Torricelli’s Law

Bernoulli’s Equation

Bernoulli Equation; PrincipleThe Bernoulli’s equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids. It is one of the most important/useful equations in fluid mechanics. It puts into a relation pressure and velocity in an inviscid incompressible flow. Bernoulli’s equation has some restrictions in its applicability, they summarized in following points:

  • steady flow system,
  • density is constant (which also means the fluid is incompressible),
  • no work is done on or by the fluid,
  • no heat is transferred to or from the fluid,
  • no change occurs in the internal energy,
  • the equation relates the states at two points along a single streamline (not conditions on two different streamlines)

Under these conditions, the general energy equation is simplified to:

Bernoulli Theorem - Equation
This equation is the most famous equation in fluid dynamics. The Bernoulli’s equation describes the qualitative behavior flowing fluid that is usually labeled with the term Bernoulli’s effect. This effect causes the lowering of fluid pressure in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy. The dimensions of terms in the equation are kinetic energy per unit volume.

Torricelli’s law

Torricelli’s law
Source: wikipedia.org – CC BY-SA

Torricelli’s law, also known as Torricelli’s principle, or Torricelli’s theorem, statement in fluid dynamics that the speed, v, of fluid flowing out of an orifice under the force of gravity in a tank is proportional to the square root of the vertical distance, h, between the liquid surface and the centre of the orifice and to the square root of twice the acceleration caused by gravity (g = 9.81 N/kg near the surface of the earth).

In other words, the efflux velocity of the fluid from the orifice is the same as that it would have acquired by falling a height h under gravity. The law was discovered by and named after the Italian scientist Evangelista Torricelli, in 1643. It was later shown to be a particular case of Bernoulli’s principle.
Bernoulli Theorem - Equation

The Torricelli’s equation is derived for a specific condition. The orifice must be small and viscosity and other losses must be ignored. If a fluid is flowing through a very small orifice (for example at the bottom of a large tank) then the velocity of the fluid at the large end can be neglected in Bernoulli’s Equation. Moreover the speed of efflux is independent of the direction of flow. In that case the efflux speed of fluid flowing through the orifice given by following formula:

v = √2gh

See above:

Bernoulli’s Principle