- #1
Jarl
- 10
- 0
Hi from Spain, I hope somebody could answer the following doubt,
In the typical problem of the water deposit open on the top and with a hole that allow the water to escape through, the theoretical velocity of water when it leaves the deposit and enter in the air does not depend on the size of the hole but only on the height diference betwen the exit hole and the water surface. This is the so called Torricelli’s theorem and can be derived by applying the Bernoulli’s formula between the top of the water and the exit, supposing the pressure to be the same in these two points (the atmospheric pressure). The same could be applied if we put a hose in the hole so that the water escapes from the deposit through the hose. According to this, the water velocity just after the outlet of the hose should be independent on its diameter (as far as the viscosity is negligible).
However, it is an empirical fact that if we narrow or block partially the outlet of the hose with the finger or anything, the water velocity increases (it is easy to see looking at the distance reached by the water). It seems as if the theory fails here. Why can’t we apply Bernoulli’s equation here in the same way as in the well-known problem of the deposit?. How could we calculate the exit velocity in this situation, given the size of the hole and the height of water in the deposit?
Actually we have viscosity but as far as I know its effect is to reduce the velocity, not to increase it, so I think viscosity is not the reason. Maybe turbulence?. Perhaps, but the increase in velocity can be seen also if we narrow the end of the hose smoothly, squasching it, and it does not seem to be a situation prone to turbulence.
Maybe the pressure of the water at the end of the hose is lower than atmospheric and the continuous flux breaks into drops that we perceive as a continuous stream?. If so, many Physics books would be lying us.
Regards
In the typical problem of the water deposit open on the top and with a hole that allow the water to escape through, the theoretical velocity of water when it leaves the deposit and enter in the air does not depend on the size of the hole but only on the height diference betwen the exit hole and the water surface. This is the so called Torricelli’s theorem and can be derived by applying the Bernoulli’s formula between the top of the water and the exit, supposing the pressure to be the same in these two points (the atmospheric pressure). The same could be applied if we put a hose in the hole so that the water escapes from the deposit through the hose. According to this, the water velocity just after the outlet of the hose should be independent on its diameter (as far as the viscosity is negligible).
However, it is an empirical fact that if we narrow or block partially the outlet of the hose with the finger or anything, the water velocity increases (it is easy to see looking at the distance reached by the water). It seems as if the theory fails here. Why can’t we apply Bernoulli’s equation here in the same way as in the well-known problem of the deposit?. How could we calculate the exit velocity in this situation, given the size of the hole and the height of water in the deposit?
Actually we have viscosity but as far as I know its effect is to reduce the velocity, not to increase it, so I think viscosity is not the reason. Maybe turbulence?. Perhaps, but the increase in velocity can be seen also if we narrow the end of the hose smoothly, squasching it, and it does not seem to be a situation prone to turbulence.
Maybe the pressure of the water at the end of the hose is lower than atmospheric and the continuous flux breaks into drops that we perceive as a continuous stream?. If so, many Physics books would be lying us.
Regards
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