1. What is Pressure?
In fluid mechanics, pressure is defined as:
Pressure = Force exerted by a fluid per unit area
𝑃
=
𝐹
𝐴
P=
A
F
Where:
𝑃
P = Pressure (N/m² or Pascal, Pa)
𝐹
F = Force (N)
𝐴
A = Area (m²)
Important points:
Fluids exert force in all directions
Pressure at a point in a fluid is same in all directions (Pascal’s Law)
Pressure always acts normal (perpendicular) to the surface
2. Units of Pressure
Unit Symbol Value
Pascal Pa 1 N/m²
kPa kPa 10³ Pa
Bar bar 10⁵ Pa
Atmosphere atm 1.013 × 10⁵ Pa
mm of Hg mmHg 133.3 Pa
m of water m H₂O 9.81 kPa
3. Types of Pressure
(a) Atmospheric Pressure
Pressure exerted by air on earth surface.
𝑃
𝑎
𝑡
𝑚
=
1.013
×
10
5
Pa
P
atm
=1.013×10
5
Pa
(b) Absolute Pressure
Pressure measured relative to perfect vacuum
𝑃
𝑎
𝑏
𝑠
=
𝑃
𝑎
𝑡
𝑚
+
𝑃
𝑔
𝑎
𝑢
𝑔
𝑒
P
abs
=P
atm
+P
gauge
(c) Gauge Pressure
Pressure measured above atmospheric pressure
𝑃
𝑔
𝑎
𝑢
𝑔
𝑒
=
𝑃
𝑎
𝑏
𝑠
−
𝑃
𝑎
𝑡
𝑚
P
gauge
=P
abs
−P
atm
(d) Vacuum Pressure
Pressure below atmospheric pressure
𝑃
𝑣
𝑎
𝑐
𝑢
𝑢
𝑚
=
𝑃
𝑎
𝑡
𝑚
−
𝑃
𝑎
𝑏
𝑠
P
vacuum
=P
atm
−P
abs
4. Pressure Variation in a Static Fluid
Consider a fluid at rest.
Pressure increases with depth due to weight of fluid.
𝑃
=
𝜌
𝑔
ℎ
P=ρgh
Where:
𝜌
ρ = Density of fluid (kg/m³)
𝑔
g = Acceleration due to gravity (9.81 m/s²)
ℎ
h = Depth below free surface (m)
Important conclusions:
Condition Result
Same horizontal level Same pressure
Greater depth Greater pressure
Independent of container shape True
This is called Hydrostatic Law
5. Pascal’s Law
Pressure applied to a confined fluid is transmitted equally in all directions.
Used in:
Hydraulic press
Hydraulic jack
Hydraulic brakes
6. Measurement of Pressure
Pressure is measured using manometers and mechanical gauges
A. Manometers
Manometers use liquid column height to measure pressure.
1. Piezometer
Simplest type of manometer.
A vertical glass tube connected to a pipe.
𝑃
=
𝜌
𝑔
ℎ
P=ρgh
Limitations:
Cannot measure gas pressure
Cannot measure high pressure
Not suitable for vacuum pressure
2. U-Tube Manometer
U-shaped tube containing mercury or water.
Used to measure:
Gauge pressure
Vacuum pressure
Differential pressure
Working:
Pressure difference balances liquid column height.
𝑃
𝐴
−
𝑃
𝐵
=
𝜌
𝑔
ℎ
P
A
−P
B
=ρgh
3. Differential Manometer
Measures pressure difference between two points
Types:
U-tube differential manometer
Inverted U-tube manometer (for small pressure difference)
B. Mechanical Pressure Gauges
1. Bourdon Tube Pressure Gauge
Most common in engineering practice.
Construction:
Curved metal tube (C-shaped)
Working:
Pressure increases → tube tends to straighten
Movement converted to pointer reading
Uses:
Boilers
Compressors
Hydraulic systems
Range: Up to 1000 bar
2. Diaphragm Pressure Gauge
Uses flexible diaphragm.
Suitable for:
Low pressure
Vacuum pressure
Gas pressure
3. Dead Weight Pressure Gauge
Highly accurate device.
Principle:
Pressure balanced by known weight
𝑃
=
𝑊
𝐴
P=
A
W
Used for:
Calibration of other gauges
7. Simple Numerical Example
A diver is 5 m below water surface. Find pressure.
𝑃
=
𝜌
𝑔
ℎ
P=ρgh
𝑃
=
1000
×
9.81
×
5
P=1000×9.81×5
𝑃
=
49
,
050
Pa
=
49.05
kPa
P=49,050Pa=49.05kPa
(This is gauge pressure)
8. Importance in Civil Engineering
Pressure concepts are used in:
Design of dams
Water tanks
Pipelines
Hydraulic structures
Groundwater flow
Tags:
Fluid Mechanics