3.2 PRESSURE IN LIQUIDS

UNDERSTANDING PRESSURE IN LIQUIDS

• Learning outcomes:

Relate depth to pressure in a liquid

Relate density to pressure in a liquid

Explain pressure in a liquid and state that P = hpg

Describe applications of pressure in liquids

Solve problems involving pressure in liquids.

The arrows represent pressure on the swimmer. The arrows from all directions because the water exerts pressure in all direction. That’s why swimmers feel the water pressure on all parts of theirs body when they are underwater.

introduction

A diver experiences discomfort to his body and ears when he dives deep underwater. Why is it happen?

EXISTENCE OF PRESSURE IN A LIQUID

KINETIC THEORY OF MATTER

Molecules of a liquid are closely arranged but free to move

The molecules in a liquid are downward pull by the force of gravity

And contribute to the weight of water

A column of liquid exerts a pressure on the layer of liquid below

CHARACTERISTICS OF PRESSURE IN A LIQUID

The pressure at a point in a liquid, at a particular depth, acts equally in all directions

The pressure does not depend on the shape or size

(surface area)

The pressure in a liquid is affected by the force of gravity.

Force of gravity Pressure

The pressure in a liquid increased with depth.

The pressure at a point in a liquid depends on its vertical distance from the surface of the liquid.

A liquid with a higher density exerts a higher pressure, If other factors remain constant. ( a liquid of the same volume with a higher density has a higher weight)

DERIVING FORMULA FOR PRESSURE IN A LIQUID.

h

A

Liquid density, p

Uniform column

P

A = area of base

h = Depth of base

g = Gravitational field strength

p = density of liquid

The formula for the pressure at a depth, h in the liquid:

Volume of liquid column, V = Ah

Mass of liquid column, m = pV

= Ahp

Weight of liquid column, W = mg

= Ahpg

The force acting on the surface area A is the weight of the liquid column above it.

Pressure, P = Weight of liquid column

Area of base of liquid column

= W = Ahpg

A A

P = hpg

APPLICATIONS OF PRESSURE IN LIQUIDS

• Public water supply system

The reservoir is placed at an elevated location so that the water will have sufficient pressure to flow to consumers located at lower grounds

Every home has water tank above the roof as storage and to have a constant water pressure.

Constructing of dams

Dams are built across rivers to stop the river flows and to form the lake for water supply

The high water pressure is used to drive water turbines to generate electricity

The water at the bottom of the dam is at the higher pressure than at the top. Hence, the wall of the dam has to be thicker at the base to sustain this higher water pressure.

CHECK YOUR PROGRESS

An air bubble is at a depth of 3 m below the surface of lake. What is the pressure of water on the air bubble?

(take density of water = 1000 kgm-3 )

h = 3 m

P = hpg

= 3 x 1000 x 10

= 30 000 N m-2

= 30 KPa

Calculate the water pressure at the bottom of the dam when the water is at maximum level. ( take density of water = 1000 kg-3; g = 10 N kg-1 )

• water pressure at the base of dam = hpg

• P = 25 x 1000 x 10• = 250 000 N m-2

• = 250 KPa

25 m

The figure shows a dam with a depth of 25 m.

• A submarine has a surface area of 300 m2. the density of sea water is 1050 kgm-3.

a) At what depth under the sea, will the additional pressure on the submarine be 5x105 Pa?

b) If the submarine is at the depth determined in a), calculate the force exerted by the sea water on the surface of the submarine. ( take g = 10 N kg-1 )

a) P = hpg

5 x 105 Nm-2 = hpg

h = 5 x 105 N m-2

( 1050 kg m-3) ( 10 N kg-1)

= 47.62 m

b) Force, F = Pressure x Surface area

= 5 x 105 x 300

= 1.5 x 108 N

KNOW YOUR FACTS

• Total pressure = Atmospheric pressure + liquid pressure

• P = P atm + Pliquid

• = ( 76 cm Hg / 105 N m-2 ) + hpg

EXERCISES

a) A diving pool measure 40m long, 20m wide and 30m deep. Pradesh dives to a depth of 18m. What is the pressure on him due to the water? ( density of water is 1000 kgm-3 )

b) A tall cylinder contains mercury to a depth of 50 cm. Find the pressure it exerts at the base. ( density of mercury = 13 600 kgm-3)

c) What is the pressure exerted by water of density 1 000 kgm-3 at a point 20m below the water surface ?