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1 Brad Peterson, P.E.

2 New Website: Mr. Peterson s Address:

3 Lesson 1, Properties of Fluids, 2009 Sept 04, Rev Sept 18 Lesson 2, Fluid Statics, 2009 Sept 11, Rev Sept 18 Lesson 3, Hydrostatic Force on Surfaces, 2009 Sept 25 Lesson 4, Buoyancy and Flotation, 2009 Sept 25 Lesson 5, Translation/Rotation of Liquid Masses, 2009 Oct 16 Lesson 6, Dimensional i Analysis/Hydraulic li Similitude, ili maybe? Lesson 7, Fundamentals of Fluid Flow, 2009 Oct 23, Oct 30 Lesson 8, Flow in Closed Conduits, 2009 Nov 6 Lesson 9, Complex Pipeline Systems, 2009 Nov 13, Nov 20 Lesson 10, Flow in Open Channels, 2009 Nov 27, Dec 04 Lesson 11, Flow of Compressible Fluids, maybe? Lesson 12, Measurement of Flow of Fluids, 2009 Dec 11 Lesson 13, Forces Developed by Moving Fluids Lesson 14, Fluid Machinery

4

5 Many devices are used to measure the flow of fluids: For velocity: Pitot tubes, Current meters, Anemometers.

6 Many devices are used to measure the flow of fluids (cont): For quantity: Orifices, Tubes, Nozzles, Venturi meters, Weirs, Meters.

7 Many devices are used to measure the flow of fluids (cont): For quantity: Orifices, Tubes, Nozzles, Venturi meters, Weirs, Meters.

8 To use the devices, the Bernoulli Equation and knowledge of fluid characteristics is used.

9 Measures stagnation pressure (at B), which exceeds the local static pressure (at A), to determine velocity head. h A hb

10 Velocity (V) at Point B is zero. Apply the Bernoulli equation, next slide h A h B

11 2 2 p A V A no loss p B V B za 2g assumed 2g V 0; z z B A B so, 2 pa VA pb 2g z B

12 2 A A B p V p 2g p p 2 B A p p V g B A B A p p h h d With no friction: 2 V gd g

13 h h d B A h A h B

14 A small amount of friction normally occurs, so a coefficient of velocity c V (see discussion on following slides) is sometimes used: c V actual velocity theoretical velocity V c 2gd V to assume cv 1 provides sufficient accuracy for most engineering problems involving i Pitot tubes.

15 The ratio of the actual velocity in a stream to the theoretical velocity that would occur without friction. c V actual velocity theoretical ti velocity

16 c C area of stream ( jet ) A jet area of opening A O opening jet

17 c actual flow Q theoretical flow also c c c, V C Q Value of c is provided in handbooks and text books and is based on experimental data For vertical, sharp-edged circular orifices: c = 065f 0.65 for dia<1cm and dhead dless than m, to c = 0.59 for dia >1m and head greater than 20m For most approximations, use c=0.6

18 H

19 2 2 pa VA no loss pb V B za zb 2 g assumed 2 g p 0; p 0; V 0; z H; z 0 A B A A B 2 VB H ; VB 2gH 2gg

20 2 V B H 2 g rearrange to: VB 2gH

21 V B 2 gh Q AV A 2gH since, in most applications, friction will occur, apply the discharge coefficient, c Q=cA 2gHH

22 A Pitot tube having a coefficient of 0.98 is used to measure the velocity of water at the center of a pipe. The stagnation pressure head is 5.67m and the static pressure head in the pipe is 4.73m. What is the velocity?

23 474m 4.74m 5.67m

24 hb ha d m m m 474m 4.74m 5.67m

25 V c 2 gd V d 5.67m4.73m 0.94m c V g m / s 2 2 V m/ s 0.94m 4.21 m/ s

26 A 100mm diameter standard orifice discharges water under a 6.1m head. What is the flow?

27 Q ca 2 gh A H area; c 0.6 total head causing flow m 2 Q m/ s 6.1m 4 3 Q 0.05 m / s

28 The tank in problem 12.9 is closed ant the air space above the water is under pressure, causing to flow to increase to 0.075m3/s. Find the pressure in the air space.

29 Q ca 2 gh / / 4 H 12.9m 0.1m m s m s H h H h 12.9m6.1m 6.8m P Z 3 2 p h P 9.8 kn / m 6.8 m 70 kn / m 70 kpa

30 Measure the flow of water in open channels There are many formulas available to calculate flow Q All formulas have limitations i i To be accurate, all must be calibrated (adjusted) experimentally or by actual on-site conditions

31

32 H head Z height

33 b H Z=0 From: / e po ett t

34 Theoretical Formula for a Rectangular Weir: 2 V V Q cb 2g H 3 2g 2g c experimental coefficient b width H depth 2 3/2 2 3/2

35 several numbers, shown in red: 2 3/2 2 3/2 V V c 2g 2 V V Q b H 3 2g 2g are combined into a coefficient, m 2 3/2 2 3/2 V V Q m b H (Eq, A) 2g 2g

36 in deep weir such as a dam, V negligible 0, so, approximate flow becomes: 2 3/2 2 3/2 0 0 Q mb H 2g 2g Q mbh 3/2, (Eq. B)

37 During a test on a 2.4m suppressed weir that was 0.9m high, the head was maintained constant at 0.3m. In 38 seconds, 29m 3 of water were collected. Find the weir factor m using equations A and B.

38 H 0.3m Z 0.9m

39 29m 38s flow depth 0.9m 0.3m 1.2m 3 3 Q m / s 3 Q m / s V m/ s A 2.4m1.2m

40 using Eq. A: V V Q mbh 2 g 2 g 2 3/2 2 3/2 2 3/2 3/ m m /2 3/2 m m m 1.90

41 using Eq. B: Q mbh 3/ m m / Equation B is OK for weirs placed high

42 During a test on a 2.4m suppressed weir that was 0.0m high, the head was maintained constant at 0.3m. In 38 seconds, 29m 3 of water were collected. Find the weir factor m using equations A and B.

43 H 0.3m Z 0.0m

44 b H Z=0 From: / e po ett t

45 29m 38s flow depth 0.0m 0.3m 0.3m 3 3 Q m / s 3 Q m / s V 1.06 m/ s A 2.4m 0.3m

46 using Eq. A: 2 3/2 2 3/2 V V Q mb H 2 g 2 g 2 3/2 3/ m m /2 3/ m m m 1.53

47 using Eq. B: Q mbh 3/ m m / , 193 Equation A must tbe used for shallow weirs

48 b H

49 A commonly used weir for flow measurement This weir has side (end) slopes of: 1 horizontal to 4 vertical Q 3.367bH H depth b width 3/2

50

51 H

52 8 tan 2 5/2 Q c gh 15 2 H depth angle of "V" bottom Terms are combined into coefficient m Q mh 5/2

New Website: M P E il Add. Mr. Peterson s Address:

New Website:   M P E il Add. Mr. Peterson s  Address: Brad Peterson, P.E. New Website: http://njut009fall.weebly.com M P E il Add Mr. Peterson s Email Address: bradpeterson@engineer.com If 6 m 3 of oil weighs 47 kn calculate its If 6 m 3 of oil weighs 47

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