A cylindrical bucket sitting on the edge of a table has a 2.85 mm diameter hole

Question

A cylindrical bucket sitting on the edge of a table has a 2.85 mm diameter hole near the bottom. Water squirts out the hole as shown in the figure below. If the height of the table is H = 1.50 m, determine the height h of the water level in the bucket.
___ cm
Clue: How does the pressure on the top surface of water compare to the pressure on the water squirting out of the hole? How does the speed at which the top surface of water is moving compare to the speed at which water is squirting out of the hole? How is the speed at which water is squirting out of the hole related to the height of the table and the range of the water?

Explanation / Answer

Given that range is R = V*sqrt(2*H/g)

0.8 = V*sqrt(2*1.5/9.8)

V = 1.45 m/s

According to toricellies theorem

h = V^2/(2*g)

h = 1.45^2/(2*9.8)

h = 0.107 m = 10.7 cm

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