Fluids, Pressure, Archimedes’ Principle
Fluids refers to the substances which can flow when an external force is applies to them. Both liquids and gases come under the category of fluids. Fluids don’t have a finite shape and take the shape of the vessel containing them. The total normal force exerted by liquid at rest on a given surface is called thrust of liquid. Thrust of the liquid is measured in Newton.
Pressure Exerted by the Liquid
Pressure of liquid or its hydrostatic pressure refers to the normal force exerted by it per unit area of the surface in its contact. Pressure exerted by a liquid column is given by p= hρg
Where, h = height of liquid column, ρ = density of liquid
and g = acceleration due to gravity
We note here that mean pressure on the walls of a vessel containing liquid up to height h is (hρg / 2).
Pascal’s Law
In 1647 the French scientist Blaise Pascal (1623–1662) discovered that water exerts the same pressure in all directions. This statement is known as Pascal’s Principle.
Pascal’s law states that increase in pressure at a point in the enclosed liquid in equilibrium is transmitted equally in all directions in liquid and to the Walls of the container. The working of hydraulic lift, hydraulic press and hydraulic brakes are based on Pascal’s law.
Atmospheric Pressure
Barometric, or atmospheric, pressure is the force exerted on a surface by the weight of the air above that surface, as measured by an instrument called a barometer.
Pressure is measured in Pounds Per Square Inch or Newton per M² (also called Pacal). It is also measured in toor and bar. 1 torr is equal to 1 mm of mercury column, while 1 bar = l05 Pa.
Pressure is greater at lower levels because the air’s molecules are squeezed under the weight of the air above. So while the average air pressure at sea level is 14.7 pounds per square inch {100000 N/m2 }, at 1,000 feet (304 meters) above sea level, the pressure drops to 14.1 pounds per square inch (around about half of the figure at sea level). Changes in air pressure bring weather changes. High pressure areas bring clear skies and fair weather; low pressure areas bring wet or stormy weather. Areas of very low pressure have serious storms, such as hurricanes.
Atmospheric Pressure at sea level is equal to:
- 76 cm of mercury column
- 980 dyne/cm2
- 100000 N/m2
Why atmospheric Pressure does not crush over body?
The atmospheric pressure does not crush our body because the pressure of the blood flowing through our circulatory system balances this pressure.
Pressure in water
We can understand this by imagining a small cube of water as shown below:
In the above cube, the middle black arrow shows force of gravity on the cube. This implies that the total downward force of the cube is larger than the upward force. Thus, pressure increases with the depth of the water. This explains why or ears hurt when we dive to the bottom of the swimming pool. It also explains why dams thicker at the bottom than at the top. Also, in Hydro power stations, the generator is placed at the lower part so that the pressure of the water is high enough to drive the turbine.
Blood Pressure
Blood pressure refers to the pressure that our blood exerts on our arteries. The fluid dynamics of blood play a major role in blood pressure. The device used to measure blood pressure is the sphygmomanometer. It is placed around the upper arm (Brachial artery), inflated, and then deflated, while a meter measures the pressure passing through that section of the arm and either a person using a stethoscope or an electronic sensor detects the pulse. The cuff is inflated until no pulse can be heard. It is then slowly lowered. As the pressure falls below the systolic pressure the pulse can be heard. When it’s below the diastolic pressure the pulse gets weaker. Also note that the Blood Pressure 120/70 means that the systolic pressure is 120 torr and the diastolic pressure 70 torr.
Why blood Pressure is taken from upper arm?
We have discussed above that pressure of a liquid is dependent on the depth of the fluid. Thus, to get the blood pressure correctly, it should be measured at a height of our heart. It cannot be measured around the heart so brachial artery in the upper arm provides convenient location. If a person is laying down, the blood pressure can be taken from any artery.
Where is the water pressure greater, in a lake 20 meters deep or in the ocean at a depth of 10 meters
In the lake, because pressure depends on height.
Where is the water pressure greater, in a lake 10 meters deep or in the ocean at a depth of 10 meters?
At similar depth, Ocean water will exert more pressure because saltwater is denser than freshwater and more pressure should be applied by seawater at same distance.
Buoyancy
When a body is partially or fully immersed in a fluid an upward force acts on it, which is known as buoyant force or simply buoyancy. The buoyant force acts at the centre of gravity of the liquid displaced by the immersed part of the body and this point is called the centre of buoyancy.
Archimedes’ Principle
The exclamation ‘Eureka!’ is famously attributed to the ancient Greek scholar Archimedes (c. 287–c. 212 BC), who is known to have devised the way to check purity of a gold crown without breaking it apart. He gave the principle that: When a body is partially or fully immersed in a liquid, it loses some of its weight and that lost weight is equal to the weight of the liquid displaced by the immersed part of the body.
If T is the observed weight of a body of density σ when it is fully immersed in a liquid of density p, then real weight of the body
w = T / ( 1 – p / σ)
Laws of Floatation
A body will float in a liquid, if the weight of the body is equal to the weight of the liquid displaced by the immersed part of the body. If W is the weight of the body and w is the buoyant force, then
- If W > w, then body will sink to the bottom of the liquid.
- If W < w, then body will float partially submerged in the liquid.
- If W = w, then body will float in liquid if its whole volume is just immersed in the liquid,
Further, the floating body will be in stable equilibrium if meta-centre (centre of buoyancy) lies vertically above the centre of gravity of the body. The floating body will be in unstable equilibrium if meta-centre (centre of buoyancy) lies vertically below the centre of gravity of the body. The floating body will be in neutral equilibrium if meta-centre (centre of buoyancy) coincides with the centre of gravity of the body.
