Fluids

Physics for Engineers
FL UID
S
FLUID
S
A fluid is a substance that cannot maintain its own shape
but takes the shape of its container.
Fluid laws assume idealized fluids that cannot be
compressed.
OB J E C T IVES
• Calculate the density of an object.
• Determine whether an object will float given its
average density.
• Calculate the forces on a submerged or partially
submerged object using Archimedes’ Principle.
• Calculate pressure as the force a system exerts over an
area.
• Explain the operation of a hydraulic system as a
function of equal pressure throughout a fluid.
• Apply the continuity equation to fluids in motion.
• Apply Bernoulli’s Principle to fluids in motion.
INC LUDES LIQUIDS AND
GAS ES :
• Liquid has no fixed shape but nearly fixed volume
• Gas has neither fixed shape or volume
• Both can flow
DENSITY
• Density is a physical property of matter that measures how much mass is contained in a given
volume. In the case of fluids, density refers to the amount of mass that is contained within a
specific volume of the fluid.
The density of a fluid is typically expressed in units of Mass per unit volume:
kilograms per cubic meter (kg/m³)or grams per milliliter (g/mL).
Density is calculated according to the simple formula:
p = m/V
m = pV
• EX. A Styrofoam cup is less dense than a ceramic cup, so the Styrofoam cup will float
in water and the ceramic cup will sink.
• EX. Helium balloons rise because helium is less dense than the surrounding air. Over
time, the helium escapes the balloon and is replaced by air, causing it to sink.
DE NSITY OF
WATER
1000 Kg per m3
1 Kg/liter
1 gram /cubic centimeter (cc)
1 cubic meter = 1000 liters

1 cubic centimeter = 1 milliliter
PRESSU
REin fluids refers to the force exerted per unit area. The pressure in a
Pressure
fluid is caused by the collisions of the fluid particles with each other and
with the walls of the container or any other surfaces in contact with the fluid.
P = F/A, or in terms of magnitude,

P = mg/A, where mg is the weight of the fluid.
Example:Air pressure is approximately 100,000 Pascals. What force is exerted
on this book when it is sitting flat on a desk? The area of the book’s cover is
0.035 m2.
PR E SSURE IN
FLUIDS
• Force per unit area
• Pressure = P = F/A
• Unit N/m2= Pascal(Pa)
• Exerted in all directions
• Force due to pressure is perpendicular to surface
in a fluid at rest
PR ESSUR E VAR IES WITH
DEPTH
The pressure in a fluid varies with depth due to the weight of the
fluid above any given point.
pgh
• Let depth be h. Assume incompressible.
• Force acting on area is mg = pVg = pAhg
• P = F/A = rgh
• Pressure at equal depths is the same
• If external pressure is also present it must be
added.
GRAVI T Y’ S EFFECT ON FLUID
PRESSURE
An imaginary
FBD for the fluid cylinder
cylinder of fluid
Imaginary
cylinder can be
any size
Example : At the surface of a freshwater lake, the pressure is 105 kPa. (a)
What is the pressure increase in going 35.0 m below the surface?
THE UNITS OF PRESSURE
1 ATM equals
1.013x105 N/m2
14.7 lbs/in2
1.013 bar
76 cm Hg
760 mm Hg
760 Torr
34 ft H2O
29.9 in Hg
PASC AL’S PR INC IPL E
A change in pressure at any point in a confined fluid is
transmitted everywhere throughout the fluid. (This is useful in
making a hydraulic lift.)
The applied force is Apply a force F1 here to a
transmitted to the piston of piston of cross-sectional area
cross-sectional area A2 here. A1.
Mathematically,
In these problems neglect

pressure due to columns of
fluid.
AR C HIM EDE S’
PR INC IPL E
An FBD for an object floating

submerged in a fluid.
The total force on the block due to

the fluid is called the buoyant force.
BUOYANT FORCE = THE WEIGHT OF THE FLUID
DISPLACED
The magnitude of the buoyant force is: equal to the weight of the fluid displaced by the object. This is
known as Archimedes' principle. Mathematically, it can be expressed as:
Buoyant force = weight of fluid displaced
Archimedes’ Principle: A fluid exerts an upward buoyant

force on a submerged object equal in magnitude to the weight
From before: of the volume of fluid displaced by the object.
The result is
Example: A flat-bottomed barge loaded with coal has a mass of 3.0105 kg.
The barge is 20.0 m long and 10.0 m wide. It floats in fresh water. What is the
depth of the barge below the waterline?
Example: A piece of metal is released under water. The volume of the metal is 50.0 cm3 and its
specific gravity is 5.0. What is its initial acceleration? (Note: when v = 0, there is no drag force.)
FBD for the Apply Newton’s 2nd Law to the

metal piece of metal:
The magnitude of the buoyant force equals the weight

of the fluid displaced by the metal.
Solve for a:
Example continued:
Since the object is completely submerged V=Vobject.
Given:
The sign is minus because gravity acts down. BF causes a < g.

FLUID FLOW
A moving fluid will exert forces parallel to the surface over which it moves,
unlike a static fluid. This gives rise to a viscous force that impedes the forward
motion of the fluid.
A steady flow is one where the velocity at a given point in a fluid is constant.
Steady flow is laminar; the fluid flows in layers. The path that the
fluid in these layers takes is called a streamline.
Streamlines do not cross.
laminar flow, also called streamline flow, type of fluid (gas or liquid) flow in
which the fluid travels smoothly or in regular paths, in contrast to turbulent flow,
in which the fluid undergoes irregular fluctuations and mixing.
Crossing streamlines would indicate a volume of fluid with two

different velocities at the same time.
An ideal fluid is incompressible, undergoes laminar flow, and has no
viscosity.
B E R NOUL L I’S
E QUAT ION
Bernoulli’s equation is a statement of energy conservation.
This is the most general equation
Work per unit Potential energy Kinetic

volume done by per unit volume energy per
the fluid unit volume
Example: Water sits in a large open jug at a height of 0.2m above the
spigot. With what velocity will the water leave the spigot when the spigot is
opened?
Example: Water sits in a large open jug at a height of 0.2m above the
spigot. With what velocity will the water leave the spigot when the spigot is
opened?

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Physics for Engineers

kilograms per cubic meter (kg/m³)or grams per milliliter (g/mL).

Density is calculated according to the simple formula:

1 cubic meter = 1000 liters

P = F/A, or in terms of magnitude,

In these problems neglect

An FBD for an object floating

The total force on the block due to

Archimedes’ Principle: A fluid exerts an upward buoyant

FBD for the Apply Newton’s 2nd Law to the

The magnitude of the buoyant force equals the weight

The sign is minus because gravity acts down. BF causes a < g.

Crossing streamlines would indicate a volume of fluid with two

This is the most general equation

Work per unit Potential energy Kinetic

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