Fluid Mechanics Help
I would like to describe the Torricelli's law at the level of A level Physics (i.e. with no prior knowledge to Bernoulli's equation and having no knowledge of pressure energy).
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.
, where g is the acceleration due to gravity.
Is there an alternative way to derive/explain this result other than using conventional Bernoulli's equation?
Thanks in advance.
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.
, where g is the acceleration due to gravity. Is there an alternative way to derive/explain this result other than using conventional Bernoulli's equation?
Thanks in advance.
Can you not derive it directly from the conservation of energy? For every unit volume of water leaving the tank, the water level in the tank drops. Thus the tank has lost some gravitational potential energy, and produced some kinetic energy, and the tank might be thought of as a device that converts energy in this way.
Equating the energy input with the energy output should give you the desired relation.
This is not entirely surprising because Bernoulli's equation is based on energy conservation.
Equating the energy input with the energy output should give you the desired relation.
This is not entirely surprising because Bernoulli's equation is based on energy conservation.
(edited 7 years ago)
Original post by mik1a
Can you not derive it directly from the conservation of energy? For every unit volume of water leaving the tank, the water level in the tank drops. Thus the tank has lost some gravitational potential energy, and produced some kinetic energy, and the tank might be thought of as a device that converts energy in this way.
Equating the energy input with the energy output should give you the desired relation.
This is not entirely surprising because Bernoulli's equation is based on energy conservation.
Equating the energy input with the energy output should give you the desired relation.
This is not entirely surprising because Bernoulli's equation is based on energy conservation.
Thank you so much. Following your argument, I could come up with the following tedious proof.
@lawlieto Here is another proof to the relation.
Posted from TSR Mobile
(edited 7 years ago)
Original post by tangotangopapa2
Thank you so much. Following your argument, I could come up with the following tedious proof.
@lawlieto Here is another proof to the relation.
Posted from TSR Mobile
@lawlieto Here is another proof to the relation.
Posted from TSR Mobile
Thank you
it actually makes sense nowQuick Reply
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