Torricelli's law

Flow- rate is called the rate of the very low viscosity (such as water) flowing a liquid or gaseous body from an opening of the vessel containing it. There must descend an equal amount of liquid from the surface to the level of the opening while the outflow of a certain liquid Quantum always, the outflow velocity is equal to the rate that would achieve a body when it to the orifice fall from the liquid level ( Torricelli's theorem, see also Bernoulli equation).

If we denote by v the outflow velocity at h, is the vertical depth of the opening below the liquid surface ( pressure altitude ) and with g the acceleration of gravity (g = 9.81 ms -2) as.

It therefore depends only on the pressure level, but not of the nature of the liquid, so that, for example, flow out at the same pressure level water and mercury at the same speed.

Since the pressure in a fluid according to all directions has a strong back, so it does not matter for the outflow velocity, if the opening in the floor or in a side wall of the vessel is whether the outflowing jet downwards, according sideways or upwards (fountain ) is directed.

If the outflowing jet cylindrical, one could calculate the per unit volume of liquid has flowed easily by multiplying the discharge velocity by the area of the opening. The beam is in the region of the cylindrical pouring spout, when the orifice is cylindrical. However, the Bernoulli energy equation is only valid in a stationary flow of an inviscid, incompressible fluid. Therefore, the discharge volume for real fluids is to calculate a correction factor. At some distance from the discharge opening of the beam is no longer cylindrical, but it contracts, so that its cross section a short distance as approximately 61 percent of that of the opening of the opening. To obtain the discharge amount for real fluids have to, therefore, the above- calculated " theoretical discharge amount " or multiplied by 0.6. This contraction of the beam ( contractio venae ) stems mainly from the fact that the fluid particles flow inside the vessel from all sides converging towards the opening and therefore arrive at the edge of the discharge opening at a speed laterally directed.

Everything so far only applies to openings in a thin vessel wall. The amount of outflow, the outflow velocity is through short cylindrical or flared outward approach tubes when the liquid adheres to the walls of the tube and fills completely, increased, reduced, however - to about half. Openings in thick wall tubes act like approach.

Also applies the Torricelli Act for the discharge velocity of ideal gases, if we mean by the pressure head h is the height of a column of gas of the density of the outflowing gas. If we denote by h ' the manometrically measured as the height of a mercury column pressure of the enclosed gas, with s' the specific weight of mercury, with s that of the gas ( both based on water as unity ), so behaves the pressure head h, the bill is to bring to the mercury column h ' as s' to s; It is therefore

And

Resulting in the list drawn up by Thomas Graham Act, that the outflow velocities of various gases are the square roots of their specific weights inversely proportional at the same pressure. For example, since the density of hydrogen gas only 1/16 of the density of oxygen gas, that flows under the same pressure of four times as fast as this.

Robert Wilhelm Bunsen was derived therefrom, a method for determining the specific gravities of the gases.

• Fluid Mechanics