what is efflux? explain with neat torricelli diagram. derive an expresssion for the speed of efflux. based on bernoullis theorem explain with diagram lift of aircrft wing
Answers
Torricelli's law describes the parting speed of a jet of water, based on the distance below the surface at which the jet starts, assuming no air resistance, viscosity, or other hindrance to the fluid flow. This diagram shows several such jets, vertically aligned, leaving the reservoir horizontally. In this case, the jets have an envelope (a concept also due to Torricelli) which is a line descending at 45 degrees from the water's surface over the jets. Each jet reaches farther than any other jet at the point where it touches the envelope, which is at twice the depth of the jet's source. The depth at which two jets cross is the sum of their source depths. Every jet (even if not leaving horizontally) takes a parabolic path whose directrix is the surface of the water.
Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing out of an orifice to the height of fluid above the opening. The law states that the speed of efflux, v, of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height h, i.e. {\displaystyle v={\sqrt {2gh}}} v = \sqrt{2gh}, where g is the acceleration due to gravity (9.81 N/kg near the surface of the earth). This last expression comes from equating the kinetic energy gained, {\displaystyle {\frac {1}{2}}mv^{2}} {\frac {1}{2}}mv^{2}, with the potential energy lost, mgh , and solving for v. The law was discovered (though not in this form) by the Italian scientist Evangelista Torricelli, in 1643. It was later shown to be a particular case of Bernoulli's principle.
