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Why does the velocity of flow decreases as the cross-sectional area of a tube increases? Basic physics gone again

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Hello everyone,

 

Why does the velocity of flow decreases as the cross-sectional area of a tube increases. If a tube was constricted for sometime, its flow rate would be low due to resistance, now if you dilate the tube, the flow rate should increase. Am I confusing flow rate with velocity of flow. When they say velocity of flow do they mean, that when you dilate the tube more particles travel slower, but since there are more particles flow rate would be high. Thanks :)

Consider the length of tubing needed to contain 1 L of fluid, and a flow rate of 1 L per second. If the overall flow of volume is the same, in the narrow tube it must be moving faster -- it has a longer length to clear in 1 second.

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