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secondary 3 | E Maths

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Why graph look like this. Shouldn't constant flow = straight line

But your y axis on the graph is height of the water, not the flow rate of water.

The cross section does not have a uniform length. It is trapezoidal at the bottom and rectangular at the top, unlike a rectangle or square, where the length is uniform across all heights of water.

At the trapezoidal portion, as you add more water, the length of the water surface at each height gets smaller.

So since the flow rate is constant , intuitively the height will increase more quickly as you have to add less water to achieve the same increase in height as compared to earlier on.

That's why you see the curve sloping upwards exponentionally up to 10cm. Your water height will not increase at a constant rate for the first 10cm (20s).

After the first 10cm, the top part of the prism is rectangular and the length is constant across any height of water. So the volume of water added to achieve a certain increase in height is the same.

Thus, the water height will increase uniformly (in a straight line) for the last 10 seconds

(N.B the thickness/width of the prism is constant)

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