Calculating Water Velocity Using Bernoulli's Equation

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The velocity of water exiting an opening can be calculated using Bernoulli's equation, specifically v = sqrt(2gh). For further analysis, kinematic equations can be applied to determine the time it takes for the water to hit the ground, the height (H), horizontal distance of flight, and acceleration due to gravity. Conservation of energy can be utilized, but momentum may not be conserved in the vertical direction because of gravitational forces. The initial geometry of the setup is crucial for accurate calculations. Overall, a combination of Bernoulli's equation and kinematic principles can effectively solve the problem.
Gamma
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The velocity of the water that comes out of the opening in the attached diagram can be found using Bernoulli equation, as

v = sqrt (2gh)

Once the water exits the hole, I am not sure how to answer questions like the following: Can I use conservation of energy and momentum. Also can I use the equations in kinematics (ie. S = ut + 1/2 a t^2, v=u+at,...)

1. Time for the water to hit the ground,
2. What is the value of H
3. What is the horizontal distance of flight of water
4. What is the acceleration ( acce. of gravity??)


Thanks a lot.

Gamma.
 

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Usually the kinematic equations are all you need assuming you know the initial geometry of the set up. I see no picture, so I can't tell.
 
Yes the pic did not show up. It is there now. Sorry.
 
How about conservation of energy and momentum? I can cosider a mass of water that exits the hole per unit time as 'm' and write the conservation lows. Is seems ok to do that.

edit: May be momentum is not conserved in the vertical direction due to the force of gravity.?
 
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You could use conservation laws also, I presume
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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