Brad Peterson, P.E.
New Website: http://njut2009fall.weebly.com Mr. Peterson s Email Address: bradpeterson@engineer.com
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
Many devices are used to measure the flow of fluids: For velocity: Pitot tubes, Current meters, Anemometers.
Many devices are used to measure the flow of fluids (cont): For quantity: Orifices, Tubes, Nozzles, Venturi meters, Weirs, Meters.
Many devices are used to measure the flow of fluids (cont): For quantity: Orifices, Tubes, Nozzles, Venturi meters, Weirs, Meters.
To use the devices, the Bernoulli Equation and knowledge of fluid characteristics is used.
Measures stagnation pressure (at B), which exceeds the local static pressure (at A), to determine velocity head. h A hb
Velocity (V) at Point B is zero. Apply the Bernoulli equation, next slide h A h B
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
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
h h d B A h A h B
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.
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
c C area of stream ( jet ) A jet area of opening A O opening jet
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 025 0.25m, to c = 0.59 for dia >1m and head greater than 20m For most approximations, use c=0.6
H
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
2 V B H 2 g rearrange to: VB 2gH
V B 2 gh Q AV A 2gH since, in most applications, friction will occur, apply the discharge coefficient, c Q=cA 2gHH
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?
474m 4.74m 5.67m
hb ha d 567 5.67 m 474 4.74 m 094 0.94 m 474m 4.74m 5.67m
V c 2 gd V d 5.67m4.73m 0.94m c V g 0.98 98 9.8 m / s 2 2 V 0.98 2 9.8 m/ s 0.94m 4.21 m/ s
A 100mm diameter standard orifice discharges water under a 6.1m head. What is the flow?
Q ca 2 gh A H area; c 0.6 total head causing flow 2 01 0.1m 2 Q 0.6 29.8 m/ s 6.1m 4 3 Q 0.05 m / s
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.
Q ca 2 gh 0.075 / 0.6 2 9.8 / 4 H 12.9m 0.1m 2 3 2 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
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
H head Z height
b H Z=0 From: http://www.lmnoeng.com/weirs/cipoletti.htm / e po ett t
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
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
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)
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.
H 0.3m Z 0.9m
29m 38s flow depth 0.9m 0.3m 1.2m 3 3 Q 0.763 m / s 3 Q 0.763 m / s V 0.265 m/ s A 2.4m1.2m
using Eq. A: V V Q mbh 2 g 2 g 2 3/2 2 3/2 2 3/2 3/2 2 3 0.265 0.265 0763 0.763 m m24 2.4 03 0.3 2 2 2 9.8 2 9.8 3 3/2 3/2 m m 0.763 2.4 0.3 0.00358 00358 0.00358 00358 m 1.90
using Eq. B: Q mbh 3/2 0.763 m2.4 0.3 m 1.93 3/2 1.90 1.93 Equation B is OK for weirs placed high
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.
H 0.3m Z 0.0m
b H Z=0 From: http://www.lmnoeng.com/weirs/cipoletti.htm / e po ett t
29m 38s flow depth 0.0m 0.3m 0.3m 3 3 Q 0.763 m / s 3 Q 0.763 m / s V 1.06 m/ s A 2.4m 0.3m
using Eq. A: 2 3/2 2 3/2 V V Q mb H 2 g 2 g 2 3/2 3/2 2 3 1.06 1.06 0763 m m24 03 2 2 0.763 2.4 0.3 2 9.8 2 9.8 3 3/2 3/2 0.763 m m2.4 0.3 0.0573 0573 0.05730573 m 1.53
using Eq. B: Q mbh 3/2 0.763 m2.4 0.3 m 1.93 3/2 153 1.53 1.93, 193 Equation A must tbe used for shallow weirs
b H
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
H
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