Please help?

Question

A water tank open to the atmosphere at the top has two holes punched in its side, one above the other. The holes are 4.00 cm and 14.3 cm above the floor. How high does water stand in the tank if the two streams of water hit the floor at the same place?

Answer 1

Oddly enough, the velocity of the water leaving the hole is the same as if it had dropped through a height equal to the depth of the hole.

Let H be the depth of the water in the tank. Then

1/2 m v1 ^ 2 = m g (H - h1)
1/2 m v2 ^ 2 = m g (H - h2)

The masses cancel out and you have

1/2 v1 ^ 2 = g ( H - h1 )
1/2 v2 ^ 2 = g ( H - h2 )

Now the horizontal distance traveled is found from kinematics. In each case, the travel time is found from the vertical dimension:

y - yo = voy t + 1/2 a t^2

where y - yo is the height of the hole, voy is zero, and a is -9.8 m/s^2. Solve for the two times (one for each hole).

Now the horizontal displacement is simply

x = vox t

Solve for both holes, keeping in mind that the horizontal displacement x is the same for each. You now have enough information to answer the question!

Answer 2

Some assumptions are needed here. One such is that the velocity of water exiting a hole depends strictly on the pressure head (there is no friction loss). Another is that the holes propel the water strictly horizontally -- neither hole is drilled at an angle. Given these (entirely plausible) assumptions, we proceed as follows: calculate the velocity of water coming through the hole, in terms of the water height h, using conservation of energy; use s = 0.5 g t^2 to determine how long the water from each hole falls before reaching the floor (s being given and g being 9.8 m/sec^2); use s = v t to determine how far from the bottom of the tank each stream hits (v from the energy conservation, and t from the previous step); put all this algebra together, and you will wind up being able to compute h.

Postscript: previous answer appears to be correct also.

Answer 3

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Answer 4

I calculated 13.88 cm for the total height (from "floor" to surface of water).