Nowadays. a Pitot tubing would be of usage as a speed indicator on airplanes. It is besides found utile in industries where speed measurings are required. where an wind gauge may non be the most efficient instrument to utilize. There are three types of Pitot tubings: Pitot tubings. Inactive tubings. and Pitot-Static tubings.

The simple Pitot tubing basically consists of a tubing set at – normally – 90° . with an unfastened terminal indicating straight towards the fluid flow. As the fluid flows in the tubing. it becomes dead since there is no direct gap at the other terminal for it to go out from. As the inert fluid rises. it creates a force per unit area of its ain. This force per unit area is tantamount to the dynamic force per unit area. which can be seen as the kinetic energy of the fluid per unit weight.

F. X. Pitot originally used this device to analyse the force per unit area created by the stagnating fluid at the other terminal of the tubing. He did this by ciphering the amount of the dynamic force per unit area and inactive force per unit area. The force per unit area created by the dead fluid ( stagnation force per unit area ) is found where the speed constituent is zero. Using these rules. it is possible to find a fluids speed.

This has manifested itself in the signifier of the Bernoulli equation. It describes this phenomenon as it states that an inviscid fluid’s addition in speed is accompanied with a coincident lessening in force per unit area or in the fluid’s possible energy. However. this equation works on two premises – the first. that the fluid is incompressible ; the 2nd. that clash caused by syrupy forces are to be considered negligible. The Bernoulli equation can however be used for compressible flows. but merely at low Mach Numberss.

In the experiment. we measured the radial speed profile at a cross-section of a pipe utilizing the Pitot tubing. As the Pitot investigation is shifted along the pipe. we can enter the stagnancy force per unit area and inactive force per unit area at that cross-section of the pipe. The speed of the inviscid fluid can now

be found utilizing both force per unit areas.

The smaller the diameter of the Pitot tubing is. the more accurate the flow speed. If the Pitot tubing has excessively big a diameter. consequences for the fluid’s flow could be inaccurate due to the difference in speed between the fluid against the tubing walls and the fluid in the center of the tubing.

Background and Theory

One of the most cardinal equations in the field of unstable mechanics is the Bernoulli Equation:

As stated in the debut. this equation is based on the premise that the denseness and speed of the fluid are changeless.

If we so multiply both sides of the Bernoulli equation ( combining weight. 1 ) by the denominator denseness ( ) . the consequence is:

We can presume. for the Venturi tubing. that. as it is placed on a horizontal surface and hence does non alter tallness. This means that height corsets changeless. Subsequently. combining weight. 2 can be rephrased into:

At this point. a figure of things can be done to the Bernoulli equation. It is possible to do usage of the relationship found in the Continuity equation. which states that the volumetric flow rate – the volume of fluid go throughing a point in the system. per unit clip – is equal to the merchandise of the cross-sectional country ( A ) and the mean flow of speed ( V ) :

The permutation is performed as such. and the new equation can be rearranged with regard to:

Here. we can profit from the basic equation associating volumes ( V ) . mass ( m ) and denseness ( :

By spliting by clip ( T ) both sides of equation ( combining weight. 6 ) by terminal up with:

and therefore:

( ) = Mass Flow Rate

If we now substitute combining weight. 6b into combining weight. 5. the result becomes:

Pitot tubings are used to cipher force per unit area at a certain point. To make this. two points are selected inside the airflow – the first. situated at the entryway of the tubing. which is besides referred to as the “stagnation point” ; the 2nd is situated farther off from the tubing.

We can use the Bernoulli equation ( combining weight. 1 ) to both these points. As they are both at the same degree tallness ( omega ) is changeless. Therefore:

The stagnancy point is called so because it is the point where there is no air flow. where 5 = 0. With this new information. we can one time more re-arrange the expression to be:

The cross subdivision of the pipe used in the experiment should now be looked at.

Its is represented below:

( Fig. 1 )

When R = 0 you will happen that speed reaches a maximal. with the opposite consequence when R=0. Taking from the continuity equation ( combining weight. 4 ) once more. and by replacing it into ( combining weight. 6b ) we get:

Rewriting this with regard to the flow traveling through the round gives us:

R = radius

= denseness of air

= increase of mass flow rate

= speed ( at distance R from the centre line )

The expression for the country of a cross sectional pipe is known as:

Substitute ( combining weight. 12 ) into ( combining weight. 11 ) :

Here. if we could specify over. so incorporating the above equation would give us. However this is non the instance. We must sum up the cylindrical elements where each measuring was taken. This can be written as:

is the measuring at

is the measuring at

Apparatus

Experimental Procedure

1. Record the room temperature from the barometer.

2. Put up the setup as shown above in the diagram.

3. Calibrate the electronic manometer used doing certain the power supply is turned off.

4. Once the manometer has been calibrated bend on the power supply.

5. In order to take the measuring of the force per unit area difference across the Venturi tubing. the pipe linking the Pitot tubing to the manometer must be sealed.

6. Once the pipe has been sealed. turn on the power supply to obtain a low velocity and take the reading.

7. Then keeping the same flow. seal off the tubing linking the venture with the manometer and open the tubing linking the Pitot tubing.

8. Making certain that the Pitot tubing is at the lowest tallness. take the reading.

9. After that addition the tallness of the Pitot tubing by 2mm until

10. Once the Pitot tubing readings has been obtained. shut the Pitot tubing and open the venture tubing and alter the velocity to a medium flow and repeat measure 7-9.

11. Once step 10 has been completed. alter the flow to a higher velocity and reiterate the measure 7-9 to obtain the concluding set of informations.

Consequences

Table 1 – High air flow

|Height / omega |Radius / R |Pressure / P |Pressure difference |v ( Rhode Island ) |v ( Rhode Island ) R | | ( x10-2 m ) | ( ten 10 -3 m ) | ( mmH2O ) | ( ?p ) | ( ms-1 ) | ( m2s-1 ) | |26. 1 |13. 05 |60. 0 |588. 60 |31. 32 |0. 41 | |26. 3 |13. 15 |66. 2 |649. 42 |32. 90 |0. 43 | |26. 5 |13. 25 |69. 4 |680. 81 |33. 69 |0. 45 | |26. 7 |13. 35 |73. 6 |722. 02 |34. 69 |0. 46 | |26. 9 |13. 45 |83. 3 |817. 17 |36. 90 |0. 50 | |27. 1 |13. 55 |86. 7 |850. 53 |37. 65 |0. 51 | |27. 3 |13. 65 |87. 5 |858. 38 |37. 82 |0. 52 | |27. 5 |13. 75 |87. 9 |862. 30 |37. 91 |0. 52 | |27. 7 |13. 85 |88. 5 |868. 19 |38. 04 |0. 53 |

|Height / omega |Radius / R |Pressure / P |Pressure difference |v ( Rhode Island ) |v ( Rhode Island ) R | | ( x10-2 m )

| ( ten 10 -3 m ) | ( mmH2O ) | ( ?p ) | ( ms-1 ) | ( m2s-1 ) | |26. 1 |13. 05 |42. 00 |412. 02 |26. 20 |0. 34 | |26. 3 |13. 15 |46. 60 |457. 15 |27. 60 |0. 36 | |26. 5 |13. 25 |53. 90 |528. 76 |29. 69 |0. 39 | |26. 7 |13. 35 |56. 80 |557. 21 |30. 47 |0. 41 | |26. 9 |13. 45 |59. 10 |579. 77 |31. 09 |0. 42 | |27. 1 |13. 55 |62. 30 |611. 16 |31. 92 |0. 43 | |27. 3 |13. 65 |64. 50 |632. 75 |32. 47 |0. 44 | |27. 5 |13. 75 |65. 70 |644. 52 |32. 77 |0. 45 | |27. 7 |13. 85 |66. 30 |650. 40 |32. 92 |0. 46 |

Table 2 – Medium air flow

|Height / omega |Radius / R |Pressure / P |Pressure difference |v ( Rhode Island ) |v ( Rhode Island ) R | | ( x10-2 m ) | ( ten 10 -3 m ) | ( mmH2O ) | ( ?p ) | ( ms-1 ) | ( m2s-1 ) | |26. 1 |13. 05 |0. 0296 |290. 38 |22. 00 |0. 29 | |26. 3 |13. 15 |0. 033 |323. 73 |23. 23 |0. 31 | |26. 5 |13. 25 |0. 0371 |363. 95 |24. 63 |0. 33 | |26. 7 |13. 35 |0. 0402 |394. 36 |25. 64 |0. 34 | |26. 9 |13. 45 |0. 0405 |397. 31 |25. 73 |0. 35 | |27. 1 |13. 55 |0. 0423 |414. 96 |26. 30 |0. 36 | |27. 3 |13. 65 |0. 0435 |426. 74 |26. 67 |0. 36 | |27. 5 |13. 75 |0. 0441 |432. 62 |26. 85 |0. 37 | |27. 7 |13. 85 |0. 0448 |439. 49 |27. 06 |0. 37 |

Table 3 – Lower air flow

For Table 1. 2 and 3:

Refer to appendix 1 for natural set of informations.

Refer to appendix 2 to see how radius ( R ) in the above tabular arraies were obtained.

Refer to appendix 3 to see how force per unit area difference was calculated utilizing the natural information

Refer to appendix 4 to see how the speed ( v ( Rhode Island ) ) was calculated with the usage of equation 8 from the above derivation.

Venturi Tube

Table 4:

|Flow |VENTURI READING OF PRESSURE ( mmH2O ) |Pressure difference ( ) /Pa |Mass flow rate ( ) /kgs-1 | |Setting | | | | |Low |43 |191. 31 |0. 015 | |Medium |60 |47. 11 | | |High |85 |4. 91 |2. 37 |

Refer to appendix 5 to see how the mass flow rate was calculated for the Venturi tubing with the aid of equation ( 6 ) from the derivation portion.

Graph

Mentions

hypertext transfer protocol: //www. grc. National Aeronautics and Space Administration. gov/WWW/K-12/airplane/bern. hypertext markup language accessed on 28/12/10 at 12:20

hypertext transfer protocol: //www. centennialofflight. gov/essay/Theories_of_Flight/Ideal_Fluid_Flow/TH7G3. htm accessed on 13/11/10 at 17:08

hypertext transfer protocol: //gallica. bnf. fr/ark: /12148/bpt6k408489d. image. f354 accessed on 28/12/10 at 13:31

Munson et Al. 2009. Fundamentalss of Fluid Mechanics. 6th edition. Wiley: Hoboken

hypertext transfer protocol: //www. grc. National Aeronautics and Space Administration. gov/WWW/K-12/airplane/pitot. html # accessed on 28/12/10 at 13. 35