3.2.3 Applications of Liquid Pressure

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Dam


  1. The wall of the dam is built thicker at the bottom to withstand a higher pressure.
  2. The generator is placed at the lower part so that the pressure of the water is high enough to drive the turbine.

Submarine


In deep sea, the pressure of the water is tremendously high. Hence the body of the submarine is thick and built by strong material

Measuring Blood Pressure


When measuring blood pressure, the inflatable cuff of the sphygmomanometer should be at the same level with the heart so that the pressure measured is equal to the blood pressure of the heart.

Intravenous Transfusion


For intravenous transfusion (IV), the bottle is hung at an elevated position to ensure that the liquid in the IV bottle gains sufficient pressure to flow into the vein of the patient.

Water Tower


The water tower is built at high place so that the water has sufficient pressure to flow to consumer’s house.

 

3.2.2 Nature of Liquid Pressure

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The pressure caused by a liquid has the following characteristics:

  1. Pressure in liquid does not depends on
    1. the shape of the container.

      Eventhough the shape of the containers are different, the pressure at the bottom are still the same if the depth of water are the same.
    2. the size of the container.

      Eventhough the size of the two container are different, the pressure at the bottom are still the same if the depth of water are the same.
    3. the area of its surface.

      Eventhough the area of A and B are different, the pressure at the two areas are still the same if the depth of water are the same.

Pressure Increases with Depth

  1. The deeper the liquid, the faster the liquid spurts out.
  2. In conclusion, the pressure in a liquid increases with depth.

Pressure Depends on the Vertical Depth, But not the Length of Liquid Column.


Pressure at A = Pressure at B

All Points at the Same Level in a Liquid are at the Same Pressure


The level of the surface of a liquid in a container is always the same because for a given liquid, the pressure is always equal at the same level.

Pressure Does Not Depend on the Surface Area of the Object.


Pressure exerted on the small fish
= Pressure exerted on the big fish

Pressure Acts in All Direction


The pressure at any point of a liquid acts equally in all direction.

 

 

3.2.1 Liquid Pressure

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  1. Pressure in liquid is owing to the weight of the liquid acting on the surface of any objects in the liquid.
  2. Pressure of a liquid is directly proportional to
    1. the gravitational field strength
    2. the depth
    3. density of the liquid.
  3. Pressure in liquids is not affected by the size or shape of the object.
  4. The pressure caused by a liquid and the pressure in a liquid can be determined by using the equation below:

Pressure Caused by Liquid




Pressure in Liquid


Example 1:


The diagram shows 2 fishes in water. The density of the water is 1025 kg/m³. The surface area of fish A is 300 cm² and the surface area of fish B is 2000cm². Find
a. the pressure exerted by the water on fish A.
b. the pressure exerted by the water on fish B.
c. the force exerted by the water on fish A.
d. the force exerted by the water on fish B.

Answer:
This question would like us to compare the liquid pressure exerted on 2 objects of different size in the same depth of water.

a.
Depth, h = 2m
Density, ρ = 1025 kg/m³
Gravitational Field Strength, g = 10 N/kg

Pressure exerted by water on fish A,


b. Pressure exerted by water on fish B,


(Note: Pressure exerted both fishes are the same. Pressure caused by liquid is not affected by the size or shape of the objects)

c. Surface area of fish A, A1 = 300 cm² = 0.03 m²

Force exerted by the liquid pressure,


d. Surface area of fish B, A2 = 2000cm² = 0.2 m²

Force exerted by the liquid pressure,



Example 2:


Figure above shows the cross section of a sea near a seaside. Find the difference of the pressure between point A and point B. [Density of seawater = 1050kg/m³]

Answer:
Density, ρ = 1050kg/m³
Gravitational Field Strength, g = 10 N/kg

At point A:
Depth, h = 0.8 m


At point B:
Depth, h = 3 m


Pressure Difference



Example 3:
Find the pressure at a depth of 20 m in water when the atmospheric pressure is 100000 Pa. The density of water is 1000 kg/m³.

Answer:
(Caution: Pressure in liquid = Pressure caused by liquid + Atmospheric Pressure)

Depth, h = 20m
Density,  = 1000 kg/m³
Gravitational Field Strength, g = 10 N/kg
Atmospheric Pressure, Patm = 100000 Pa

Pressure in water,



  1. Usually, a U-tube is used to compare and measure density of liquids.
  2. The density of the 2 liquids is related by the equation:

Example 4:


Figure above shows a U-tube filled with water and liquid P. Liquid P is insoluble in water. Given that the density of water is 1000kg/m³, find the density of liquid P.

Answer:
h1 = 10cm
h2 = 12 cm
ρ1 = 1000kg/m³
ρ2 = ?



The density of liquid P = 833 kg/m³


Example 5:

The diagram shows a U-tube filled with two types of liquid, X and Y which are not mixable. If the density of liquid X and liquid Y are 1200 kg/m³ and 800 kg/m³ respectively, find the value of h.

Answer:
h1 = 10cm
h2 = h
ρ1 = 800kg/m³
ρ2 = 1200kg/m³


 

3.1.1 Understanding Pressure

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  1. The definition of pressure
  2. The formula of pressure (you need this formula to do lot of calculation.)
  3. The SI unit of pressure
  4. Factors affecting the magnitude of pressure

Pressure

Pressure is defined as the force acting normally per unit area. (Here, the word "normally" means perpendicularly.)

   

Example

As shown in the diagram above, a 20N force acts on a 4cm² surface. The force is shared equally by the surface, hence each 1 cm² of the surface withstand a force of 5N (20N/4).

The force (5N) acts on 1 unit area (1cm²) is said to be the pressure acting on the surface. Therefore, the pressure acting on the surface is 5N/cm².

Mathematically,

Unit of Pressure

The SI unit of pressure is Pascal (Pa). 1 Pa is equal to1 newton per metre2 (N/m²).

1 N/m² = 1 Pa

Factors Affecting the Magnitude of Pressure

Factors that affect the pressure acting on a surface.
  1. Magnitude of the force.
    The larger the force, the higher the pressure.
  2. Contact area.
    The larger the contact area, the lower the pressure.

Finding the force acted on a surface when the pressure and surface area are given.

Example:
A force F is acting on a surface of area 20cm², produces a pressure 2500Pa on the surface. Find the magnitude of the force.

Answer:
This is a pretty direct question. We just need to write the formula and then substitute all the related value that we have into the formula and then solve it.

 However, we need to be careful about the unit. If the pressure is in Pa, then the unit of area must be in m².

1 m² = 10000 cm²

From the question,
A = 20 cm² = 0.002 m²
P = 2500 Pa


Example 2:

A block of wood 3 m long, 5 m wide and 1 m thick is placed on a table. If the density of the wood is 900 kgm-3, find

a. the lowest pressure
b.the highest pressure

on the table due to the block.

Answer:
a.
Step 1: Finding the weight of the block
The volume of the block = 3 x 5 x 1 = 15m³.

Mass = Density x Volume

Mass of the block, m = (900)(15)= 13500 kg

Weight of the block = mg = 13500 x 10 = 135,000N

Step 2: Determine the surface area
The pressure exerted on a surface is inversely proportional to the area of the surface. The bigger the surface, the lower the pressure.

For the wooden block, the biggest surface, A = 5 x 3 = 15m²

Step 3: Finding pressure
 

b.
The pressure is the highest when the surface area is the smallest.

The smallest surface area of the block = 1 x 3 = 3m²

The highest pressure,


Example 3:
Two cubes made of the same material; one has sides twice as the other, lying on a table. Standing on one face, the small cube exerts a pressure M on the table. What is the pressure (in term of M) exerted by the larger cube standing on one of its faces, on the table?

Answer:

For the small cube,

Surface area = x²
Volume = x³
Mass = m
Weight = mg

Pressure,


For the big cube,
Surface area = 4x²
Volume = 8x³
Mass = 8m (Because the volume is 8 times greater)
Weight = 8mg

Pressure,


 

2.12.5 Factors that Affect the Elasticity Springs

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Arrangement in series: Arrangement in parallel:
Extension = x × number of spring
Stiffness decreases
Spring constant = k/number of spring		 Extension = x ÷ number of spring
Stiffness increases
Spring constant = k × number of spring

Factors Affecting the Stiffness of Spring

Material type of spring

(A steel spring is stiffer than a copper spring)
Stiffer Less Stiff

Diameter of wire of spring

(The greater the diameter of the wire, the stiffer the spring)
Stiffer Less Stiff

Diameter of the spring

(The smaller the diameter of spring, the stiffer the spring)
Stiffer Less Stiff

Length of the string

(Shorter spring is stiffer)
Stiffer Less Stiff

 

2.12.4 Elastic Potential Energy

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Elastic Potential Energy

Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing.

Formula:


Example:


Diagram above shows a spring with a load of mass 0.5kg. The extention of the spring is 6cm, find the energy stored in the spring.

 Answer:
The energy stored in the spring is the elestic potential energy.


 

2.12.2 Hooke’s Law

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Hooke's Law states that if a spring is not stretched beyond its elastic limit, the force that acts on it is directly proportional to the extension of the spring.

Elastic Limit

The elastic limit of a spring is defined as the maximum force that can be applied to a spring such that the spring will be able to be restored to its original length when the force is removed.

Equation derived from Hooke's Law

From Hook's Law, we can derived that

Spring Constant

Spring constant is defined as the ratio of the force applied on a spring to the extension of the spring.

It is a measure of the stiffness of a spring or elastic object.

Graph of Streching Force - Extension

Gradient = Spring constant

Area below the graph = Work done

F-x graph and spring constant

The higher the gradient, the greater the spring constant and the harder (stiffer) spring.

For example, the stiffness of spring A is greater than spring B.

 

2.12.1 Elasticity

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Elasticity is the ability of a sub-stance to recover its original shape and size after distortion.

Forces Between Atoms

The intermolecular forces consist of an attractive force and a repulsive force.

  • At the equilibrium distance d, the attractive force equal to the repulsive force.
  • If the 2 atoms are brought closer, the repulsive force will dominate, produces a net repulsive force between the atoms.
  • If the 2 atoms are brought furhter, the attractive force will dominate, produces a net attractive force between the atoms.

Graph of Forces Between 2 atoms


x0 = Equilibrium Distance

When the particles are compressed, x < x0, the attractive force between the particles increases.

If the distance x exceeds the elastic limit, the attractive force will decreases.