A bucket of water shaped as a perfect cylinder has a diameter of 20 cm.
The bucket is partially filled with water to a height of 15 cm. A small hole in the side
of the bucket (5 cm from the bottom of the bucket) has a diameter of 3 mm. How fast
does the water flow out the hole?

Question

anonymous · Answer

apply Bernoulli's eq. and the equality of volume change rates, A v = a v_0, the end result is easily seen (note that P = P_0 = atmospheric pressure):

$$v_0= \sqrt{2gh/[1-(a/A)^{2}}\approx \sqrt{2gh}$$
where h is the height of the hole above the surface (10 cm), a and A are the surface areas of the hole and bucket, respectively.

anonymous · Answer

Yes thanks so much! I get it now!

anonymous · Answer

My pleasure!