FLUID MECHANICS
Pressure
• is the force applied perpendicular to the surface of
an object per unit area over which that force is
distributed
• Pressure is a scalar quantity. There is no direction
associated with pressure, but the direction of the
force associated with pressure is perpendicular to
the surface on which the pressure acts.
• The SI unit of pressure is Pa.
1 Pa = 1N/m^2
1 torr = 133.3Pa
1 bar = 10^5 Pa
Pressure Formula :
P=F/A
Density
• defined as mass per unit volume.
• measurement of how tightly a material is packed together.
• The SI unit for density is the kilogram per cubic meter (kg/m3). For
many situations, however, this as an inconvenient unit, and we often
use grams per cubic centimeter (g/cm3) for the densities of solids
and liquids, and grams per liter (g/L) for gases
FORMULA:
𝑃=
𝑀
𝑉
, 𝑤ℎ𝑒𝑟𝑒 𝑃 𝑖𝑠 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 , 𝑀 𝑖𝑠 𝑚𝑎𝑠𝑠
𝑎𝑛𝑑 𝑉 𝑖𝑠 𝑣𝑜𝑙𝑢𝑚𝑒.
Note: The density of solids remains almost constant, however, the
density of a fluid will vary depending on pressure and temperature
Specific Gravity
• Also called relative density
• The specific gravity of an object is the density of
that object divided by the density of water.
• The density of water is 1,000 kilograms per
meter cubed.
Hydrostatic Pressure
• is proportional to the depth measured from the
surface as the weight of the fluid increases when
a downward force is applied.
• “The pressure exerted by a fluid at equilibrium at
any point of time due to the force of gravity”
Pressure variation with depth in a static fluid
• For an incompressible fluid, density is not
The same everywhere.
• Consider an imaginary fluid volume, the
Sum of all force on this volume must be zero
As it is in equilibrium: F2 – F1 – mg = 0
Pressure variation at a depth below the
surface of a liquid open to atmosphere.
• The pressure exerted by the air in
the atmosphere is greater close to
Earth’s surface and decreases as you
go higher above the surface.
• FORMULA:
P=Patm +ρgh ,
where P = pressure
Patm = atmospheric pressure,
h=depth/height,ρ = mass density of
fluid , g = acceleration due to gravity.
Gauge Pressure
TERMS:
• Gauge pressure is the amount by which Absolute Pressure:
->absolute pressure is the pressure of
the absolute pressure exceeds
having no matter inside a space, or a
atmospheric pressure.
perfect vacuum.
• is the pressure relative to atmosphericAtmospheric Pressure:
pressure. Gauge pressure is positive ->is the force exerted at any given point on the Earth’s
for pressures above atmospheric
surface by the weight of the air above that point. In short: the
that surrounds the Earth creates atmospheric pressure
pressure, and negative for pressures air
and this pressure is determined by the collective weight of air
below it.
molecules.
Pgauge = Pabs – Patm
=1 atmp = 1.013x10^5 Pa = 14.7lb/in^2 (psi)
=760mm Hg
=760 torr
Pgauge = Gauge Pressure
=1.013 bar
Pabs = Absolute Pressure
Patm = Atmospheric Pressure
Pascal’s Principle
• The pressure applied to a confined fluid increases the pressure
throughout the same amount
• in a fluid at rest in a closed container, a pressure change in one
part is transmitted without loss to every portion of the fluid and to
the walls of the container
𝑃1 = 𝑃2
F1/A1 = F2/A2
P= Pressure
F= Force
A = area (perpendicular to
the force)
Archimedes Principle
• When a body is immersed in a fluid, it is
subjected to an upward force which is equal
to the weight of the fluid displaced.
BF = ρgV
BF = Buoyant Force
Ρ = density of fluid
G= gravitational force
V=volume of the body
What Is a Buoyant Force?
The buoyant force is the
upward force exerted on
an object wholly or partly
immersed in a fluid. This
upward force is also
called Upthrust. Due to
the buoyant force, a body
submerged partially or
fully in a fluid appears to
lose its weight, i.e.
appears to be lighter.
Problem:
1.If the absolute pressure at the bottom of the ocean is 120kPa, how
deep is the water at this point?
Sp. Gr of sea water = 1.03
Density of water = 9.81kN/m^3
Patmp = 101.325kPa = 14.7psi = 1 atm