25.4=391.16mm 15.2inchesx25.4=386.08mm 37.32 11mm 13.5inchesx25.4=342.9mm 13.4inchesx25.4=340.36mm 43.163 10mm 12.6inchesx25.4=320.04mm 12inchesx25.4=304.8mm 46.414 10mm 10inchesx25.4=254mm 9.8inchesx25.4=248.92mm 49.85 10mm 5.5inchesx25.4=139.7mm 5.5inchesx25.4=139.7mm 70

Volume conversion:15lbs×0.4535923=6.804kg∴6.804kg÷1000=6.804x10-3m³

1 St reading: Coefficient of contraction: Coefficient of velocity:Cc= Avc

AoCv=Va

Vt

7

Cc= [𝛑 (0.0105) /4]/ [𝛑 (0.0127) /4] ² ²Cv=√(2x9.81x0.38608)/ Cc= 0.684 √(2x9.81x0.39116)Cv= 0.993Coefficient of discharge:

Cd= QaQt

Cd= [6.804X10-3/37.3] /{[𝛑(0.0127) /4] (√2x9.81x0.39116)}²

Cd= 0.52

2 nd reading: Coefficient of contraction: Coefficient of velocity:Cc= Avc

AoCv=Va

Vt

Cc= [(0.011) /4]/[𝛑(0.0127) /4]² ²

Cv=√(2x9.81x0.34036)/ √(2x9.81x0.3429)Cc= 0.75 Cv= 0.996Coefficient of discharge:Cd= Qa

Qt

Cd= [6.804x10-3/43.16]/ { [𝛑 (0.0127) /4] √ (2x9.81x0.3429) }²

Cd=0.488

3 rd reading: Coefficient of contraction: Coefficient of velocity:Cc= Avc

AoCv= Va

Vt

Cc= [(0.01) /4]/[𝛑(0.0127) /4]² ² Cv=√(2x9.81x0.3048)/ √(2x9.81x0.32004)Cc= 0.62 Cv= 0.976Coefficient of discharge:Cd= Qa

Qt

Cd= [6.804x10-3/46.41]/{ [𝛑(0.0127) /4]√(2x9.81x0.32004) }²

Cd= 0.462

4 th reading: Coefficient of contraction: Coefficient of velocity:Cc= Avc

AoCv= Va

Vt

Cc= [(0.01) /4]/[𝛑(0.0127) /4]² ²

Cv=√(2x9.81x0.24892)/ √(2x9.81x0.254)Cc= 0.62 Cv= 0.99Coefficient of discharge:Cd= Qa

Qt

Cd= [6.804x10-3/49.8]/{[𝛑(0.0127) /4]√(2x9.81x0.254) }²

9

Cd= 0.4835 th reading: Coefficient of contraction: Coefficient of velocity:Cc= Avc

AoCv= Va

Vt

Cc= [(0.01) /4]/[𝛑(0.0127) /4]² ² Cv=√(2x9.81x0.1397)/ √(2x9.81x0.1397)Cc= 0.62 Cv= 1Coefficient of discharge:Cd= Qa

Qt

Cd= [6.804x10-3/70]/{[𝛑(0.0127) /4]√(2x9.81x0.1397) }²

Cd= 0.463

 Number of readings H(m) √H (m) Qt= Ao√2gH (m /s)³

1 0.39116 0.625 0.000351  2 0.3429 0.586 0.000329  3 0.32004 0.566 0.000317  4 0.254 0.504 0.000283  5 0.1397 0.374 0.00021  

10

Line graph showing H versus Qt and √H versus Qt:

0.0003509 0.0003286 0.0003174 0.0002828 0.00020970

0.1

0.2

0.3

0.4

0.5

0.6

0.7

H(m)√H (m)

 Number of readings H(m) Vt= √2gH (m/s)1 0.39116 2.77

2 0.3429 2.594

3 0.32004 2.506 4 0.254 2.232 5 0.139 1.656

11

7

Line graph showing H versus V

1.6 1.8 2 2.2 2.4 2.6 2.8 30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

H(m)

Discussion:The results obtained in this practical investigation indicate that the vena contracta produced losses in the orifice. These losses induced, were expressed through the coefficients of contraction, velocity and discharge (flow rate). The height of water decreased after each reading was taken which means that the velocity and pressure also decreased.

12

The area of the vena contracta affected the coefficient of contraction; as the area reduced, the value of the coefficient of contraction decreased. Actual velocity affected the coefficient of velocity; as the actual head value decreased after each reading, the coefficient of velocity value decreased as well. Actual flow rate affected the coefficient of discharge; as time increased after each reading, the actual flow rate together with the coefficient of discharge decreased.The line graph illustrating the head value (H) and the square root of the head value versus the theoretical flow rate (Qt) shows as the head values decreased after each reading was taken, the theoretical flow rate decreased as well. The decreasing lines on the graph show this relationship. Errors encountered during this experiment affected the slope of the graph and should have been straight decreasing lines.The line graph illustrating the head value (H) versus the theoretical velocity of the fluid (Vt) shows that as the head values decreased after each reading was taken, the theoretical velocity decreased as well. This relationship is indicated on the decreasing slope of the line. Errors encountered during this experiment affected the slope of the graph and should have been a straight decreasing line.Errors encountered in this practical investigation include the following: timing taken could have been inaccurate, readings were not taken at eye level, the diameter of the vena contracta could have been measured incorrectly using the calliper and external forces surrounding this experiment could have affected the readings recorded. These errors are evident in the equations to calculate the coefficient of discharge (Cd=Qa/Qt) and (Cd=CcxCv) which should have been identical but are different.The most common function of an orifice meter is to measure the flow of fluid in piping systems. It is used to increase the pressure of fluid in the pipe, decrease its flow rate and increase the velocity of the fluid through the system. Accuracy is reduced due to low flow rates in the piping systems and the wear of the orifice plates. An orifice meter can also be used in natural environments to control the flow of water in flood-relief dams.Conclusion:The hypothesis of this investigation is proved correct and concludes that losses occurred in the orifice due to the vena contracta. The coefficients of contraction, velocity and discharge calculated, indicated that these losses exist. Reduction in the head values of the fluid result in smaller coefficients of contraction, velocity and discharge.13

References: Meyer C.F. Principles of Fluid Mechanics. 1995. Pretoria: CFM Publications Orifice plate- Wikipedia. 2011. http://www.en.wikipedia.org. (Accessed 21/04/2011).

14