Fluids Online Test 9th science Lesson 3 questions in English

A small iron nail sinks in water, whereas a huge ship of heavy mass floats on sea water. Astronauts have to wear a special suit while traveling in space. All these have a common reason called ‘pressure’.

If the pressure increases in a solid, based on its inherent properties, it experiences tension and ultimately deforms or breaks. In the case of fluids, it causes them to flow rather than to deform.

When you stand on loose sand, the force is acting on an area equal to the area of your feet. When you lie down, the same force acts on an area of your whole body, which is larger than the area of your feet. Thus, the force acting perpendicular to the surface is called thrust.

The force per unit area acting on an object concerned is called pressure. Thus, we can say thrust on a unit area is pressure. Pressure = Thrust / Area of contact.

In SI units, the unit of thrust is newton (denoted as N).

The unit of pressure is newton per square metre or newton metre–2 (denoted as Nm-2).

In the honour of the great French scientist, Blaise Pascal, 1 newton per square metre is called as 1 pascal denoted as Pa. 1 Pa = 1 N m-2.

All the flowing substances, both liquids and gases are called fluids. Like solids, fluids also have weight and therefore exert pressure. When filled in a container, the pressure of the fluid is exerted in all directions and at all points of the fluid. Since the molecules of a fluid are in constant, rapid motion, particles are likely to move equally in any direction.

Pressure in fluids is calculated as shown below. Fluid Pressure = Total force exerted by the fluid / Area over which the force is exerted = F / A.

The force exerted due to the pressure of a liquid on a body submerged in it and on the walls of the container is always perpendicular to the surface.

Pressure exerted by a liquid at a point is determined by, (i) depth (h) (ii) density of the liquid (ρ) (iii) acceleration due to gravity (g).

The weight of the man (thrust),
F = mg = 90Kg * 10ms-2 = 900 N
Pressure, p = F/A = 900N / 0.036 m2 = 25000 Pa

We know that, thrust at the bottom of the column (F) = weight of the liquid.
Therefore, F = mg (1)
We can get the mass of the liquid by multiplying the volume of the liquid and its density. Mass, m = ρV (2)
Volume of the liquid column, V = Area of cross section (A) × Height (h) = Ah (3)
Substituting (3) in (2)
Mass, m = ρAh (4)
Substituting (4) in (1)
Force = mg = ρAhg
Pressure, P = Thrust (F) / Area (A) = mg / A = ρ(Ah)g / A = ρhg
∴Pressure due to a liquid column, P = hρg.

Earth is surrounded by a layer of air up to certain height (nearly 300 km) and this layer of air around the earth is called atmosphere of the earth. Since air occupies space and has weight, it also exerts pressure. This pressure is called atmospheric pressure.

The air gets ‘thinner’ with increasing altitude. Hence, the atmospheric pressure decreases as we go up in mountains. On the other hand, air gets heavier as we go down below sea level like mines.

The atmospheric pressure we normally refer is the air pressure at sea level.

Human lung is well adapted to breathe at a pressure of sea level (101.3 k Pa). As the pressure falls at greater altitudes, mountain climbers need special breathing equipments with oxygen cylinders. Similar special equipment’s are used by people who work in mines where the pressure is greater than that of sea level.

The instrument used to measure atmospheric pressure is called barometer.

A mercury barometer, first designed by an Italian Physicist Torricelli, 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. This is done by closing the open end of the mercury filled tube with the thumb and then opening it after immersing it in to a trough of mercury.

On a typical day at sea level, the height of the mercury column is 760 mm.

Pressure, P = hρg
= (760 3 10–3m) 3 (13600 kgm-3) 3 (9.8 ms-2)
= 1.013 × 105 Pa.

Pressure P = 1.013 × 105 Pa is called one atmospheric pressure (atm). There is also another unit called (bar) that is also used to express such high values of pressure.
1 atm = 1.013 × 105 Pa.
1 bar = 1 × 105 Pa.
Hence, 1 atm = 1.013 bar.
Expressing the value in kilopascal gives 101.3 k Pa. This means that, on each 1 m2 of surface, the force acting is 1.013 k N.

Pressure due to water = hρwg
= 0.85 m × 1000 kg m-3 × 10 m s-2 = 8500 Pa.
Pressure due to kerosene = hρkg
= 0.85 m × 800 kg m-3 × 10 ms-2 = 6800 Pa.

The absolute pressure is zero-referenced against a perfect vacuum and gauge pressure is zero referenced against atmospheric pressure.
For pressures higher than atmospheric pressure, absolute pressure = atmospheric pressure + gauge pressure
For pressures lower than atmospheric pressure, absolute pressure = atmospheric pressure – gauge pressure.

In petrol bunks, the tyre pressure of vehicles is measured in a unit called psi. It stands for pascal per inch, an old system of unit for measuring pressure.

Pascal’s law became the basis for one of the important machines ever developed, the hydraulic press. It consists of two cylinders of different cross-sectional areas.

Pascal’s principle is named after Blaise Pascal (1623-1662), a French mathematician and physicist. The law states that the external pressure applied on an incompressible liquid is transmitted uniformly throughout the liquid. Pascal’s law can be demonstrated with the help of a glass vessel having holes all over its surface. Fill it with water. Push the piston. The water rushes out of the holes in the vessel with the same pressure.

The force F2 that acts on the larger piston is greater than the force F1 acting on the smaller piston. Hydraulic systems working in this way are known as force multipliers.
Pressure on piston of small area ‘a’ is given by, P = F1 / A1 (1)
Applying Pascal’s law, the pressure on large piston of area A will be the same as that on small piston. Therefore, P = F2 / A2 (2)
Comparing equations (1) and (2), we get F1 / A1 = F2 / A2. or F2 = F1 × (A2 / A1).
Since, the ratio A2 / A1 is greater than 1, the force F2 that acts on the larger piston is greater than the force F1.

Given: Area covered by the vehicle on the piston A1 = 0.5 m2
Weight of the vehicle, F1 = 2000 kg × 9.8 m s-2
Area on which force F2 is applied, A2 = 0.03 m2
Solution:
P1 = P2 ; F1 / A1 = F2 /A2 and F2 = (F1 / A1) × A2 ;
F2 = (2000 × 9.8) 0.03 0.5 = 1176 N

Let us assume that the mass of the flask be 80 g. So, the mass of the flask filled with water is 330 g and the mass of flask filled with kerosene is 280 g. Mass of water only is 250 g and kerosene only is 200 g. Mass per unit volume of water is 250/250 cm3. This is 1g/cm3. Mass per unit volume of kerosene is 200 g/250 cm3. This is 0.8 g/cm3. The result 1 g/cm3 and 0.8 gcm3 are the densities of water and kerosene respectively. Therefore, the density of a substance is the mass per unit volume of a given substance.

The SI unit of density is kilogram per meter cubic (kg/m3) also gram per centimetre cubic (g/cm3).

The symbol for density is rho (ρ).

We can compare the densities of two substances by finding their masses. But, generally density of a substance is compared with the density of water at 4 °C because density of water at that temperature is 1g/cm3.

Density of any other substance with respect to the density of water at 4 °C is called the relative density. Thus, relative density of a substance is defined as ratio of density of the substance to density of water at 4 °C.

Density = Mass / Volume
∴ Relative density = (Mass of the substance/Volume of the substance) \ (Mass of water/Volume of water)
Since the volume of the substance is equal to the volume of water,
Relative density = Mass of certain volume of substance / Mass of equal volume of water (at 4°C)

Relative density can be measured using Pycnometer also called density bottle. It consists of ground glass stopper with a fine hole through it. The function of the hole in a stopper is that, when the bottle is filled and the stopper is inserted, the excess liquid rises through the hole and runs down outside the bottle. By this way the bottle will always contain the same volume of whatever the liquid is filled in, provided the temperature remains constant. Thus, the density of a given volume of a substance to the density of equal volume of referenced substance is called relative density or specific gravity of the given substance.

Density = Mass / Volume
= 1155g / (12 cm × 11 cm × 3.5 cm) = 1155 g / 462 cm3
= 2.5 g cm-3
The mystery material is denser than the water. So, it sinks.
If the density of a substance is less than the density of the liquid it will float.

A direct-reading instrument used for measuring the density or relative density of the liquid is called hydrometer. Hydrometer is based on the principle of flotation, i.e., the weight of the liquid displaced by the immersed portion of the hydrometer is equal to the weight of the hydrometer.

Hydrometers may be calibrated for different uses such saccharometer for measuring the density of sugar in a liquid and alcoholometer for measuring higher levels of alcohol in spirits.

One form of hydrometer is a lactometer, an instrument used to check the purity of milk. The lactometer works on the principle of gravity of milk.

The lactometer consists of a long-graduated test tube with a cylindrical bulb with the graduation ranging from 15 at the top to 45 at the bottom. The test tube is filled with air. This air chamber causes the instrument to float. The spherical bulb is filled with mercury to cause the lactometer to sink up to the proper level and to float in an upright position in the milk.

Inside the lactometer there may be a thermometer extending from the bulb up into the upper part of the test tube where the scale is located. The correct lactometer reading is obtained only at the temperature of 60 °F. A lactometer measures the cream content of milk. More the cream, lower the lactometer floats in the milk. The average reading of normal milk is 32.

We already saw that a body experiences an upward force due to the fluid surrounding, when it is partially or fully immersed in to it. We also know that pressure is more at the bottom and less at the top of the liquid.

The pressure difference causes a force on the object and pushes it upward. This force is called buoyant force and the phenomenon is called buoyancy.

Most buoyant objects are those with a relatively high volume and low density. If the object weighs less than the amount of water it has displaced (density is less), buoyant force will be more and it will float (such object is known as positively buoyant). But, if the object weighs more than the amount of water it has displaced (density is more), buoyant force is less and the object will sink (such object is known as negatively buoyant).

Cartesian diver is an experiment that demonstrates the principle of buoyancy. It is a pen cap with clay. The Cartesian diver contains just enough liquid that it barely floats in a bath of the liquid; its remaining volume is filled with air. When pressing the bath, the additional water enters the diver, thus increasing the average density of the diver, and thus it sinks.

Archimedes principle is the consequence of Pascal’s law. According to legend, Archimedes devised the principle of the ‘hydrostatic balance’ after he noticed his own apparent loss in weight while sitting in his bath. Archimedes principle states that ‘a body immersed in a fluid experiences a vertical upward buoyant force equal to the weight of the fluid it displaces’.

When a body is partially or completely immersed in a fluid at rest, it experiences an upthrust which is equal to the weight of the fluid displaced by it. Due to the upthrust acting on the body, it apparently loses a part of its weight and the apparent loss of weight is equal to the upthrust.

Thus, for a body either partially or completely immersed in a fluid,
Upthrust = Weight of the fluid displaced = Apparent loss of weight of the body
Apparent weight of an object = True weight of an object in air – Upthrust (weight of water displaced).

The centre of gravity of the floating body and the centre of buoyancy are in the same vertical line. The point through which the force of buoyancy is supposed to act is known as centre of buoyancy.

Flotation therapy uses water that contains Epsom salts rich in magnesium. As a floater relaxes, he or she is absorbing this magnesium through the skin. Magnesium helps the body to process insulin, which lowers a person’s risk of developing Type 2 Diabetes.

Atmospheric pressure in the laboratory,
P = hρg = 732 × 10-3 × 1.36 × 104 × 9.8
= 9.76 × 104 Pa (or) 0.976 × 105 Pa