Lesson 2.4 Liquids
Objectives
This lesson deals with liquids, pressures in liquids and
buoyancy. On completion of the lesson, you should be able
to estimate pressures at different depth in a fluid. You
should also be able to discuss Archimedes’ Principle
and Pascal’s Law.
Overview
Liquid particles move about but gravity and forces of
attraction between liquid particles keep them in the
bottom of a container. Different liquids have different
densities. We can measure liquid densities by measuring
the mass of a known volume of liquid.
Pressures in liquids are
transmitted in all directions - liquid levels are
constant. Pressure in liquids is caused by the weight of
liquid above the point of measurement.
Pressure in liquids causes
buoyant forces on objects immersed in liquids. The
buoyant forces are in the upward direction - if the
surface of the immersed object is not parallel with the
ground, the vertical component of the pressure causes
buoyancy. If the volume of an object is more than the
volume of liquid with the same weight, it will float. We
can determine the density of an object that can be
immersed in a liquid by weighing it in the liquid.
Liquid particles are
constantly moving and they can move with relative freedom
inside the liquid.
There are forces of
attraction between the particles and these keep the
liquid in the bottom of the container and help to keep
too many of the molecules from evaporating into the air
above the surface.
MINI
LAB
Use a Eureka can to measure the volume of water displaced
by a submerged object. Weigh the object and determine its
density.
Weigh the object in air and in water and calculate its
density.
EXPERIMENT:
Eureka
Purpose: To show how a Eureka can can be used to
measure the volume of an object when submerged.
Equipment:
Metal object with mass between 100 and 500 grams
Eureka can
Detergent
Measuring cylinder
Spring balance
String
Procedure:
- Attach a piece of
string to the object.
- Weigh the object in
air.
- Place a few drops of
detergent in the Eureka can.
- Fill the Eureka can
until it overflows. Wait until the process of
overflowing is complete.
- Attach the string to
a spring balance and lower the object slowly into
the water.
- Measure the weight of
the object when it is submerged.
- Measure the quantity
of liquid that overflows when the object is
lowered into the water. This can either be done
by collecting the overflow or by measuring the
amount needed to re-fill the can.
Calculations
The difference between the
mass of the object in air and the apparent mass when
submerged is equivalent to the mass of water displaced.
If the density of water is
assumed to be 1 g/cm3, the mass of the water
displaced in grams is numerically equal to the volume in
cm3.
Calculate the density by
dividing the mass in air by the volume.
Check the estimation of
the volume by measuring the volume of liquid overflow
from the Eureka can.
Pressure in Liquids
Because liquid particles can move, forces can be
transferred through the liquid. The weight of the liquid
creates pressure that increases with depth. The weight of
liquid above a point increases as the liquid gets deeper
and deeper. This weight causes pressure.
Pressure acts in all directions.
Pressure & Density
Different liquids have different densities. Because the
different atoms have different weights and because
different forces of attraction hold different particles
together, the amount of liquid in a particular space can
vary. We often compare the density of a liquid with the
density of water (at 4ēC)
Buoyancy
Archimedes Principle states that the buoyant force on a
submerged object is equal to the weight of the fluid that
is displaced by the object.
Pressure in liquids acts in all directions. Any object
inside a liquid is exposed to the pressure forces. The
upward component of these pressure forces creates
buoyancy.
Even if an object sinks in a liquid it experiences an
upward force due to the pressure in the liquid.
Weight of an Object In
Water
The difference between the weight of this object in the
liquid and its weight in air is the buoyancy of the
object.
Floating
If the buoyant force acting on an object is greater than
its weight in air, it will float.
If the buoyant force is less than its weight in air, it
will sink.
If it sinks, it displaces its own volume of liquid.
If it floats, it displaces its own weight of liquid.
Hydraulics
Pascal's law states that when there is an increase in
pressure at any point in a confined fluid, there is an
equal increase at every other point in the container.
The ability of a liquid to exert pressure in all
directions is used in hydraulic equipment to great
advantage. Hydraulic jacks and other types of hydraulic
equipment work on this principle to multiply the
mechanical force a number of times.
P = F
/ A :
Pressure = force ¸ area
Where: P = pressure (N/m2)
(or Pa)
F = force in
Newtons (N)
and A = area (m2)
r = m /
v : Density = mass
¸ volume
Where: r = density (kg/m3) (or g/cm3)
m = mass (kg)
and v = volume (m3)
Example
2.4.1: Buoyancy
An object with a volume of 50 cm3 and a
density of 1400 kg/m3 is placed in water with
a density of 1000 kg/m3. What will be the
buoyant force acting on the object?
Solution
The buoyant force on the object is equivalent to the
weight of the water that it displaces.
Since it is denser than water, it will not float and it
will displace its own volume of water.
50 cm3 is equivalent to 50 / 1,000,000 m3.
Since the density of water
is 1000 kg/m3,
the mass of 50 cm3
of water is (50 / 1,000,000) x 1000 kg = 0.05 kg
The weight of 0.05 kg = 9.81
x 0.05 = 0.4905 N
Example
2.4.2: Hydraulics
A hydraulic jack has a small piston with a radius of 2cm
and a larger piston with a radius of 6 cm. The pistons
are at the same level in the fluid. How much force
is exerted on the circular surface of the larger piston
if the smaller piston exerts a force of 500 N on the oil
connecting the circular surfaces of the two pistons?
Solution
Pressure on small piston = pressure on large piston.
(Force on small piston / area of small piston) = (Force
on large piston / area of large piston)
Force on large piston = Force on small piston x (area of
large piston / area of small piston)
= 500 N x { [p x 62 ] / [p x 22 ]} = 500 x 9 = 4500 N.
Questions
- A fluid with no upper
surface is called a ………….
- The ratio of mass to
volume is called ……………
- A rock will sink in
water because its ……………
is more than that of water.
- Pressure is the ratio
of force applied to the ……… over
which it is applied.
- A blunt knife does
not cut as easily as a sharp knife does because
force is applied over a ……….. area.
- What is the pressure
(above atmospheric pressure) at a depth of 5
meters in a fresh water lake? Assume that the
density of the water is 1000 kg/m3.
- What would the
pressure be at a depth of 5 meters in a lake
filled with salt water with a density of 1100 kg/m3?
- If an object with a
volume of 5 cm3 sinks in water with a
density of 1000 kg/m3, what mass of
water does it displace?
- What is Archimedes’
Principle?
- If an object with a
mass of 300 grams floats in water, what mass of
water does it displace?
- If an object with a
volume of 5 cm3 sinks in water with a
density of 1000 kg/m3, does a buoyant
force act on the object? Why?
- If an object with a
volume of 4 cm3 and a density of 1100
kg/m3 is placed in water with a
density of 1000 kg/m3, will it sink or
float?
- If an object with a
volume of 4 cm3 and a density of 1100
kg/m3 is placed in water with a
density of 1000 kg/m3, what will be
the buoyant force acting on the object?
- An object with a
density of 1200 kg/m3 has a volume of
10 cm3. What is its weight in Newtons?
What weight of water with a density of 1000 kg/m3
would it displace? If it is completely submerged
in the water and suspended at the end of a thin
thread attached to a balance, what weight would
the balance indicate?
- What is Pascal’s
Law?
- A hydraulic jack has
a small piston with a diameter of 1cm and a
larger piston with a diameter of 3cm. How much
pressure is exerted on the circular surface of
the larger piston if the smaller piston exerts a
pressure of 300 kPa on the oil connecting the
circular surfaces of the two pistons? (Assume
that the surfaces of the pistons are at the same
depth in the oil)
- A hydraulic jack has
a small piston with a diameter of 1cm and a
larger piston with a diameter of 4cm. How much force
is exerted on the circular surface of the larger
piston if the smaller piston exerts a force of
300 N on the oil connecting the circular surfaces
of the two pistons? (Assume that the surfaces of
the pistons are at the same depth in the oil)
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