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GCSE maths question

Hi, could anyone help me with this question?

A cylindrical pipe is 3 m long and has a radius of 10 cm. Water flows into the pipe at a rate of 3 litres per minute.
How long does it take for the water to have a maximum depth of 16 cm?

Thanks

Reply 1

Anonymouspsych

Original post by ksurdy2307

To begin with I will assume you know how to work out the volume of a cylinder.

It is worth knowing that 1000 litres = 1 m^3

To solve the problem you need to be working with the same units across all the measurements.

So to answer the question, you need to firstly work out the volume of water that is contained within the pipe when the depth is 16cm. Then convert the volume into cubic metres.

Then using the formula Volumetric Flow Rate = Volume / time , you should be able to answer the question.

Reply 2

majorinf

How would I work out the volume of water when the depth is 16 cm, i.e. how do you work out the area of the major segment of a circle?

Reply 3

Anonymouspsych

Original post by ksurdy2307

How would I work out the volume of water when the depth is 16 cm, i.e. how do you work out the area of the major segment of a circle?

Hmmm, I see where you are coming from. Is there any more information to this question? Because it doesn't say whether the pipe is vertical or horizontal in orientation but seeing as this is a gcse question, I would assume that you can assume that the pipe is vertically aligned. I think the way you are imagining the problem is as if the pipe was horizontal and so that the cross section is going to be a varying segment of the whole circle but that is a much more complicated problem (too complex for gcse).

You can assume that the water rises cylindrically at all times, so essentially the profile of the water is a cylinder at all times.

So volume of water = area of cross section * height at that instant

Reply 4

majorinf

The diagram next to the question suggests that the pipe is horizontally aligned.

Reply 5

AGrizzlyBearo

Original post by ksurdy2307

The diagram next to the question suggests that the pipe is horizontally aligned.

Can you post a picture of the question and diagram?

Reply 6

Anonymouspsych

Original post by ksurdy2307

The diagram next to the question suggests that the pipe is horizontally aligned.

Alright in that case, this isn't as easy of a question but it is still not that bad.

The profile of the water in this case would be a prism with the major segment of the circle being the cross section. We already know the length is 3m so we just need to work out what the area of the major segment is.

The area of the major segment = area of circle - area of minor segment . The area of the minor segment can be worked out using simple trigonometry to find the angle of the minor sector, and then area of minor segment = area of minor sector - area of triangle .

Then you proceed like I mentioned earlier.