2 – Principles of Hydrostatics, Slides of Fluid Mechanics

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ENGR. BON RYAN ANIBAN

Pressure is the force per unit area exerted by a liquid or gas on a body or surface, with the force acting

perpendicular to the surface uniformly in all directions.

Force, 𝐹

Area, 𝐴

N

m

2

lb

in

2

(psi)

Types of Pressure

Atmospheric pressure

Pressure caused by the air above a point

Gage Pressure

Pressure measured above or below the

atmosphere

Atmospheric Pressure

under normal condition

at sea level

= 1 atm

= 101325 Pa

= 760 mmHg

Decreasing Atmospheric

Pressure

Gage Pressure at any

free surface level of

fluid

= 0 Pa

Increasing Gage

Pressure

Absolute

Pressure

Absolute Pressure

p

abs

= p

gage

+ p

atm

- measured using barometer

- measured using manometer

VARIATIONS IN PRESSURE

a

L

F

1

F

2

P

1

and p 2

are gage pressures

p

1

p

2

θ

y

x

W

By Equilibrium

Σ𝐹x = 0 → +

2

1

− 𝑊sin𝜃 = 0

Force, 𝐹

Area, 𝐴

since

then

2

1

𝑎 − 𝛾(𝑎𝐿)sin𝜃 = 0

h

𝐿sin𝜃 = ℎ

2

1

− 𝛾(𝐿)sin𝜃 = 0

2

1

2

1

This means that the

difference in pressure

between any two points

in a homogeneous fluid at

rest is equal to he product

of the unit weight of the

fluid (γ) to the vertical

distance (h) between any

points.

liquid surface

θ

VARIATIONS IN PRESSURE

liquid surface

a

L

F

1

F

2

P

1

and p 2

are gage pressures

p

1

p

2

θ

y

x

W

By Equilibrium

Σ𝐹x = 0 → +

2

1

− 𝑊sin𝜃 = 0

Force, 𝐹

Area, 𝐴

since

then

2

1

𝑎 − 𝛾(𝑎𝐿)sin𝜃 = 0

h

but 𝐿sin𝜃 = ℎ

2

1

− 𝛾(𝐿)sin𝜃 = 0

2

1

2

1

This means that any

change in pressure at

point 1 would cause an

equal change at point 2.

Therefore; a pressure

applied at any point in a

liquid at rest transmitted

equally and undiminished

to every other point of the

liquid

If the pressure at a point in the ocean is 60 kPa. What is the pressure 27 meters below this point?

Solution

Note :

specific gravity s of salt water is 𝟏. 𝟎𝟑

2

1

kN

m

3

x 1. 03 27 m + 60kN/m

2

p

1

= 60 kPa

27 m

2

= (^) 332.816 kPa

A pressure gage 6 m above the bottom of an open tank containing a liquid reads 90 kPa. Another gage height 4m from the

bottom reads 103 kPa. (a)Determine the specific weight of the liquid. (b) Determine the total height of the liquid in side the

tank.

Solution

103 kPa

90 kPa

2 m

4 m

6 m

h

2

1

103 kPa = 𝛾( 2 ) + 90

𝛾 = 6. 5 kN/m

3

x

Solving for the unit wt.

Solving for the total height of liquid.

kN

m

3

x = 13. 846 m

ℎ = 19. 946 m

Open

The small piston A of a hydraulic lift has a cross-sectional area of 32.3 sq.cm while that of larger piston B is 3230 sq.cm with

the latter lower than piston A by 4.6 m. If the intervening passages are filled with oil whose specific gravity is 0.78. What is

the required force at piston A that will hold the net weight at piston B in position.

Solution

W = 44 kN

A = 0. 323 m

2

A = 0. 00323 m

2

4. 6 m

Oil, s = 0. 78

F

A

B

2

1

= ( 9. 81 x 0. 78 )( 4. 6 )

1. 326 kN

PRESSURE BELOW LAYER OF DIFFERENT LIQUIDS

p

bottom

bottom

1

1

Liquid 1

h

1

Liquid 2

Liquid 3

h

2

h

3

Air pressure in gage = p

A

2

2

3

3

𝐴

bottom

𝐴

For the tank shown in the Figure,. Determine the value of h 3

Solution No

bottom

oil

oil

water

water

Solve the pressure at the bottom

considering left tank

1. 4 m

2. 5 m

h 3

oil

s = 0.

water

water

p bottom

p bottom

= 24. 525 kPa

Solve the pressure at the bottom

considering right tank

bottom

water

water

Note:

Pressure is equal at any level of same fluid

24. 525 = 9. 81 (h 3

h 3

= 2. 5 m

PRESSURE HEAD

It is the height “ h ” of a column of homogeneous liquid of unit weight ( γ ) that will produce an intensity of

pressure ( p ).

pressure, 𝑝

unit wt. , γ

= m

Converting pressure head of fluid A to fluid B

𝐵

𝐴

𝐴

𝐵

A

h A

B

h B

Same pressure, p

γ 𝐵

𝐵

= γ 𝐴

𝐴

γ A

γ B

𝐵

𝐴

𝐴

𝐵

or

MANOMETER

A manometer is a tube, usually bent in form a U, containing a liquid of known specific gravity, the surface f

which moves proportionally to changes of pressure. It is used to measure pressure.

Types of Manometer

Open manometer is a tube bent into a U-

shape to contain one or more fluids of

different specific gravities. It is used to

measure pressure.

Differential manometer cannot measure

pressure but can measure pressure

difference. Frequently in hydraulic problems,

difference in pressure is more useful

information than the pressure itself.

In the figure shown, determine the difference between the pressure of points A and B.

Solution No

Add pressure if going down and

subtract if going up

2

= Σγℎ + p 1

𝐴

𝐵

𝐴

𝐵

= 10. 323 kN