CHAPTER 02

PRESSURE

&

Fluid statics

1

PRESSURE

1. Defined as a normal force exerted by a fluid per unit area

P = F/A

2. The pressure at any point in a fluid is the same in all direction.

3. The only forces between adjacent surface are pressure forces normal to the surfaces.

4. There are no shearing stresses present in a fluid at rest

2

Cont. PRESSURE

A

C B

Acosθ

Asinθ P2

P3

P1

A

θ

Consider a small triangular element ABC at a

point in a fluid, if area AC is A, then area

AB=Asinθ and area BC=Acosθ.

For horizontal equilibrium,

For vertical equilibrium,

Thus, the pressure at any point in a fluid is the

same in all direction.

21

21 sinsin

pp

ApAp

31

21 coscos

pp

ApAp

3

Pressure increases with depth:

Relationship Between Pressure and Depth

Cont. PRESSURE

zgP

and 011 PgzP 022 PgzP

So, we obtain:

4

Cont. PRESSURE

Pressure At a Point

5

Cont. PRESSURE

6

Cont. PRESSURE

7

1. The pressure at a point within a fluid mass will be

designated as either an absolute pressure or a gage

pressure.

2. Absolute pressure is measured relative to a

perfect vacuum (absolute zero pressure), where as

gage pressure is measured relative to the local

atmospheric pressure.

Cont. PRESSURE

8

Cont. PRESSURE

9

A barometer is a scientific instrument used to measure atmospheric pressure. It can measure the pressure exerted by the atmosphere by using mercury. (using water might be difficult)

BAROMETER

10

~ One of the apparatus we use to measure the pressure in a tank. ~ Mainly consist of glass or plastic U-Tube (different fluid : oil, mercury, water).

MANOMETER

CB PP

ρfluid

ρ1, fluid 1

A

B C

h1

h2

D

ρ2, fluid 2

Air

11ghPP AB

22ghPP DC

Air

11

A pressure gage connected to a chamber reads

65kPa at a location where the atmospheric

pressure is 1.013 bar. Determine the absolute

pressure in the chamber. If the pressure give

reading -10 kPa. Also determine the absolute

pressure

EXAMPLE 01

12

Figure show a manometer with an angle of 200 that used to measure air pressure in a closed tank. The specific gravity of manometric fluid that had been used in this type of manometer is 0.75. If atmospheric pressure is 200kPa, find the absolute pressure in closed tank in unit of kPa. [ g = 9.81 m/s2 ]

EXAMPLE 02

A

In gas, pressure is equal regardless of elevation except for

big difference (hundred meters) of elevation

13

BUOYANCY

The difference between two

forces, FB (upward) and FT

(downward) is a net upward force

called Buoyant Force.

The buoyant force is caused by

the increase of pressure in a fluid

with depth.

( )B Bottom Top f f f fF F F g s h A ghA ghA gV

14

STABILITY

A floating body is:

• Stable if the center of gravity G is below the centroid B of the body or if

the metacenter M is above point G.

• Unstable if the point M is below point G.

B

G

15

A crane is used to lower weights into the sea (density 1025 kg/m3) for an underwater construction project. Determine the tension in the rope of the crane due to a rectangular 0.4m x 0.4m x 3m concrete block (density 2300 kg/m3) when it is (a) suspended in the air and (b) completely immersed in water.

EXAMPLE 03

(a) (b) 16

HYDROSTATIC

FORCES

SUBMERGED PLANE SURFACES

SUBMERGED CURVED SURFACES

Fluid static (hydrostatic forces) is used to determine the force acting

on submerged bodies.

It is necessary to calculate the magnitudes and locations of forces

that act on plane and curved surfaces. 17

SUBMERGED PLANE SURFACES

AghF c sincc yh c

xxcp

Ay

Iyy

18

SUBMERGED PLANE SURFACES

19

SUBMERGED PLANE SURFACES

Area and Moments of Inertia for Some Common Geometries

20

EXAMPLE 04

1.2m wide and 2m high rectangular gate shown below is laying underwater at angle of 30° with the horizontal water surface. Determine the force F acting on the gate and the vertical center of pressure, hP

21

30º

yC

yP

hC

hP

8.6 m

Gate

Water

2 m

EXAMPLE 05

2.0m wide rectangular gate shown in figure is hinged at B and making an angle of 45° with the horizontal. Determine the minimum force F required to open the water gate which act on the gate center.

2m

5m

22

SUBMERGED CURVED SURFACES

AhgFh

gVFv 22

VHR FFF

H

V

F

F1tan

23

SUBMERGED CURVED SURFACES

24

EXAMPLE 06

Determine the forces acting on a curved surface. i) The horizontal force, FH

ii) The vertical force, FV and iii) Resultant force, FR

Width=2m

25

EXAMPLE 07

Determine the forces acting on a curved surface. i) The horizontal force, FH

ii) The vertical force, FV and iii) Resultant force, FR

Width=1m

4

2xy

26