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3.2 Pressure In Liquid

Introduction

Liquids have pressure because of their weights.

For example, if you try to put your finger over the end  of a tap when it is turned on, you can feel the pressure of the water in the pipe. This is just caused by the weight of water in the pipes all the way back up to the cold water in the loft. The force of gravity acts on liquids, pulling them downwards into the container.

 

Calculating pressure in a liquid

 

Say that a vertical  column of liquid  with a density r  and a horizontal  area A .

Consider an object  is placed at point X  at  a depth h below the surface area of the liquid.

clip_image002

 The pressure P due the liquid exerted on the object at point X  can be written as:

 

                       P = F

                              A

                            = W

                                A

                            = mg                                      (because W = mg)

                                 A

                             =  r V g                     (because r = m )

                                                                                      V

                             =   r Ah g               (because V = Ah)       

                                         A

                             =  r h g            

 

From  the final expression , we can say that the pressure at any point in a liquid at rest is directly proportional to the density of liquid  and the depth.

The pressure in the liquid is not dependent on the surface area and the shape of a container.

Example  1

If the density of sea water is 1150 kgm-3,calculate the pressure below 40m of sea water due to the water alone.

Solution

 

 

 

 

 

 

Example  2

The figure shows  a cylinder containing liquid mercury.

            clip_image004

What is the pressure caused by the liquid mercury at the point P?

[ Density of liquid mercury is 1.36 x 105 kg m-3 ]

 

Solution

 

 

 

 

 

 

Example 3

 

The pressure of hot water emerging from a tap is 1 x 105 Pa. What is the force exerted by the water on a person’s thumb  ,if the person places his thumb over the outlet of the tap and stops the hot water flowing.  [ The area of the tap is 10-4 m2 ]

 

Solution

 

 

 

Applications of pressure in liquids

 

1  Water tank

Normally a water tank is placed at higher level so as to supply water at greater pressure.

2  Dam

The wall of a dam is much thicker at the bottom than at the top because it must withstand the increased lateral pressure in depths of the water.

3   Submarine

Submarine is built with thick wall so as  to withstand enormous pressure at greater depth.

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