What pressure is needed to maintain flow when the pipe diameter is halved?

[physea]

Hello!

You apply a pressure to a pipe to maintain a specific flow.

If the pipe diameter becomes half, how much pressure you need to apply to maintain the flow?

Thanks!

 

[BvU]

Depends . The friction factor in the pressure drop formula changes.

 

[physea]

How does the friction factor changes?
Also, what if we ignore friction?

 

[BvU]

For half the diameter at the same flow the speed quadruples (assuming pipe is filled with the fluid under consideration), so the Reynolds number quadruples too. That has an effect on the friction factor (see link). If you ignore that, you still have (see second link) a factor $v^2/D = 32$ increase in pressure drop over the pipe.

(Did you look at the links I gave? Understand them ?)

Ignoring friction/viscous effects altogether leads to $\Delta p=0$ which isn't appropriate, I would guess.

 

[physea]

So, as I expected, the velocity will increase and the pressure will drop inside the thinner tube.

The question is:
- if we maintain the pressure at the beginning of the tube, what will happen to the flow rate?
- similarly, if we maintain the flow rate, how should we adjust the pressure at the beginning of the tube?

 

[BvU]

(Did you look at the links I gave? Understand them ?)

There must be something that isn't clear to you is my impression when I read your post #5.