The word efflux means fluid outflow. Torricelli discovered that the speed of efflux from an open tank is given by a formula identical to that of a freely falling body. Consider a tank containing a liquid of density ρ with a small hole in its side at a height y1 from the bottom .
The air above the liquid, whose surface is at height y2, is at pressure P. From the equation of continuity we have
If the cross sectional area of the tank A2 is much larger than that of the hole (A2 >>A1), then we may take the fluid to be approximately at rest at the top, i.e. v2 = 0. Now applying the Bernoulli equation at points 1 and 2 and noting that at the hole P1 = Pa, the atmospheric pressure
When P >>Pa and 2 g h may be ignored, the speed of efflux is determined by the container pressure. Such a situation occurs in rocket propulsion. On the other hand if the tank is open to the atmosphere, then P = Pa then V1=(2gh)½
This is the speed of a freely falling body. This equation is known as Torricelli’s law.
Hydrostatics topics :
Stream line flow
What is pressure ?
Pressure variation with depth
Pascal's Law
The air above the liquid, whose surface is at height y2, is at pressure P. From the equation of continuity we have
If the cross sectional area of the tank A2 is much larger than that of the hole (A2 >>A1), then we may take the fluid to be approximately at rest at the top, i.e. v2 = 0. Now applying the Bernoulli equation at points 1 and 2 and noting that at the hole P1 = Pa, the atmospheric pressureWhen P >>Pa and 2 g h may be ignored, the speed of efflux is determined by the container pressure. Such a situation occurs in rocket propulsion. On the other hand if the tank is open to the atmosphere, then P = Pa then V1=(2gh)½
This is the speed of a freely falling body. This equation is known as Torricelli’s law.
Hydrostatics topics :
Problems on Bernoulli's theorem and Its Applications
Blood flow and heart attactStream line flow
What is pressure ?
Pressure variation with depth
Pascal's Law
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