PRESSURE IN FLUIDS

PRESSURE IN FLUID

Concept Of Pressure

The term fluid refers to any substance that can flow. It applies to both liquids and gases. Pressure is defined as the perpendicular force per unit area acting on a surface. P =  , since force F is measured in Newtons and the area A is measure in square metres, the S.I unit of pressure P is Newton per square metre (N m^-2). Pressure can also be measured in mm Hg or in bars.

1 Pascal = 1.013x 10⁵ Nm;  1 bar = 10⁵ Nm^-2 or 10 Pascals;  1 millibar (mb) = 10^-3 bar = 100 Pascal.

Pressure is a scalar quantity, it has magnitude but no direction.

Example

In an hydraulic press, a force of 20N is applied to a piston of area 0.2 m². If the area of the other piston is 2 m², calculate the force exerted on it.

Solution

F₁ = 20 N, A₁ = 0.2m², F₂ = ?, A₂ = 2m²;    P =  ;         =  ; F₂ =  =    = 200N

Pressure in a liquid

Liquid exert pressure in all directions. Other important characteristics of liquid pressure are

i.                      The pressure at all points at the same level within a liquid is the same.

ii.                     The pressure in a liquid increases in direct proportion to the depth of the liquid.

iii.                    The pressure in different liquids at the same depth varies directly with density.

The pressure due to a liquid is known as hydrostatic pressure. The formula for this pressure is P = h g, where p is the hydrostatic pressure (Nm-2)  at a depth h (m) in a liquid of density  (Kgm^-3)

Example

What is the length of the liquid column in a barometer tube that would support an atmospheric pressure of 102000 Nm^-2 if the density of the liquid is 2600Kgm^-3? (g= 10ms^-2)         .

Solution

P = 102000 Nm^-2 ,  h= ?,   =2600Kgm^-3 , g=  10ms^-2)                           P = h g; h =  =  =  3.92m

Pascal’s Principle

The principle deals with the transmission of pressure in fluids. Pascal’s principle states that the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the wall of the containing vessel.

Application of Pascal’s principle

The hydraulic press: this press consists of two cylinders R and S of different diameters. The cylinder is filled with oil or water are joined by a connecting tube and a tight piston is fitted in each cylinder. Barber chairs, dentist chairs, vehicle lifts and jacks and hydraulic brakes are all devices that make use of the principle of the hydraulic press. The formula involve is   =    ;   =   . Where A₁, A₂, f, and F₂ are smaller area, larger area, smaller force and larger force respectively. The greater the ratio of the cross-sectional areas of the pistons, the greater the mechanical advantage of the press.

Atmospheric Pressure

The atmospheric is the whole volume of air surrounding us. The atmosphere consists of a mixture of gases, some dust particles and water vapour. It extends to a height of a few hundred kilometers above sea level.

The atmosphere exerts some pressure on the surface of the earth, because its air has a lot of weight. The pressure is called atmospheric pressure. At sea level, it is about 10⁵ Pa decreasing upwards with height. We do not feel this atmospheric pressure because every cell of our body maintains an internal pressure that just balances an external pressure.

In the same way the pressure inside a balloon balances the outside pressure of the atmosphere. An automobile tyre can however maintain pressure much greater than the external pressure because of its rigidity. Hence tyre gauges register the pressure over and above atmospheric pressure.

Simple Barometer

The barometer is an instrument for measuring atmospheric pressure. It consists of a long glass tube (closed at one end, open at the other) filled with mercury and turned upside down into a container of mercury. The barometer works by balancing the mercury in the glass tube against the outside air pressure, just like a set of scales. As air pressure increases i.e as the air becomes heavier, it pushes more of the mercury up into the tube. As air pressure decreases, more of the mercury drain from the tube. So the level of mercury in the tube provides a pricise measure of air pressure. The simple barometer is not an accurate instrument as it can contain air or water vapour instead of vacuum. It is also bulky and not convenient for carrying about.

Practical uses of barometer

There are two types of barometer in practical use: I. the Fortin barometer          II. Aneroid barometer

The Fortin Barometer is used for measuring atmospheric pressure in the laboratory. It gives more accurate reading than the simple barometer. This barometer was enclosed in a metal case with glass windows through which the mercury level can be seen at the top and the bottom of the metal case. It have a leather bag to contain the mercury. The graduation of the instrument has a main scale and a vernier scale which moves over the main scale.

The Aneroid Barometer consists of a corrugated steel box which is partially evacuated of air. The top surface of the box is held by a strong spring, S, which prevents it from collapsing. When the pressure rises, the top of the box is pressed inwards; when the air pressure falls, the top of the box moves upwards.

It advantages is that it contain no liquid and small, more convenient to carry about. Aneroid barometer can be used as altimeter to measure the height of a place. Though it is not very accurate in measuring atmospheric pressure.

Application Of  Atmospheric  And Gas Pressure 

 I. The siphon : this is a device used to remove liquids from receptacles which cannot be lifted or easily reached, or cannot otherwise be emptied more conveniently. Liquid can only be transferred from points at higher levels to points of lower levels.

It consists of a bent flexible tube with one end dipping below the liquid surface in the vessel of liquid and the other at the point of lower level. For siphon to function efficiently (i) the tube must be filled by the liquid  (ii) one end must be lower than the other (iii) the height h₁ must be less than the barometric height of the liquid.

 II. The Syringe: the device consists of a piston which fits tightly into a cylinder. The cylinder has a nozzle at one end. When the nozzle is dipped into a liquid and the piston is pulled up, atmospheric pressure forces the liquid up the cylinder. When the piston is pushed down, the liquid is forced out or ejected through the nozzle. It is commonly used for injecting liquid medicine into the body.

 III. The bicycle pump: this is a compression pump used to compress air from atmosphere into the bicycle tyre. It consists a piston which can move in and out of a cylindrical tube or barrel. At the end of this piston is a leather washer. The pump is connected to the bicycle tyre which usually has a rubber valve in it. When the piston is drawn out, the air pressure in the barrel is reduced below atmospheric pressure.

IV. The force pump: This pump is used when it is required to lift water continuously to a height above 10 m. its component parts consists of a piston that can move up and down a barrel, and  a side tube of the barrel connecting it to an air chamber. There are two valves and an exit pipe projecting into the air chamber.

Assignment

1.  A pressure that can support a column of water 60 cm high support a column of a given salt solution 50 cm high. The density of the salt solution is

Solution

P_w = 60 cm,  P_s = 50 cm,  _w = 1gcm-3 , _s= ?;    = ; _s =  =    = 1.2 gcm^-3.

2. a. What is the pressure exerted by a 50 Kg girl as she places her weight on the heel of one shoe if the heel area is 0.002 m²?

 (b) Calculate the pressure due to sea-water at a depth of 600 m. take density of sea-water= 1030 Kgm^-3.