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Question
Why does velocity increase when water flowing in broader pipe enters a narrow pipe?
Solution
Consider a tube of flow as shown in the figure. All the fluid that passes through a tube of flow must pass through any cross section that cuts the tube of flow. Consider section A1 and A2 located at points A and B respectively. If mass m of the fluid enters the section A1 then equal mass of fluid should leave the section A2.
By the equation of continuity,
A1v1 = A2v2
∴ v2 = (A1/A2)v1
For the same volume to pass points A and B in a given time, the speed must be greater at point B.
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