Buku bab 2

JJ309: Fluid Mechanics

2.0 Fluid Static

1. If a fluid is within a container then the depth of an object placed in that fluid can be measured. The deeper the object is placed in the fluid, the more pressure it experiences

The formula that gives the pressure, p on an object submerged in a fluid is:

ghp ρ=

Where,

ρ (rho) - the density of the fluid, g- the acceleration of gravity h - the height of the fluid above the object

2. Example Problems: a. A barometer shows the reading 750mm merkury. Determine; i. Atmosphere pressure in unit SI ii. The head of water for that pressure (100 kN/m2,10.2m) 10


b. What is the pressure experienced at a point on the bottom of a swimming pool 9 meters in depth? The density of water is 1.00 x 103 kg/m3.(88.3kN/m2)

c. Assume standard atmospheric conditions. Determine the pressure in kN/m2

for the pressure below: i. depth 6m below under free space water. ii. At the 9m under surface of oil with specific gravity 0.75.

(58.86kN/m2,66.22 kN/m2)

11


d. Find the height of water column, h which is equivalent to the pressure , p of 20 N/m2 . Take into consideration specific weight of water , ω is 1000 kg/m2 x 9.81 m/s2 (2.03x10-3m)

e. A fluid in piezometer increased 1.5 m high from point A in a pipeline system . What is the value of pressure in point A in N/m2 if the fluid is :

i. Mercury with specific gravity 13.6 ii. Salted water with specific gravity 1.24

(200.1240x103N/m2,18.24 x103N/m2)

A

12


f. Find the head, h of water corresponding to an intensity of pressure, p of 340 000 N/m2. Take into consideration that the mass density, ρ of water is 100kg/m3

(h=34.65m)

g. A Bourdon pressure gauge attached to a boiler located at sea level shows a reading pressure 10 bar . If atmospheric pressure is 1.01 bar , determine :

i. The absolute pressure in kN/m2

ii. The pressure head of water , h (1101 kN/m2, 112.2m)

13


3. Pascal’s Law and Hyraulic Jack

i. State the Pascal’s Law

ii. Describe hydraulic Jack

4. Example :

a. A force, F of 900 N is applied to the smaller cylinder of an hydraulic jack. The

area, a of a small piston is 22 cm2 and the area A of a larger piston is 250

cm2. What load, W can be lifted on the larger piston if :

i. the pistons are at the same level.

ii. the large piston is 0.8 m below the smaller piston.

Consider the mass density ρ of the liquid in the jack is 103 kg/m3

(10.227 kN,10.423kN)

14


b. Two cylinders with pistons are connected by a pipe containing water. Their diameters are 75 mm and 600 mm respectively and the face of the smaller piston is 6 m above the larger. What force on the smaller piston is required to maintain a load of 3500 kg on the larger piston?(275.91 N)

c. A force, F of 650 N is applied to applied to a smaller cylinder of hydraulic jack.

The area of small piston is 15cm2 and area of the larger pispon is 150cm2. Mass

density of the liquid in the jack 103 kg/ m3 Sketh each situation below and

calculate the load if, (6500N, 6595.6N, 6441.14N)

i. The piston are the same level

ii. The large piston is 0.65 m below the smaller piston

iii. The small piston is 0.40m below the large piston

15


d. A diameter of big piston in hydraulic jack is three times bigger than the diameter of small piston. The small diameter is 630 mm and is used to support a weight of 40 kN. Find the force which is needed to rise up the big piston 2 m above the small piston. Given the specific gravity of oil is 0.85. (313.23kN)

e. A force , F = 500 N is applied to the smaller cylinder of hydraulic jack . The area, a of a small piston is 20 cm2 while the area, A of a large piston is 200 cm2 . What mass can be lifted on the larger piston. (509.68 kg)

16


f. A hydraulic press has a diameter ratio between the two pistons of 8:1 . The diameter of the larger piston is 600 mm and it is required to support a mass of 3500 kg . the press is filled with a hydraulic fluid of specific gravity 0.8 . Calculate the force required on the smaller piston to provide the required force ;

i. When the two pistons are at same level ii. When the smaller piston is 2.6 m below the larger piston.

(536.48 N, 627.92 N)

g. A hydraulic jack has diameter cylinder 5 cm and 18 cm. A force has put on small cylinder to lift the load 1100 kg at bigger cylinder. Determine force F for lift the both cylinders. (832.6N)

17


h. A area of big piston in hydraulic jack is three times bigger than the area of small piston. The small diameter is 630 mm and is used to support a weight of 40 KN. Find the force which is needed to rise up the big piston 2 m above the small piston. Given the specific gravity of oil is 0.85 (104.4kN)

i. The diameter of plunger and ram of a hydraulic press are 30 mm and 200 mm respectively. Find the weight lifted by the hydraulic press when the force applied at the plunger is 400N and the difference level between plunger and ram is 0.5 m. Given ρ fluids is 1065 kg/m3 ( 17929.9N)

18


5. Concept of manometer i.Manometer Simple

ii.Manometer U tube

iii.Manometer Differential

19


6.Example a. Assume that Patm= 101.3 kN/m2 water flow in pipe and in merkuri in manometer a= 1m h=0.4 m. Determine the absolute pressure. As figure a (38.1kPa)

Figure a

20


b. A U tube manometer is used to measure the pressure of oil (s= 0.8) flowing in a pipeline as in figure b. Its right limb is open to the atmosphere and the left limb is connected to the pipe. The centre of the pipe is 9 cm below the level of mercury in the right limb. If the difference of mercury level in the two limbs is 15 cm, determine the gauge pressure of the oil in the pipe in KPa. (19.541 KPa)

Fig. b

9 cm

15 cm

s merkury 13.6

21


c. Determine absolute pressure at A if Patm = 101.3 kN/m2, h1=20cm,h2= 40 cm as fig c (45.971kPa)

merkury figure c.

water

22


d. For a gauge pressure in pipe is 5kN/m2, determine the specific gravity of the liquid B in the figure given below. (6.54)

e. Find the level of h if P1 is absolute pressure 150kN/m2, ρm= 13.6 x103

kg/m2 and in pipe is water in fig. e. (0.401m)

Fig. e

500mm

12cm

water

Liquid B

h

23


f. One end of a manometer contain mercury is open to atmosphere, while the other end of the tube is connected to pipe in which a fluid of specific gravity 0.85 is flowing. Find the gauge pressure the fluid flowing in pipe. (26.271kN/m2)

Fig.f

24


g. A U tube manometer measures the pressure difference between two points A and B in a fluid as shown in Figure d. The U tube contains mercury. Calculate the difference in pressure at pipe A and B if h1 = 160 cm, h2 = 50 cm and h3 = 80 cm. The liquid at A and B is water ρ = 1000kg/m3 and the specific gravity of mercury is 13.6.1 (53955N/m2)

Figure g

25


h. The figure e below shown a U tube manometer . The specific gravity of mercury is 13.6 . If the pressure difference between point B and A is 47 kN/m2 , h = 12cm and a = 43 cm , determine the height of b .(3.71m)

Figure h

b

a

water

merkury

26


i. A manometer U tube is using to measure between A and B in pipe has water and in manometer has mercury. Determine the differential pressure between pipe A and B, if a =150 cm, b = 70 cm and c = 45 cm. Figure f (47.77kN/m2)

Figure i

27


j. Figure g shown U tube manometer. If the differential of pressure between X andY is 50KN/m2 , h=2m and a=0.85m determine b (0.4719m)

Figure j

28

JJ309: Flu

k

id Mechanics

. Figure kA air pre

(84.2

s

k shows a dssure is 10

F8kPa)

differential 00kN/m2. Fi

igure k

manometernd the abso

29

r connectedolute press

d at two poure at B

ints A nd B. At


l. A U-tube manometer is connected to a closed tank containing air and water as shown in Figure h. At the closed end of the manometer the absolute air pressure is 140kPa. Determine the reading on the pressure gage for a differential reading of 1.5-m on the manometer. Express your answer in gauge pressure value. Assume standard atmospheric pressure and neglect the weight of the air columns in the manometer. (64.5 kPa)

Figure l 30


m. A U-tube manometer contains oil, mercury, and water as shown in Figure i. For the column heights indicated what is the pressure differential between pipes A and B? (-15.1kPa )

Figure m

31


n. A U-tube manometer is connected to a closed tank as shown in Figure j. The air pressure in the tank is 120 Pa and the liquid in the tank is oil (γ = 12000 N/m

3). The absolute pressure at point A is 20 kPa. Determine: (a) the depth of

oil, z, and (b) the differential reading, h, on the manometer. Patm = 101.3 kPa (z = 1.66 m, h = 1.33 m )

Figure n 32


o. The inverted U-tube manometer of Figure k contains oil (SG = 0.9) and water as shown. The pressure differential between pipes A and B, p

A − p

B, is −5 kPa. Determine

the differential reading, h. (0.46 mm )

Fig.o

33


j. In the figure below, fluid Q is water and fluid P is oil (specific gravity = 0.9). If h = 69 cm and z = 23 cm, what is the difference in pressure in kN/m2 between A and B?(-1.579kN/m2)

34


k. Figure m belows shows a u-tube manometer that used to measure the pressure difference between pipe P and pipe Q that contains water. If the fluid in u-tube is oil with specific gravity 0f 0.9, calculate the pressure difference between these two pipes in kN/m3 . Given M =80 cm and N = 25 cm.(1667.7 Pa)

Figure p 35


r. For the inclined-tube manometer of Figure n, the pressure in pipe A is 8 kPa. The

fluid in both pipes A and B is water, and the gage fluid in the manometer has a specific gravity of 2.6. What is the pressure in pipe B corresponding to the differential reading shown?(5.51kPa )

fig.r

36


s. A piston having a cross-sectional area of 0.07 m2 is located in a cylinder containing

water as shown in Figure o. An open U-tube manometer is connected to the cylinder as shown. For h

1 = 60 mm and h = 100 mm, what is the value of the applied force, P,

acting on the piston? The weight of the piston is negligible (892.7 N)

Fig. s

37


1. Pressure Measurement

Piezometer, Barometer

Bourdon gauge Sketch important parts of bourdon gauge Explain mechanism of a bourdon gauge 38


2. Buoyancy

Define Buoyancy Force

Buoyancy is the upward force that an object feels from the water and when compared to the weight of the object Buoyant Force=Weight of Displaced Fluid

R2

R 1 = R2

ρ1 g1 v1 = ρ2 g2 v2

R1

39


3. Example Question a. A rectangular pontoon has a width B of 6 m, a length l of 12 m, and a draught D of

1.5 m in fresh water (density 1000 kg/m3). Calculate :

a) the weight of the pontoon b) its draught in sea water (density 1025 kg/m3) c) the load (in kiloNewtons) that can be supported by the pontoon in fresh

water if the maximum draught permissible is 2 m. (1059.5kN, 1.46m, 14126kN,353.1kN)

b. 8 cm side cube weighing 4N is immersed in a liquid of relative density 0.8 contained in a rectangular tank of cross- sectional area 12cm x 12cm. If the tank contained liquid to a height of 6.4 cm before the immersion determine the levels of the bottom of the cube and the liquid surface. (x =0.063m)

40

Education

Buku bab 2