Pressure in liquids

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The pressure to the red area is the same, in all three cases, even though the containers are different. This is known as hydrostatic paradox.

Fluid pressure is a measurement of the force per unit area. Fluid pressure can be caused by gravity, acceleration, or forces in a closed container. Since a fluid has no definite shape, its pressure applies in all directions. Fluid pressure can also be amplified through hydraulic mechanisms and changes with the velocity of the fluid.

In a fluid column, as the depth increases, the pressure increases as well. Pressure (P) increases because as you go deeper, fluid at a lower depth has to support fluid above it as well. Therefore to define fluid pressure, we can say that it is the pressure at a point within a fluid arising due to the weight of the fluid.

Pressure in liquids is equally divided in all directions, therefore if a force is applied to one point of the liquid, it will be transmitted to all other points within the liquid.

The pressure in fluids can be calculated using the following relation:

P = hρg (Pressure = Height or Depth of the liquid × Density of the liquid × Gravitational pull (9.81m/s)).

Pressure is a scalar quantity. The SI Unit (International System of Unit) of pressure is the Pascal, or Newton per meter squared (N/m^2).

Points along the same depth will have the same pressure, while points at different depths will have different pressure.

An object that is partly, or completely submerged in a fluid experiences a greater pressure on its bottom surface than on its top surface. This causes a resultant force upwards. This force is called upthrust, and is also known as buoyancy

For moving containers, the pressure changes,(Acceleration is the acceleration of the container)-.

For a vertical acceleration in the upward direction, the pressure in fluids= P = ρh (g+a)

For a vertical acceleration in the downward, the pressure in fluids= P = ρh (g-a)

For a horizontal acceleration, the pressure in fluids= tan θ

For any random angle of acceleration, the pressure in fluids= ρh (g + a sinθ)


the pressures a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible – that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.

Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. When this distinction is important, the term total pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.

The pressure does not depend on the amount of liquid present. Volume is not the important factor – depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does. (The total force applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon. But for a given 5-foot (1.5 m)-wide section of each dam, the 10 ft (3.0 m) deep water will apply one quarter the force of 20 ft (6.1 m) deep water). A person will feel the same pressure whether their head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. If four vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference what vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.

Restating this as energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth. Mathematically, it is described by Bernoulli's equation, where velocity head is zero and comparisons per unit volume in the vessel are

Terms have the same meaning as in section Fluid pressure.