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.