CHAPTER 2: HYDROSTATIC

By:Mohamad Hidayat Jamal

Department of Hydraulics and HydrologyFaculty of Civil Engineering

Universiti Teknologi Malaysia

Recap???

• Classification – gasses and liquids

• Real and Ideal fluids

• Fluid properties – Density, specific gravity, viscosity and etc.

• Any questions???

Contents

• Introduction To Hydrostatics• Pressure in Fluids• Pressure at a points and Pressure

Variations (Pascal’s Law)• Pressure measurements• Hydrostatics Forces on Submerged

Plane Surface• Pressure Distribution in Fluids

CHAPTER 2: HYDROSTATICS

WHAT – HYDROSTATICS?

Defined as the balance of forces in a fluids at rest (fluid static) – free from any shear stresses and forces due to static pressure.

Pressure?A normal force exerted by a fluid per unit area.

P = Force/Area or (F/A)Units:1 N/m² = 1 Pa 1 Bar = 105 Pa = 100 kPa1 atm = 101,325 Pa = 101.325 kPa = 1.01325 Bar

Pressure in Fluid

Hydrostatic equation or pressure in fluid:

Pressure will increase if the water depth increases (from the water surface)

P gh

Atm., Absolute, Vacuum & Gauge PressureAtmospheric pressure (Pressure in the air around us), Pa

- Called reference pressure (10.35 m H2O or 760 mm Hg

- +ve pressure – above atm.- -ve pressure/vacuum – below atm.Vacuum pressure- Below atm.Absolute Pressure (mutlak)- Actual pressure at a given point- Measured relative to absolute vacuum (absolute zero

pressure). Mostly to read zero in the atm.Gauge Pressure (measured using pressure gauge)- Difference between the absolute pressure and the atm.- P gh

aP gh P

Atm., Absolute, Vacuum & Gauge Pressure

Pressure at a Point

• Pressure at any point in a fluid is the same in all direction (known as Pascal Law)

• It has magnitude but not at specific direction

• P1 = P2 = P3 = P

Pressure variation with elevation (Pascal’s Law)

Fluid at rest is independent of the shape or cross section of the container.

Pressure is the same at all points on a horizontal plane

Pressure changes with vertical distance.

Pressure variation with elevation (Pascal’s Law)

Pressure Measurement

Barometer

Piezometer

Manometer

- Simple

- Differential, right U-tube

- Differential, inverted U-tube

Barometer

Device to measure atmospheric pressure

By inverting mercury tube into mercury container that is open to the atmosphere

atm mP gh

5 2

5

10 /

10760

13.56*9.81

atm

atm m

atm

P N m

P gh

Ph mmHg

g

Piezometer

To measure a pressure in flowing liquid using piezometer tube

Principle; The liquid rises up the piezometer tube until atmospheric pressure and the weight of the column of liquid in the tube generate a pressure equal the pressure in the pipe/conduit.

The pressure at the center line of the pipe flow is given as:

P gh

Manometer (a) Simple

Pressure can be estimated by measuring fluid elevation

Commonly used to measure small or moderate pressure

P1 = P2 = gh

Manometer (b & c) U-Tube

Hydrostatic Forces on Submerged Plane Surface

Submerged plate/plane surface will having force exerted from the liquid

The force on each element area – normal to the surface

e.g.: Dam, storage tank, ship and etc.

When analyzing forces on submerged surfaces, the atmospheric pressure can be subtracted.

Pressure on a plane immerged surface

The hydrostatic forces are varies depend on its depth

F = P*AP gAx

Pressure on a plane immerged surface

Location of the pressure:

GIh xAx

Geometric Properties (Area & Moment Inertia)

Pressure on a curved surface

Pressure on a curved surface

1 1( ) / 2x h h h

1 *1

/

A h

area mwidth

/V volume mwidth

GIh xAx

HP gAx vP gV

2 2( H vR P P 1tan v

H

P

P

Pressure Distribution

Pressure Distribution

Pressure is calculated per unit width only

Rectangular distribution

Triangular distribution

/ 2x h

/ 3x h

( / 3) ( / 2)........a bP h P hx

P

21/ 2 .........P gh

21/ 2P gh

2P gh

SUMMARY OF CHAPTER 2

1. Pressure in Fluids – types of pressure

2. Pressure at a points and Pressure Variations (Pascal’s Law) – depends on their elevation.

3. Pressure measurements – Barometer, Manometer and piezometer.

4. Hydrostatics Forces on Submerged Plane Surface –Due to difference shape (circular, rectangular and triangular)

5. Hydrostatics Forces on Submerged Curved Vane

6. Pressure Distribution in Fluids – Application to sluice gate, dam and etc.