If a pipe diameter decreases by half, does flow speed...?

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Assuming the flow rate (Q) is constant:

original formula Q= Area x Vel. ----> Q/Area = V

So area ---> pi(r^2)

So I would assume it would increase by 4?.....
 
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Unless it is an ideal fluid. Flow rate would be constant for an ideal fluid and would follow the continuity equation: cross sectional area decreases, velocity increases.