I'm teaching a grade 9 math course that deals with volumes of pyramids, cones, prisms, and cylinders and I wanted to come up with an interesting situation that uses the 1/3 volume factor. I know that fluids are tricky but I was wondering if the logic I've used here is a valid simplification or not? It's fine if they learn more details should they take physics some other time, but I don't want to tell them anything wrong. Here's the example:

"Water flowing through a cylindrical hose flows through a cone-shaped spout at the end. If water is flowing through the hose at 3 cm/s, how fast is it flowing through the cone tip? You can assume that water cannot be compressed to take up less volume.

Answer: The volume of the spout is one-third of the volume of the hose. As the water gets to the end of the hose, the water is squished into a smaller space. So, the water must flow faster to compensate. Logically, the water must flow through the cone 3 times as fast. So, water should be passing through the cone at a rate of 9 cm/s.

This 9cm/s should be considered an average rate. In reality, the water coming out of the tiny tip would be moving faster, but water at the base of the cone where it is the widest would be traveling more slowly."

EDIT: Thanks so much for helping me think through this problem, everyone. I enjoyed reading all of your answers and am grateful you took the time to write at such length. I am going to shelve this problem as is for the grade 9s, but if I do get a chance to pose it with another age group then I'll be able to do it properly then.