A jet of water squirts out horizontally from a
hole on the side of the tank as shown below.
If the hole has a diameter of 3.57 mm , what
is the height of the water above the hole in
the tank?
Answer in units of cm.

The velocity of the flowing fluid out of the opening is given by Torricelli's law.

Reasons:

The given diameter of the hole, d ≈ 3.57 mm (small hole)

By Torricelli's law, we have;

v = √(2·g·h)

By Newton's Laws of motion, we have;

Therefore;

Making, h the subject, of the above equation, gives;

The value for the height above the hole, h ≈ 8.803 × 10⁻² m = 8.803 cm.

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h=31.6 cm

Explanation:

Conservation of Energy in Fluids

Let's first take care of the motion magnitudes. We know the height and horizontal distance the jet of water has. It's similar to a horizontal launch of an object at a speed vo. The horizontal distance traveled is

And the vertical distance is

From this last equation, we solve for t

Now we find vo

Now we can set up the conditions for the conservation of energy for the fluid, assuming ideal conditions (no friction, compression, etc) we can state

solving for h