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If a water pipe has a large diameter at the start and a small diameter at the end what part of the pipe would the water flow faster?

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If there are no losses and no storing between the beginning $A$ and the end $B$, you can calculate the velocities based on the principle of continuity. $$ Q_A= Q_B $$ whereas in a homogeneous flow $Q$ is equal to the cross-sectional area times the flow velocity: $$ Q=A\cdot v $$

With the proportions of the two cross-sectional areas you can now determine, which part should have the higher velocity.

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If a water pipe has a large diameter at the start and a small diameter at the end what part of the pipe would the water flow faster?

If there are no losses of the fluid between the wide point and the narrow point, then the flow will be faster at the narrow point.

This is because if you take the flow rates: $$\dot{Q}_{start} =A_{start} \times V_{start} = \dot{Q}_{finish} =A_{finish} \times V_{finish}$$

The final velocity is given then by the ratio of the areas:

$$V_{finish} = \frac{A_{start}}{A_{finish}} \times V_{start}$$

If then, $A_{start} > A_{finish}$ like in your case, then the fraction $\frac{A_{start}}{A_{finish}}>1$ and $ V_{finish} >V_{start}$

For the opposite case the finishing velocity is less than the start, naturally.

This behavior has all kinds of interesting applications such as in diffusers and nozzles and jet engines, although things are less straightforward once compressibility becomes an issue.

For low Reynolds number and low mach number cases this kind of thing can be explored with tools such as Bernoulli's principle and can be readily seen in the Venturi effect.

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  • $\begingroup$ If you have stationary flow and an incompressible fluid (e.g. water is approximately incompressible) then losses do not matter. Viscosity is not a parameter in the continuity equation. $\endgroup$
    – MrYouMath
    Commented Apr 26, 2017 at 17:00

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