This document discusses fluid statics and dynamics, including:
- Pressure increases with depth in a liquid according to the equation P=ρgh.
- Density is defined as mass per unit volume. Relative density compares a substance's density to that of water.
- Archimedes' principle states that the upthrust on an object in a fluid is equal to the weight of the fluid displaced by the object.
- For an object to float, its weight must equal the weight of the fluid it displaces according to the principle of floatation.
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PHYSICS FLUID.pptx
1. Fluid statics and Dynamic
Pressure and Density
• Fluid statics is the study of the fluids at rest
and their stationary interactions with solid
bodies.
• Fluid unlike solids are substances that can
flow. Hence the term fluids include both
liquids and gases. Liquid and gases differ
markedly in their compressibilities; a gas is
easily compressed. While a liquid is practically
incompressible
2. Fluid statics and Dynamic
Pressure and Density
• Pressure
• Pressure is generally defined as the force
acting normally per unit area. Thus;
• Pressure , P= force/area
• The S.I. unit of pressure is Newton per meter2
(Nm-2). This unit is also called Pascal, after the
French mathematician and scientist, Blaise
Pascal, who did much important work on fluid
pressure.
4. Fluid statics and Dynamic
Pressure and Density
• Observations show that in a liquid at rest, the
pressure, P, increases uniformly with depth, h,
of the object below the liquid surface and
with its density, , according to the relation:
• Where g is the acceleration due to gravity.
Since , it follows that the pressure in a
liquid is the same at all points on the same
horizontal surface.
5. Fluid statics and Dynamic
Pressure and Density
Density and Relative density
• The density of a substance is defined as its mass per unit volume. Thus;
density = mass/volume
• When the mass is in kg and the volume is m3 , then the density is in Kg/m3 .
• Thus a metal block of mass 9000kg and volume 1.5 m3 has a density of 6000kg/m3
. The density of water (at 4oc ) is 1000 kg/m3 or 1g/cm3 .
• Since the density of water is 1g/cm3 , the density of a substance is often
expressed compared to that of water. This is called the relative density of the
substance. Thus;
• Relative density = Density of substance/Density of water
• If equal volumes of the substance and water are chosen, then the densities are
numerically equal to the masses. Hence;
• Since relative density is a ratio or number. It has no units. The relative density of
mercury is 13.6 times that of water, since the density of water is 1000 kg/m3 and
the density of mercury is 13600kg/m3 .
6. Fluid statics and Dynamic
Pressure and Density
• Archimedes’ Principle
• It is a common experience that an object immersed in a
fluid appears to lose it weight. The apparent weight is due
to a resultant upward force on the object owing to the
pressure of the fluid on it. This upward force is called
upthrust or buoyant-force or upward-force of the fluid on
the object.
• A Greek scientist, Archimedes was the first to carry out an
experiment to measure the upthrust of a liquid. The result
of the experiment, now called
• Archimedes’ principle, states that: The upthrust on a body
partially or wholly immersed in a fluid is equal to the weight
of the fluid displace.
7. Fluid statics and Dynamic
Pressure and Density
Upthrust = weight of water displaced
Upthrust = real weight – apparent weight
weight of water displaced = real weight –
apparent weight
8. Fluid statics and Dynamic
Pressure and Density
Example 1
• A solid weighs 11 N when suspended in air
and 9 N, when suspended in water, Calculate
(i) the volume of the solid
(ii) its density.
9. Fluid statics and Dynamic
Pressure and Density
• Solution
(i) Weight of water displaced = upthrust = real weight – apparent
weight
11 N – 9 N = 2 N
mg =2 N
Mass of water displaced = 2/10 = 0.2kg
• Since water has a density of 1000kg/m3, 1000kg mass of water will
occupy a volume of 1m3 . Thus the volume of water displaced is
0.0002 m3 . This is equal to the volume of the solid; a solid displaces
its own volume when completely immersed in a fluid.
(ii)
10. Fluid statics and Dynamic
Pressure and Density
Measurement of relative density by Archimedes’ principle
• The relative density or density of a solid can be determined by the
use of Archimedes’ principle.
• Using this method, the solid is first weighed in the air, say Mo . It is
totally immersed in water and weighed, say, M1 .
• From Archimedes’ principle, the upthrust on the solid is equal to
the weight of water displaced.
• Thus, upthrust = Mo– M1 = weight of water displace
• .
• .
• .
11. Fluid statics and Dynamic
Pressure and Density
• Measurement of relative density by Archimedes’ principle
• The same consideration can be utilized to find the relative
density of a liquid. The solid is first weighed in the air (Mo )
and then weighed totally immersed in the liquid (M1 )
whose relative density is to be determined. It is finally
weighed once more totally immersed in water (M2 ).
• .
• .
• .
• .
12. Fluid statics and Dynamic
Pressure and Density
• Example 2
A piece of metal weighs 100g in air and 60g in
water . What will it weigh in alcohol of relative
density 0.8.
14. Fluid statics and Dynamic
Pressure and Density
Floating Bodies
• A floating body is in equilibrium under the influence of two forces, the weight and
the upthrust due to the fluid.
• From Archimedes’ principle the upthrust is equal to the weight of the fluid
displaced.
• It follows that when a body floats in a fluid, its weight must be equal to the weight
of the fluid it will displace. As a result the total resultant force acting on the body
is Zero. This is called the principle of floatation.
• The law of flotation states that when a body floats in a liquid, the weight of the
liquid displaced by its immersed part is equal to the weight of the body. Hence,
upthrust = weight of the body
We can equally look at floatation in terms of density variation
• For instance, Ice has a density of 0.9 gcm-3 and Float in water of density 1 gcm-3
with about 90% of its volume submerged.
• A metal block of density, say, 8 gcm-3 when left on the surface of water quickly
sinks to the bottom of the water. If the same metal block is immersed into mercury
of density 13.6 gcm-3 , it float on the surface of the mercury.
• What this means is that a solid floats in liquid if its density is less than that of the
liquid. In the same vein and for the same reason, a liquid settles over a denser
one; example oil is less dense than water and settles on the surface of water.
15. Fluid statics and Dynamic
Pressure and Density
• Example 2:
• A cube of wood of side 5cm has a mass of 75g.
What fraction of its volume will be submerged
when it floats.
• (i) in water
• (ii) in alcohol of density 0.8 g/cm3
16. Fluid statics and Dynamic
Pressure and Density
Solution:
i) mass of wood = mass of displaced liquid= 75 g
volume of water displaced = 75 cm3 = Volume of wood under water.
Total volume of cube = 5 X 5 X 5 = 125 cm3
Fraction of wood under water = 75/125 = 3/5
ii) Mass of alcohol displaced = 75 g
Volume of alcohol displaced = 93.75 cm3 = Volume of wood
under alcohol
Fraction of wood under alcohol = 93.75/125 = 3/4
17. Fluid statics and Dynamic
Pressure and Density
• Fluid flow is the volume of fluid that moves
past a certain point per unit time.
• It is mathematically represented as
Q = volume/time.
19. Fluid statics and Dynamic
Pressure and Density
• Explanation of the derivation
The key relation here is that the flow in section-1 i.e. (How much volume passing through section1)
must be equal to the flow in section -2.
20. Fluid statics and Dynamic
Pressure and Density
Example
• Blood flows through aorta of radius 1.0cm
with a speed of 30cm/s. Find the speed with
which it will flow through a capillary of cross
sectional area 2000cm2.
