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Suppose there are two tanks, tank A and tank B, of equal size and both are very large.
Suppose the bottom of tank A is at an elevation that is higher than the top of tank B.
Suppose there is a very small tube relative to the size of the tanks that connects the bottom of tank A to the bottom of tank B.
Suppose tank A and tank B are both half full of water.
Suppose the tube is completely full of water.
Take point 'a' as the top of the water surface in tank A and take point 'b' to be the top of the water surface in tank B.
Suppose point 'a' has an elevation that is a height, h, meters greater than point 'b'.
Then, points 'a' and 'b' are at a pressure of 1 atm and the velocity, v, of the decrease in the water level in tank A equals the velocity of the increase in the water level in tank B.
Bernoulli's Equation would seem to give the inconsistent equation.
##P_{atm} + \rho g h + \frac{\rho v^2}{2} = P_{atm} + \rho g 0 + \frac{\rho v^2}{2} \implies ##
##\rho g h = 0 \implies ##
##h = 0 ## contradiction.
where ρ is equal to the density of water.
Where is my mistake?
Thanks to the community in helping me understand the limitations and consequences of bernoulli's equation.
Suppose the bottom of tank A is at an elevation that is higher than the top of tank B.
Suppose there is a very small tube relative to the size of the tanks that connects the bottom of tank A to the bottom of tank B.
Suppose tank A and tank B are both half full of water.
Suppose the tube is completely full of water.
Take point 'a' as the top of the water surface in tank A and take point 'b' to be the top of the water surface in tank B.
Suppose point 'a' has an elevation that is a height, h, meters greater than point 'b'.
Then, points 'a' and 'b' are at a pressure of 1 atm and the velocity, v, of the decrease in the water level in tank A equals the velocity of the increase in the water level in tank B.
Bernoulli's Equation would seem to give the inconsistent equation.
##P_{atm} + \rho g h + \frac{\rho v^2}{2} = P_{atm} + \rho g 0 + \frac{\rho v^2}{2} \implies ##
##\rho g h = 0 \implies ##
##h = 0 ## contradiction.
where ρ is equal to the density of water.
Where is my mistake?
Thanks to the community in helping me understand the limitations and consequences of bernoulli's equation.