so if those diameters are the ID of the pipe, the diameter ratios are 5:7.5:10, and the time for the water to leave would be proportional to the squares, or 25:56:100
normalizing, that is about 1:2:4
Sp by my numbers, it should take 4 times as long for the 10 cm pipe as the 5 cm pipe, because the volume is 4 times. The velocity of the flow would be the same in each case as that depends on the height which is the same.
I am going to go for simple. The 10 cm pipe is twice the diameter of the 5 cm pipe and the area of the pipe is according to the equation Area = pi r squared . What this means is that the area of the 10 cm pipe is 4 times that of the 5 cm pipe. That being said the height then for the 2 L of water is 4 times higher in the 5 cm pipe than in the 10 cm pipe.
At the start this will give the 5 inch pipe 4 times the pressure to push water out of the same size hole. Now if you look up the pressure drop through an orifice plate or sharp hole like you have, it obeys what is called the square root rule. To double the flow through an orifice you need 4 times the pressure. So guess what, you have 4 times the pressure and your flow rate to start with is twice the flow in the 5 cm hole as compared to the 10 cm hole. So twice the flow rate for the same amount of liquid the 5 cm pipe drains in half the time.
To sum this up find the ratio of the areas A 10 cm/ A 5 cm, then take the square root of this to get the relationship of the time from 10 cm to 5 cm.
For 7.5 it will take about 1.5 times longer to drain the 7.5 cm pipe as compared to the 5 cm pipe.
The relationship of time is the same as the relationship of the diameters.
< put /exactly 2L/ of water in /each/ pipe. Obviously each pipe had /different heights/ of water which affects the velocity of the water when I eventually remove the blue tack >
It's not at all obvious why some responders (mentioning no names) find it difficult to do something as basic as reading the question.
Anyway, you have the key to your question IN your question, when you mention the Torricelli law. If you think about what is happening when the two pipes contain the same volume of water, you will find that the velocity for the 10cm pipe is /always/ exactly half that of the 5cm pipe, because h in the larger pipe is always one quarter of that in the smaller. Thus, it /must/ take exactly twice the time to drain the same volume of water - a neat experiment!
The pressure at the hole is dependent on the height of the water above the hole. The smaller pipe has more height so it drains faster.
The pressure is ~.433 psi per foot of height above the hole.
Good pipes don't leak.
I have three PVC pipes one with a diameter of 5cm, one with 7.5cm and the other with a 10cm diameter. I filled i put a lid on one end and drilled an 8mm (diameter) hole in the side of the pipe. I than filled the pipe with water until it leaked out of the hole. Then I blocked it with blue tack and put exactly 2L of water in each pipe. Obviously each pipe had different heights of water which affects the velocity of the water when i eventually remove the blue tack, (Torricelli law v = square root of 2gh.) I timed the length of time it took for each pipe to drain the 2L of water and it appeared the 10cm diameter pipe took twice the amount of time to drain the water than the 5cm pipe.
I am wondering whether the size of the pipe as a proportional affect to the time ot takes to drain a set amount of water.
Is there a mathematical relationship (eg is there a formula) to predict the time it takes for water to drain from a pipe based on the area of the base.
