Question

The ratio of the volume of water in Bottle
P to the volume of water in Bottle Q is
3: 4. Rajeev drank 40 mL of the water
from Bottle P and the ratio then became
13:20. How much water was there in
bottle P at first?​

Answer 1

Answer:

1

down vote

favorite

2

Say there is a water bottle that is filled with 300 mL of water and has a circular hole with a radius of 2 mm. In this bottle, the water sits 7.8cm above the top of the hole (which has been drilled 1.5cm above the bottom of the bottle).

According to Bernoulli's law the velocity v of the water flowing out is equal to 2gh−−−√

Therefore for the setup above, v=2∗9.81 m/s2∗0.078 m−−−−−−−−−−−−−−−−−−−√=1.24 m/s

Using this, the flow rate can be calculated as Q = Av = π(0.002 m)2∗1.24 m/s=0.000016 m3/s=16 mL/s

This doesn't seem accurate considering that the experimental flow rate is equal to 8 mL/s (40 mL over 5 seconds). However I understand that it ignores viscosity (and other things?)

I'm wondering a few things, firstly, does the theoretical math here apply to the situation I'm describing? The hole in the bottle isn't exactly a pipe and the only examples I've seen with water flow involve pipes.

Secondly, can Poiseuille's Law be used to determine the flow rate instead, with a more accurate result? (From what I understand Q=πPR^4/8nl, however I don't understand what P is, seeing as in Bernoulli's law pressure cancels and as aforementioned this isn't a typical pipe example.)

Thirdly, I assume the theoretical flow rate will still be different from the experimental flow rate, what factors cause this?