Fluid Mohammad Ali Sofyan, M.Pd..

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1 Fluid Mohammad Ali Sofyan, M.Pd.

2 Standard of Competency: Applying the concepts and principles of classical mechanics to continuous systems in solving problems. Basic Competency: Analyzing the laws relating to static and dynamic fuides and their application in everyday life.

3 What is Fluid?

4 Why should we study fluid?

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9 Keyword Fluid : Fluida Pressure : Tekanan Hydraulic : Hidrolik
Flow : Mengair Float : Mengapung / Melayang Sink : Tenggelam Density : Masa Jenis

10 Hydrostatic Pressure Pressure Pressure, force per unit area.
Information: P = pressure (N/ 𝑚 2 ) F = force (N) A = surface area ( 𝑚 2 ) The unit of pressure in SI is N/ 𝑚 2 (pascal), abbreviated Pa. For the unit of air pressure the atmospheric (atm), mercury (cmHg) or millibar (mb) units are used. 1 mb = 10–3 bar 1 bar = 105 Pa 1 atm = 76 cmHg = 1,01 × 105 Pa 1 mmHg = 1 torr = 1,316 × 10–3 atm = 133,3 Pa

11 EXAMPLE If the mass of the beam is 8 kg, determine the pressure applied by the beam to the base!

12 EXERCISE What is the maximum and minimum pressure which is it possible to do by the beam?

13 Fluid Pressure Fluid pressure on static fluid is called hydrostatic pressure. Information: P = hydrostatic pressure (N / m2) ρ = density of liquid (kg/m3) g = acceleration due to gravity (m/s2) h = depth of liquid (m) If the atmospheric pressure on the surface of the liquid is Po, the absolute pressure at that point or point is at depth h is

14 EXAMPLE If the earth's gravitational acceleration is 10 m/s2, then determine the hydrostatic pressure experienced by fish?

15 EXERCISE A diving diver with a depth of 3 m, density of water 1,000 kg/m3, the gravitational constant at that place is 10 m/s2. Then the hydrostatic pressure is…. At the bottom of a pool the water is detected by a hydrostatic pressure gauge showing the figure of 50,000 pascals. So what is the depth of the pool of water?

16 The gravity of the liquid that presses on the base of the vessel is called the hydrostatic force.
The main laws of hydrostatics: "Hydrostatic pressure at any point on a flat plane in a stationary type of liquid, the same amount."

17 According to the main laws of hydrostatics:
Information: x = density of liquid x (kg/m3) h1 = high liquid x (m) h2 = high standard liquid (m) = density of standard liquid (water)(kg/m3)

18 EXAMPLE The U pipe is filled with mercury and liquid oil as shown in the picture! If the height of H2 oil is 27.2 cm, the density of oil is 0.8 gr/cm3 and the density of Hg is 13.6 gr/cm3 determine the height of mercury (h1)!

19 EXERCISE A U pipe is filled with 3 different liquid substances so as shown below If ρ1, ρ2 and ρ3 are the density of liquid 1, 2 and 3, respectively, and h1, h2, h3 are the height of each liquid as shown in the picture above, determine the equation to determine the density of liquid 1.

20 Pascal’s Law "The pressure exerted on liquid in a confined space is transmitted equally in all directions. " Because the pressure on both suckers is the same: Information: F1 = force on cross section 1 (N) F2 = force on cross section 2 (N) A1 = cross-sectional area 1 (m2) A2 = cross-sectional area 2 (m2)

21 EXAMPLE A child wants to raise a stone with a mass of 1 ton with a tool like the following picture! If the cross-sectional area of ​​a large pipe is 250 times the cross-sectional area of ​​a small pipe and the pressure of the liquid filling of the pipe is neglected, determine the minimum force that the child must apply so the stone can be lifted!

22 EXERCISE A hydraulic jack is used to lift weights.
If the radius of the small pipe is 2 cm and the radius of the large pipe is 18 cm, determine the minimum force required to lift 81 kg!

23 Archimedes’ Law Buoyancy
If an object is put into fluid in whole or in part, the object will have an buoyancy of the weight of the fluid being removed. The buoyancy on objects in a liquid is: Information: FA = lifting force (N) ρ = liquid density (kg/m3) V = the volume of objects in the fluid (m3) g = acceleration of gravity (m/s2)

24 Effect of buoyancy on Objects
Floats, conditions:  object <  liquid substances W sinking object = buoyancy of fluid Hovering, terms:  object =  liquid W object = buoyancy of fluid.

25 Application of Buoyancy
Sink, conditions:  objects >  liquid substances W object > buoyancy of fluid Application of Buoyancy Ship So that the ship is always in a normal state (not sinking) then the force of work to the water must pass through the center of gravity of the ship

26 Shipyard After the ship entered the shipyard, the seawater in the shipyard was released so that the shipyard was lifted. Air Balloon Balloons filled with gas whose density is smaller than the density of air. If the buoyancy is greater than the weight of the balloon, the balloon will lift.

27 EXAMPLE An object is partially immersed in a liquid which has a density of 0.75 gr/cm3 as shown in the following image! If the volume of the immersed object is 0.8 of the total volume, determine the density of the object!

28 EXERCISE A child inserts a 500 gram M object in a broken glass filled with water, spilled water is collected with a measuring cup as shown in the following picture: If the Earth's gravitational acceleration is 10 m/s2 determine the apparent weight of objects in the water!

29 Fluid Pressure Measuring Instruments
The difference in absolute P and the atmospheric pressure Pat is called the gauge pressure. Absolute pressure P is obtained from the sum of gauge pressure and atmospheric pressure. Information: P = absolute pressure on the tube (N/m2) Pgauge = gauge pressure = ρgh Pat = current atmospheric pressure (N/m2)

30 Liquid Surface Tension
Liquid surface tension, a complicated force experienced by each unit of length in the liquid surface. Information:  = surface tension (N / m) F = force that touches the surface of the liquid (N) l = length (m)

31 Nilai Tegangan Permukaan Beberapa Zat () pada Berbagai Suhu

32 Meniscus and Capillarity
Meniscus, symptoms of curvature of the surface of the liquid in the vessel due to the influence of cohesion and adhesion of the liquid and the jar.

33 Capillarity Capillarity, the event of rising or falling of liquid in the capillary tube compared to the liquid outside it due to the influence of cohesion and adhesion. Length of rise / fall of liquid (y) in capillary tubes is calculated by, information:  = liquid surface tension (N/m) Ө = contact angle ρ = density of fluid (kg/m3) r = radius of base (m) g = gravitational acceleration (m/s2)

34 Ideal Fluid and Continuity Equation
The ideal fluid, has the following characteristics: Fluid that is not compressible (does not change in volume due to pressure), Frictionless flowing, both from the surrounding fluid layer, as well as from the wall where it passes. Laminar flow, fluid flow that follows a certain water line or current line.

35 Continuity Equation Relationship between cross-sectional area and fluid velocity in the pipe is: Continuity Equation : Information: Q = discharge (m3/s) V = fluid’s volume (m3) v = velocity of fluid (m/s) t = time (s) A = cross-sectional area (m2) The value of A.v is called discharge:

36 The underground water pipe has a shape like the following picture!
1 Ahmad fills a bucket that has a capacity of 20 liters with water from a faucet like the following picture! If the cross-sectional area of ​​the faucet with a D2 diameter is 2 cm2 and the speed of water flow in the faucet is 10 m / s specify: The underground water pipe has a shape like the following picture! If the cross-sectional area of ​​the large pipe is 5 m2, the cross-sectional area of ​​the small pipe is 2 m2 and the speed of water flow in the large pipe is 15 m / s, determine the speed of the water when flowing on the small pipe! 2

37 Bernoulli’s Law Bernoulli’s Equation:

38 On Horizontal Pipe Bernoulli’s Equation:
On horizontal pipe, h1 = h2, so:

39 Pipes for channeling water stick to a house wall as shown in the following picture! The ratio of the cross-sectional area of ​​large pipes and small pipes is 4: 1. The position of the big pipe is 5 m above the ground and the small pipe is 1 m above the ground. The speed of water flow in large pipes is 36 km/h with a pressure of 9.1 x 105 Pa. Determine: a) The speed of the water in a small pipe b) Pressure difference in the two pipes c) Pressure on small pipes (ρ = 1000 kg / m3)

40 Theory of Torricelli Speed ​​(v) of liquid coming out of the hole:
𝑣 𝑡 = 𝑣+2𝑔 ℎ 1 vt Time (t) required for liquid to come out of the hole until it touches the floor: Information: h = surface distance of liquid to hole (m) g = gravitational acceleration (m/s2)

41 Discharge (Q) liquid that comes out of the hole
Horizontal distance (x) where the liquid on the floor falls from the wall of the vessel: Discharge (Q) liquid that comes out of the hole Information: A = hole cross-sectional area (m2) v = the speed of the liquid coming out of the hole (m/s) t = the time of the liquid from the hole to the floor (s) 𝑥=2 ℎ. ℎ 1

42 water tank with leak hole is shown in the following picture!
1 water tank with leak hole is shown in the following picture! on the small pipe! The distance of the hole to the ground is 10 m and the distance of the hole to the surface of the water is 3.2 m. Determine: a) Speed ​​of water discharge b) The furthest horizontal distance reached by water c) The time required for a water leak to touch the ground

43 Venturimeter Venturimeter, alat untuk meng ukur kecepatan aliran zat cair dalam pipa. Keterangan: v1 = kecepatan aliran air cair pada penampang lebar (m/s) a = luas penampang pipa sempit (m2) A = luas penampang pipa lebar (m2)  = massa jenis fluida (kg/m3) ’ = massa jenis fluida dalam manometer (kg/m3)

44 Venturimeter dengan pipa-pipa pengukur beda tekanan.
Kecepatan aliran air pada penampang lebar dihitung dengan:

45 Tabung Pitot Tabung pitot, alat yang digunakan untuk mengukur
kecepatan aliran gas. Keterangan: v1 = kecepatan aliran air gas dalam tabung (m/s)  = massa jenis gas (kg/m3) ’ = massa jenis zat cair dalam manometer (kg/m3) g = percepatan gravitasi (m/s2) h = selisih tinggi permukaan zat cair dalam manometer (m)

46 Gaya Angkat Pada Pesawat Terbang
Pada sayap pesawat, berlaku persamaan Bernoulli. Karena sayap pesawat tipis tinggi sayap dianggap sama h1 = h2 sehingga persamaan Bernouli menjadi: Karena v1 < v2 maka P1 > P2. Selisih tekanan antara sisi atas dan bawah sayap itulah yang menimbulkan gaya angkat pada sayap.

47 Alat Penyemprot Nyamuk dan Parfum
Jika pengisap ditekan, udara ke luar dengan cepat dari lubang pipa kecil yang ada di ujung A. Tekanan pada tempat ini menjadi sangat kecil. Cairan zat insektisida yang berada di ujung B terhisap menuju ujung pompa A. Cairan insektisida tersebut akan tersembur (tersemprot) oleh udara yang keluar dari ujung pompa A.

48 Viskositas dan Hukum Stokes
Viskositas (kekentalan), gesekan pada fluida. Fluida, baik zat cair maupun gas mempunyai viskositas. Jenis alat pengukur viskositas zat cair yang disebut viskosimeter. Zat cair lebih kental dibanding gas, sehingga gerak benda di dalam zat cair akan mendapatkan gesekan yang lebih besar dibanding di dalam gas.

49 Viskositas Beberapa Fluida

50 Hukum Stokes Gaya gesek terhadap bola yang bergerak di dalam fluida diam disebut dengan gaya Stokes. Gaya gesek Stokes dirumuskan dengan: Keterangan: Fs = gaya gesekan Stokes (N)  = koefisien viskositas (N/m2) r = jari-jari bola (m) v = kecepatan relatif bola terhadap fluida (m/s)

51 Jika sebuah bola jatuh ke dalam fluida yang kental, selama bola bergerak di dalam fluida pada bola bekerja gaya-gaya berikut. Gaya berat bola (w) berarah vertikal ke bawah. Gaya Archimedes (FA) berarah vertikal ke atas. Gaya Stokes (FS) berarah vertikal ke atas.

52 Koefisien viskositas fluida dihitung dengan persamaan:
Keterangan:  = koefisien viskositas (Ns/m2) r = jari-jari bola (m) v = kecepatan maksimum bola (m/s)  = massa jenis bola (kg/m3) ’ = massa jenis fluida (kg/m3)

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