How Deep is the Water in the Tank if Two Streams Hit the Same Spot?

[Ed Quanta]

A water tank is open to the atmosphere and has two holes in it, one .80 m and one 3.6 m above the floor on which the tank rests. If the two streams of water strikes the floor in the same place, what is the depth of water in the tank? (Assume that the holes are very small and the tank is very large and the top surface of the water has essentially zero speed)

Any help would be appreciated. Thank you.

 

[PhanthomJay]

A water tank is open to the atmosphere and has two holes in it, one .80 m and one 3.6 m above the floor on which the tank rests. If the two streams of water strikes the floor in the same place, what is the depth of water in the tank? (Assume that the holes are very small and the tank is very large and the top surface of the water has essentially zero speed)

Any help would be appreciated. Thank you.

The water leaves the tank opening at an initial horizontal speed (which is greater at the bottom hole) but with no initial vertical speed. Are you familiar with the projectile motion equations AND Toricelli's Theorem?

 

[Ed Quanta]

No, I am not. Only Bernoulli's equation

 

[Ed Quanta]

I'd understand how to set this up if there was only one hole from which water exists the tank, but there are two holes. Anyone know how to apply Bernoulli to this?

 

[Astronuc]

The pressure in the water is a function of depth of water above that point. The pressure can be related to kinetic energy of the water, which is proportional to the square of the mean velocity (speed) of the water from the nozzle.

Think of the relationship between 'gh' and 'v²/2' where g is the acceleration of gravity, h is the height of water, and v is the mean speed of the water issuing from the holes.

Assume the water has a constant lateral velocity and accelerates downward (falls) with gravity.

 

[Ed Quanta]

Thanks, this helping me a lot. But here is what is bothering me. I can calculate how long it will take for the water exiting each hole to hit the ground using Newton's equations of motion. But all that is required is that the water exiting both holes cover the same horizontal distance. So the initial velocity exiting the bottom hole will be greater than that of the top hole. But isn't there more than one pair of initial velocities that can be selected such that both water streams will hit at the same point? Can't there be more than one correct answer for the mean velocity as a result given the information provided?


Another question I have is this. Is the pressure on both holes equal since both are open to the atmosphere?