Pressure

When a force is applied on a surface in a direction perpendicular to the surface, the force is called thrust.

Pressure is the ratio of force applied in a direction perpendicular to the surface of an object, to the area over which that force is distributed. Pressure is a scalar quantity, not a vector quantity. The SI unit of pressure is the newton per square metre, which is called the pascal (Pa). A pressure of 1 Pa is small; it approximately equals the pressure exerted by a dollar bill resting flat on a table.

Solid pressure

Pressure on a solid surface is the thrust per unit area of the surface.

Fluid pressure

Fluid pressure occurs in one of three situations:

  1. static condition
  2. an open dynamic condition, called "open channel flow" as in the ocean, swimming pool, or the atmosphere.
  3. a closed dynamic condition, called closed conduits as in water line, or gas pipe.

Hydrostatic

Blaise Pascal, a French physicist, discovered that the pressure in a fluid in equilibrium is the same everywhere, if the effect of gravity is neglected.

pascal law effect of gravityWhen the effect of gravity cannot be neglected, but the liquid is at rest, the net force acting on it should be zero.

If A and B were at the same height, i.e. h=0 then P2 - P1=0 or P1 = P2 i.e., Pressure is same at all points inside a liquid lying on the same horizontal plane.

If g = 0 at place, then P2 = P1 at any two points inside the liquid (Pascal's law neglecting effect of gravity).

Hydrodynamics

Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.

Closed bodies of fluid are either "static", when the fluid is not moving, or "dynamic", when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The equation makes some assumptions about the fluid, such as the fluid being ideal (no friction, it is inviscid, zero viscosity) and incompressible. The equation is written between any two points a and b in a system that contain the same fluid.

\frac{p_a}{\gamma}+\frac{v_a^2}{2g}+z_a=\frac{p_b}{\gamma}+\frac{v_b^2}{2g}+z_b

where:

p = pressure of the fluid
γ = ρg = density·acceleration of gravity = specific weight of the fluid.
v = velocity of the fluid
g = acceleration of gravity
z = elevation
\frac{p}{\gamma} = pressure head
\frac{v^2}{2g} = velocity head

Pressure of an ideal gas

In an ideal gas, molecules have no volume and do not interact. Pressure varies linearly with temperature, volume, and quantity according to the ideal gas law,

P=\frac{nRT}{V}

where:

P is the absolute pressure of the gas
n is the amount of substance
T is the absolute temperature
V is the volume
R is the ideal gas constant.

Liquid pressure

When a person swims under the water, water pressure is felt acting on the person's eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above you and therefore greater pressure. The pressure a liquid exerts depends on its depth.

Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:

P=\rho gh

where:

P is liquid pressure
g is gravity at the surface of overlaying material
ρ is density of liquid
h is height of liquid column or depth within a substance

 

Pressure

There are many situations in which effects of a force are better described in terms of force per unit area i.e. pressure.

Sub Topics
 

Example

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  • Pins and nails have pointed ends so that, when a pin is pressed, high pressure is applied on the surface with lesser force, as area is small.
  • Tractors with wide wheels can move over soft ground because their weight (force of gravity) is spread over a large area and so that the tractors do not sink.
  • Bags and suitcases are provided with broad handles so that a small pressure is exerted on the hands.
  • Railway tracks are laid on large concrete sleepers so that the pressure on the ground is reduced, which would otherwise, yield to weight of trains.

S.I unit of pressure is or Pascal (Pa) and its dimensional formula is [ML-1T-2 ]

Pressure exerted by a liquid column

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pressure due to a liquid column

Consider a liquid of density 'r' contained in a cylinder of cross-sectional area 'A'. Let 'h' be the height of the liquid column. The weight of liquid will exert a downward thrust on the bottom surface of the vessel. The weight of liquid inside the vessel = volume x density x g = Ahrg

Thrust or force of liquid on the area = weight of liquid = Ahrg

Pressure exerted by a liquid column = hrg

The above expression tells us why dams are broader at the bottom. The liquid pressure increases with breadth.

With a broader base, the pressure on the walls of the dam are reduced.

 

 

 

Fluids Pressure Upthrust and Flotation

The pressure exerted by a liquid on the base of the container depends on the vertical height of the liquid over it not on the area of cross-section. As one goes deeper in the swimming pool, the pressure on the ear drum is found to increase.